The matrix game theory gives a mathematical background for dealing with competitive or antagonistic situations arise in many parts of real life. Matrix games have been extensively studied and successfully applied to many fields such as economics, business, management and e-commerce as well as advertising. This paper deals with two-person matrix games whose elements of pay-off matrix are fuzzy numbers. Then the corresponding matrix game has been converted into crisp game using defuzzification techniques. The value of the matrix game for each player is obtained by solving corresponding crisp game problems using the existing method. Finally, to illustrate the proposed methodology, a practical and realistic numerical example has been applied for different defuzzification methods and the obtained results have been compared
COMPARISON OF DIFFERENT APPROXIMATIONS OF FUZZY NUMBERSijfls
The notions of interval approximations of fuzzy numbers and trapezoidal approximations of fuzzy numbers have been discussed. Comparisons have been made between the close-interval approximation, valueambiguity
interval approximation and distinct approximation with the corresponding crisp and trapezoidal fuzzy numbers. A numerical example is included to justify the above mentioned notions.
Global Domination Set in Intuitionistic Fuzzy Graphijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Using Alpha-cuts and Constraint Exploration Approach on Quadratic Programming...TELKOMNIKA JOURNAL
In this paper, we propose a computational procedure to find the optimal solution of quadratic programming
problems by using fuzzy -cuts and constraint exploration approach. We solve the problems in
the original form without using any additional information such as Lagrange’s multiplier, slack, surplus and
artificial variable. In order to find the optimal solution, we divide the calculation in two stages. In the first
stage, we determine the unconstrained minimization of the quadratic programming problem (QPP) and check
its feasibility. By unconstrained minimization we identify the violated constraints and focus our searching in
these constraints. In the second stage, we explored the feasible region along side the violated constraints
until the optimal point is achieved. A numerical example is included in this paper to illustrate the capability of
-cuts and constraint exploration to find the optimal solution of QPP.
Sensitivity Analysis of GRA Method for Interval Valued Intuitionistic Fuzzy M...ijsrd.com
The aim of this paper is to investigate the multiple attribute decision making problems with intuitionistic fuzzy information, in which the information about attribute weights are incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional gray relational analysis (GRA) method, by which the attribute weights can be determined. For the special situations where the information about attribute weights are completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. Then, based on the traditional GRA method, calculation steps for solving an interval-valued intuitionistic fuzzy environment and developed modified GRA method for interval-valued intuitionistic fuzzy multiple attributes decision-making with incompletely known attribute weight information. This paper provides a new method for sensitivity analysis of MADM problems so that by sing it and changing the weights of attributes, one can determine changes in the final results for a decision making problem. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
Kakuro: Solving the Constraint Satisfaction ProblemVarad Meru
This work was done as a part of the project for the course CS 271: Introduction to Artificial Intelligence (http://www.ics.uci.edu/~kkask/Fall-2014%20CS271/index.html), taught in Fall 2014.
umerical algorithm for solving second order nonlinear fuzzy initial value pro...IJECEIAES
The purpose of this analysis would be to provide a computational technique for the numerical solution of second-order nonlinear fuzzy initial value (FIVPs). The idea is based on the reformulation of the fifth order Runge Kutta with six stages (RK56) from crisp domain to the fuzzy domain by using the definitions and properties of fuzzy set theory to be suitable to solve second order nonlinear FIVP numerically. It is shown that the second order nonlinear FIVP can be solved by RK56 by reducing the original nonlinear equation intoa system of couple first order nonlinear FIVP. The findings indicate that the technique is very efficient and simple to implement and satisfy the Fuzzy solution properties. The method’s potential is demonstrated by solving nonlinear second-order FIVP.
COMPARISON OF DIFFERENT APPROXIMATIONS OF FUZZY NUMBERSijfls
The notions of interval approximations of fuzzy numbers and trapezoidal approximations of fuzzy numbers have been discussed. Comparisons have been made between the close-interval approximation, valueambiguity
interval approximation and distinct approximation with the corresponding crisp and trapezoidal fuzzy numbers. A numerical example is included to justify the above mentioned notions.
Global Domination Set in Intuitionistic Fuzzy Graphijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Using Alpha-cuts and Constraint Exploration Approach on Quadratic Programming...TELKOMNIKA JOURNAL
In this paper, we propose a computational procedure to find the optimal solution of quadratic programming
problems by using fuzzy -cuts and constraint exploration approach. We solve the problems in
the original form without using any additional information such as Lagrange’s multiplier, slack, surplus and
artificial variable. In order to find the optimal solution, we divide the calculation in two stages. In the first
stage, we determine the unconstrained minimization of the quadratic programming problem (QPP) and check
its feasibility. By unconstrained minimization we identify the violated constraints and focus our searching in
these constraints. In the second stage, we explored the feasible region along side the violated constraints
until the optimal point is achieved. A numerical example is included in this paper to illustrate the capability of
-cuts and constraint exploration to find the optimal solution of QPP.
Sensitivity Analysis of GRA Method for Interval Valued Intuitionistic Fuzzy M...ijsrd.com
The aim of this paper is to investigate the multiple attribute decision making problems with intuitionistic fuzzy information, in which the information about attribute weights are incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional gray relational analysis (GRA) method, by which the attribute weights can be determined. For the special situations where the information about attribute weights are completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. Then, based on the traditional GRA method, calculation steps for solving an interval-valued intuitionistic fuzzy environment and developed modified GRA method for interval-valued intuitionistic fuzzy multiple attributes decision-making with incompletely known attribute weight information. This paper provides a new method for sensitivity analysis of MADM problems so that by sing it and changing the weights of attributes, one can determine changes in the final results for a decision making problem. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
Kakuro: Solving the Constraint Satisfaction ProblemVarad Meru
This work was done as a part of the project for the course CS 271: Introduction to Artificial Intelligence (http://www.ics.uci.edu/~kkask/Fall-2014%20CS271/index.html), taught in Fall 2014.
umerical algorithm for solving second order nonlinear fuzzy initial value pro...IJECEIAES
The purpose of this analysis would be to provide a computational technique for the numerical solution of second-order nonlinear fuzzy initial value (FIVPs). The idea is based on the reformulation of the fifth order Runge Kutta with six stages (RK56) from crisp domain to the fuzzy domain by using the definitions and properties of fuzzy set theory to be suitable to solve second order nonlinear FIVP numerically. It is shown that the second order nonlinear FIVP can be solved by RK56 by reducing the original nonlinear equation intoa system of couple first order nonlinear FIVP. The findings indicate that the technique is very efficient and simple to implement and satisfy the Fuzzy solution properties. The method’s potential is demonstrated by solving nonlinear second-order FIVP.
INDUCTIVE LEARNING OF COMPLEX FUZZY RELATIONijcseit
The objective of this paper to investigate the notion of complex fuzzy set in general view. In constraint to a
traditional fuzzy set, the membership function of the complex fuzzy set, the range from [0.1] extended to a
unit circle in the complex plane. In this article the comprehensive mathematical operations on the complex
fuzzy set are presented. The basic operation of complex fuzzy set such as union, intersection, complement
of complex fuzzy set and complex fuzzy relation are studied. Also vector aggregation and fuzzy relation
over the complex fuzzy set are discussed. Two novel operations of complement and projection for complex
fuzzy relation are introduced.
Numerical solution of fuzzy differential equations by Milne’s predictor-corre...mathsjournal
The study of this paper suggests on dependency problem in fuzzy computational method by using the numerical solution of Fuzzy differential equations(FDEs) in Milne’s predictor-corrector method. This method is adopted to solve the dependency problem in fuzzy computation. We solve some fuzzy initial value problems to illustrate the theory.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular
fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to
aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of
triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A
comparison has been made betweenapproximation of triangular fuzzy systems and the corresponding fuzzy
triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular
fuzzy numbers are also found.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular
fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to
aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of
triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A
comparison has been made betweenapproximation of triangular fuzzy systems and the corresponding fuzzy
triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular
fuzzy numbers are also found.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A comparison has been made between approximation of triangular fuzzy systems and the corresponding fuzzy triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular fuzzy numbers are also found.
PROBABILISTIC INTERPRETATION OF COMPLEX FUZZY SETIJCSEIT Journal
The innovative concept of Complex Fuzzy Set is introduced. The objective of the this paper to investigate
the concept of Complex Fuzzy set in constraint to a traditional Fuzzy set , where the membership function
ranges from [0, 1], but in the Complex fuzzy set extended to a unit circle in a complex plane, where the
member ship function in the form of complex number. The Compressive study of mathematical operation of
Complex Fuzzy set is presented. The basic operation like addition, subtraction, multiplication and division
are described here. The Novel idea of this paper to measure the similarity between two fuzzy relations by
evaluating δ -equality. Here also we introduce the probabilistic interpretation of the complex fuzzy set
where we attempted to clarify the distinction between Fuzzy logic and probability.
THE WEAK SOLUTION OF BLACK-SCHOLE’S OPTION PRICING MODEL WITH TRANSACTION COSTmathsjournal
This paper considers the equation of the type
− + + = , ( , ) ∈ ℝ × (0, );
which is the Black-Scholes option pricing model that includes the presence of transaction cost. The
existence, uniqueness and continuous dependence of the weak solution of the Black-Scholes model with
transaction cost are established.The continuity of weak solution of the parameters was discussed and
similar solution as in literature obtained.
Study on Contrast Enhancement with the help of Associate Regions Histogram Eq...IJSRD
Histogram equalization is an uncomplicated and extensively used image distinction enhancement technique. The crucial drawback of histogram equalization is it transforms the brightness of the image. To overcome this drawback, different histogram Equalization methods have been projected. These methods protect the brightness on the result image but, do not have a usual look. Therefore this paper is an attempt to bridge the gap and results after the processed Associate regions are collected into one image. The mock-up result explains that the algorithm can not only improve image information successfully but also remain the imaginative image luminance well enough to make it likely to be used in video arrangement directly.
Piping For Cooling Water Circulation between Cooling Tower and CondenserIJSRD
In thermal power plant, as we know that exhaust steam from turbine goes to heat recovery unit and from there the exhaust stem goes to the condenser to condense. In shell and tube heat exchanger, cooling water as a cooling medium running inside the tubes whereas steam is inside the shell. So to have sufficient amount of cooling water, we require continuous flow of water from the cooling tower. Our main project aim is to provide a piping between condenser and cooling tower. So in this particular project, we will make basic documents such as pfd, p&id, plot plan, equipment layout, piping ga drawing, isometrics, mto, piping specifications, pump specification, calculations, and stress analysis etc.
A Survey on Data Mining Techniques for Crime Hotspots PredictionIJSRD
A crime is an act which is against the laws of a country or region. The technique which is used to find areas on a map which have high crime intensity is known as crime hotspot prediction. The technique uses the crime data which includes the area with crime rate and predict the future location with high crime intensity. The motivation of crime hotspot prediction is to raise people’s awareness regarding the dangerous location in certain time period. It can help for police resource allocation for creating a safe environment. The paper presents survey of different types of data mining techniques for crime hotspots prediction.
Human Resource Recruitment using Fuzzy Decision Making MethodIJSRD
Traditional way of recruiting personnel was through a group decision making problem under multiple criteria containing subjectivity, imprecision and vagueness. In order to keep up with increasing competition of globalization and fast technological improvements and changes, Human resource field needs the best fit employee for a job vacancy. This paper proposes a Fuzzy Decision Making (FDM) method for recruitment process of Human Resource management, which is based on the Fuzzy set theory. Different criteria of human resource recruitment process will be given fuzzy linguistic terms such as absolutely low, extremely low, very low, low, medium, high, very high, extremely high, absolutely high depends upon the importance given by the Human Resource manager. Fuzzy Scaled Weight (FSW) will be calculated for all the criteria. Cumulative Fuzzy Value (CFV) is calculated for all the applicants from Fuzzy Scaled Weight values. Interview Fuzzy Value (IFV) is given by the human resource manager for all the applicants attending interviews. Final Fuzzy Value (FFV) will be calculated aggregating both Cumulative Fuzzy Value and Interview Fuzzy Value. Finally, all the applicant records are arranged in the order of FFV values. Then, Human resource manager can select the applicants easily from the arranged list. Fuzzy Decision Making method system is developed to illustrate the above FDM method for the Human Resource recruitment process.
Effect of hyper elastic property on dynamic behaviour of IC EngineIJSRD
In this paper, concept of vibration absorber is discussed with its hyperelastic properties. Rubber pads are inserted between IC Engine and foundation. IC Engine with and without rubber pads are dynamically analysed using FEA software. Both modal and harmonic analysis are performed. The FRFs of two systems are compared for their vibration reduction. Natural frequencies and mode shapes are obtained by modal analysis whereas FRF is obtained by harmonic analysis in FEA software.
USING SSSC & STATCOM --IMPROVE TRANSIENT STABILITY--P & Q OSICALLATIONSIJSRD
In a deregulated power system, the electric power demand is extending ordinary which may lead to overloads and loss of generation. Transient stability studies put a fundamental part in power systems, which give information related to the capacity of a power structure to stay in synchronism during major disturbances resulting from either the loss of generation or transmission facilities, sudden or sustained changes. The examination of transient quality is discriminating to work the power structure more secure and this paper focuses on growing the transient relentlessness using FACTS devices like Static Synchronous Series Compensator (SSSC) and static synchronous compensator (STATCOM). These FACTS contraptions are in a perfect world set on transmission structure using Sensitivity approach framework.
Field Programmable Gate Array (FPGA) - Based Pulse Width Modulation for Singl...IJSRD
Active filtering of electric power has now become a mature technology for harmonic and reactive power compensation in two-wire (single phase), three-wire (three phase without neutral), and four-wire (three phase with neutral) ac power networks with nonlinear loads. This paper presents the simulations of Field programmable gate array (FPGA) - based single phase hybrid active power filters of two different configurations using Xilinx system generator. The former one with the hybrid combination of series active power filter and shunt passive filter is designed to mitigate the distortions in source voltage and source current due to the voltage source type harmonic load and the latter one with the hybrid combination of shunt active power filter and shunt passive filter is designed to mitigate the harmonics in source current due to the current source type harmonic load.
Most of us use e-shopping (Any product) these days and refer its rating or reviews before we download or buy that product. Amazon/Play store provide a great number of products but unfortunately few of those product reviews are fraud. Hence such products must be marked, so that they will be recognizable for rest of the users. Here we are comparing reviews from two sites so that we can get more clear idea. We can get higher probability of getting real reviews if we take data from multiple sites. We are proposing a system to develop an android application that will take reviews from two different websites for single product, and analyze them with NLP for positive or negative rating. In this, user will give two different URLs of two different sites for same product to the system as input. For every URL reviews and comments will be fetched separately and analyzed with NLP for positive negative rating. Then their rating will be combined together with average to give final rating for the product. As we are handling the big data here, we are using Hadoops map reduce. So it will be easier to decide which product reviews are fraud or not.
Compression Buckling Analysis of Vertical Tail Stiffened PanelsIJSRD
Thin structural members are susceptible to buckling under compression loading. Aircraft skin is always thin irrespective of the size of the aircraft. Therefore, when the skin undergoes compression, it is likely to buckle. Vertical tail of the aircraft experiences bending, whenever the rudder is deflected to achieve the yawing motion of the aircraft. Side load will cause the bending of the vertical tail, which introduces tension and compression stress field in the two side skins respectively. This project includes the linear static analysis of the vertical tail box structure and buckling analysis of the stiffened panels undergoing compression. A linear static buckling analysis of the vertical tail box structure will be carried out to identify the most critical panel. After that the critical panel is taken for buckling analysis.
Synthesis and Pharmacological Evaluation of Novel Heterocyclic CompoundIJSRD
2-[(4-bromo anilino)]-4-chloro-6-morpholino-1,3,5-triazine[2a] and 4-chloro-N-(4-fluorophenyl)-6-morpholino-1,3,5-triazin-2-amine [2b]were synthesized and studied for their biological activity. These compounds were prepared by the condensation of 4-bromoaniline and 4-fluoroaniline with 4-(4,6-dichloro-1,3,5-triazin-2-yl) morpholine [1] which is prepared by the reaction between 2,4,6-trichloro-1,3,5-triazine and morpholine. All the compounds were characterized by elemental analysis and spectral studies.
INDUCTIVE LEARNING OF COMPLEX FUZZY RELATIONijcseit
The objective of this paper to investigate the notion of complex fuzzy set in general view. In constraint to a
traditional fuzzy set, the membership function of the complex fuzzy set, the range from [0.1] extended to a
unit circle in the complex plane. In this article the comprehensive mathematical operations on the complex
fuzzy set are presented. The basic operation of complex fuzzy set such as union, intersection, complement
of complex fuzzy set and complex fuzzy relation are studied. Also vector aggregation and fuzzy relation
over the complex fuzzy set are discussed. Two novel operations of complement and projection for complex
fuzzy relation are introduced.
Numerical solution of fuzzy differential equations by Milne’s predictor-corre...mathsjournal
The study of this paper suggests on dependency problem in fuzzy computational method by using the numerical solution of Fuzzy differential equations(FDEs) in Milne’s predictor-corrector method. This method is adopted to solve the dependency problem in fuzzy computation. We solve some fuzzy initial value problems to illustrate the theory.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular
fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to
aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of
triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A
comparison has been made betweenapproximation of triangular fuzzy systems and the corresponding fuzzy
triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular
fuzzy numbers are also found.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular
fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to
aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of
triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A
comparison has been made betweenapproximation of triangular fuzzy systems and the corresponding fuzzy
triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular
fuzzy numbers are also found.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A comparison has been made between approximation of triangular fuzzy systems and the corresponding fuzzy triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular fuzzy numbers are also found.
PROBABILISTIC INTERPRETATION OF COMPLEX FUZZY SETIJCSEIT Journal
The innovative concept of Complex Fuzzy Set is introduced. The objective of the this paper to investigate
the concept of Complex Fuzzy set in constraint to a traditional Fuzzy set , where the membership function
ranges from [0, 1], but in the Complex fuzzy set extended to a unit circle in a complex plane, where the
member ship function in the form of complex number. The Compressive study of mathematical operation of
Complex Fuzzy set is presented. The basic operation like addition, subtraction, multiplication and division
are described here. The Novel idea of this paper to measure the similarity between two fuzzy relations by
evaluating δ -equality. Here also we introduce the probabilistic interpretation of the complex fuzzy set
where we attempted to clarify the distinction between Fuzzy logic and probability.
THE WEAK SOLUTION OF BLACK-SCHOLE’S OPTION PRICING MODEL WITH TRANSACTION COSTmathsjournal
This paper considers the equation of the type
− + + = , ( , ) ∈ ℝ × (0, );
which is the Black-Scholes option pricing model that includes the presence of transaction cost. The
existence, uniqueness and continuous dependence of the weak solution of the Black-Scholes model with
transaction cost are established.The continuity of weak solution of the parameters was discussed and
similar solution as in literature obtained.
Study on Contrast Enhancement with the help of Associate Regions Histogram Eq...IJSRD
Histogram equalization is an uncomplicated and extensively used image distinction enhancement technique. The crucial drawback of histogram equalization is it transforms the brightness of the image. To overcome this drawback, different histogram Equalization methods have been projected. These methods protect the brightness on the result image but, do not have a usual look. Therefore this paper is an attempt to bridge the gap and results after the processed Associate regions are collected into one image. The mock-up result explains that the algorithm can not only improve image information successfully but also remain the imaginative image luminance well enough to make it likely to be used in video arrangement directly.
Piping For Cooling Water Circulation between Cooling Tower and CondenserIJSRD
In thermal power plant, as we know that exhaust steam from turbine goes to heat recovery unit and from there the exhaust stem goes to the condenser to condense. In shell and tube heat exchanger, cooling water as a cooling medium running inside the tubes whereas steam is inside the shell. So to have sufficient amount of cooling water, we require continuous flow of water from the cooling tower. Our main project aim is to provide a piping between condenser and cooling tower. So in this particular project, we will make basic documents such as pfd, p&id, plot plan, equipment layout, piping ga drawing, isometrics, mto, piping specifications, pump specification, calculations, and stress analysis etc.
A Survey on Data Mining Techniques for Crime Hotspots PredictionIJSRD
A crime is an act which is against the laws of a country or region. The technique which is used to find areas on a map which have high crime intensity is known as crime hotspot prediction. The technique uses the crime data which includes the area with crime rate and predict the future location with high crime intensity. The motivation of crime hotspot prediction is to raise people’s awareness regarding the dangerous location in certain time period. It can help for police resource allocation for creating a safe environment. The paper presents survey of different types of data mining techniques for crime hotspots prediction.
Human Resource Recruitment using Fuzzy Decision Making MethodIJSRD
Traditional way of recruiting personnel was through a group decision making problem under multiple criteria containing subjectivity, imprecision and vagueness. In order to keep up with increasing competition of globalization and fast technological improvements and changes, Human resource field needs the best fit employee for a job vacancy. This paper proposes a Fuzzy Decision Making (FDM) method for recruitment process of Human Resource management, which is based on the Fuzzy set theory. Different criteria of human resource recruitment process will be given fuzzy linguistic terms such as absolutely low, extremely low, very low, low, medium, high, very high, extremely high, absolutely high depends upon the importance given by the Human Resource manager. Fuzzy Scaled Weight (FSW) will be calculated for all the criteria. Cumulative Fuzzy Value (CFV) is calculated for all the applicants from Fuzzy Scaled Weight values. Interview Fuzzy Value (IFV) is given by the human resource manager for all the applicants attending interviews. Final Fuzzy Value (FFV) will be calculated aggregating both Cumulative Fuzzy Value and Interview Fuzzy Value. Finally, all the applicant records are arranged in the order of FFV values. Then, Human resource manager can select the applicants easily from the arranged list. Fuzzy Decision Making method system is developed to illustrate the above FDM method for the Human Resource recruitment process.
Effect of hyper elastic property on dynamic behaviour of IC EngineIJSRD
In this paper, concept of vibration absorber is discussed with its hyperelastic properties. Rubber pads are inserted between IC Engine and foundation. IC Engine with and without rubber pads are dynamically analysed using FEA software. Both modal and harmonic analysis are performed. The FRFs of two systems are compared for their vibration reduction. Natural frequencies and mode shapes are obtained by modal analysis whereas FRF is obtained by harmonic analysis in FEA software.
USING SSSC & STATCOM --IMPROVE TRANSIENT STABILITY--P & Q OSICALLATIONSIJSRD
In a deregulated power system, the electric power demand is extending ordinary which may lead to overloads and loss of generation. Transient stability studies put a fundamental part in power systems, which give information related to the capacity of a power structure to stay in synchronism during major disturbances resulting from either the loss of generation or transmission facilities, sudden or sustained changes. The examination of transient quality is discriminating to work the power structure more secure and this paper focuses on growing the transient relentlessness using FACTS devices like Static Synchronous Series Compensator (SSSC) and static synchronous compensator (STATCOM). These FACTS contraptions are in a perfect world set on transmission structure using Sensitivity approach framework.
Field Programmable Gate Array (FPGA) - Based Pulse Width Modulation for Singl...IJSRD
Active filtering of electric power has now become a mature technology for harmonic and reactive power compensation in two-wire (single phase), three-wire (three phase without neutral), and four-wire (three phase with neutral) ac power networks with nonlinear loads. This paper presents the simulations of Field programmable gate array (FPGA) - based single phase hybrid active power filters of two different configurations using Xilinx system generator. The former one with the hybrid combination of series active power filter and shunt passive filter is designed to mitigate the distortions in source voltage and source current due to the voltage source type harmonic load and the latter one with the hybrid combination of shunt active power filter and shunt passive filter is designed to mitigate the harmonics in source current due to the current source type harmonic load.
Most of us use e-shopping (Any product) these days and refer its rating or reviews before we download or buy that product. Amazon/Play store provide a great number of products but unfortunately few of those product reviews are fraud. Hence such products must be marked, so that they will be recognizable for rest of the users. Here we are comparing reviews from two sites so that we can get more clear idea. We can get higher probability of getting real reviews if we take data from multiple sites. We are proposing a system to develop an android application that will take reviews from two different websites for single product, and analyze them with NLP for positive or negative rating. In this, user will give two different URLs of two different sites for same product to the system as input. For every URL reviews and comments will be fetched separately and analyzed with NLP for positive negative rating. Then their rating will be combined together with average to give final rating for the product. As we are handling the big data here, we are using Hadoops map reduce. So it will be easier to decide which product reviews are fraud or not.
Compression Buckling Analysis of Vertical Tail Stiffened PanelsIJSRD
Thin structural members are susceptible to buckling under compression loading. Aircraft skin is always thin irrespective of the size of the aircraft. Therefore, when the skin undergoes compression, it is likely to buckle. Vertical tail of the aircraft experiences bending, whenever the rudder is deflected to achieve the yawing motion of the aircraft. Side load will cause the bending of the vertical tail, which introduces tension and compression stress field in the two side skins respectively. This project includes the linear static analysis of the vertical tail box structure and buckling analysis of the stiffened panels undergoing compression. A linear static buckling analysis of the vertical tail box structure will be carried out to identify the most critical panel. After that the critical panel is taken for buckling analysis.
Synthesis and Pharmacological Evaluation of Novel Heterocyclic CompoundIJSRD
2-[(4-bromo anilino)]-4-chloro-6-morpholino-1,3,5-triazine[2a] and 4-chloro-N-(4-fluorophenyl)-6-morpholino-1,3,5-triazin-2-amine [2b]were synthesized and studied for their biological activity. These compounds were prepared by the condensation of 4-bromoaniline and 4-fluoroaniline with 4-(4,6-dichloro-1,3,5-triazin-2-yl) morpholine [1] which is prepared by the reaction between 2,4,6-trichloro-1,3,5-triazine and morpholine. All the compounds were characterized by elemental analysis and spectral studies.
Level Control of Tank System Using PID Controller-A ReviewIJSRD
This paper discusses the review of level control of tank system using PID controller. PID controller use for one or more tank system. PID has fast response. Paper present different methods of level control. Eliminate the steady state error. It is most common way of solving problems of practical control systems.
Comparative Analysis of PAPR Reduction Techniques in OFDM Using Precoding Tec...IJSRD
In this modern era, Orthogonal Frequency Division Multiplexing (OFDM) has been proved to be an explicit promising technique for wired and wireless systems because of its several advantages like high spectral efficiency, robustness against frequency selective fading, relatively simple receiver implementation etc. Besides having a number of advantages OFDM suffers from few disadvantages like high Peak to Average Power Ratio (PAPR), Intercarrier Interference (ICI), Intersymbol Interference (ISI) etc. These detrimental effects, if not compensated properly and timely, can result in system performance degradation. This paper mainly concentrates on reduction of PAPR.A comparisons have been made between various precoding techniques against conventional OFDM.
Survey on Division and Replication of Data in Cloud for Optimal Performance a...IJSRD
Outsourcing information to an outsider authoritative control, as is done in distributed computing, offers ascend to security concerns. The information trade off may happen because of assaults by different clients and hubs inside of the cloud. Hence, high efforts to establish safety are required to secure information inside of the cloud. On the other hand, the utilized security procedure should likewise consider the advancement of the information recovery time. In this paper, we propose Division and Replication of Data in the Cloud for Optimal Performance and Security (DROPS) that all in all methodologies the security and execution issues. In the DROPS procedure, we partition a record into sections, and reproduce the divided information over the cloud hubs. Each of the hubs stores just a itary part of a specific information record that guarantees that even in the event of a fruitful assault, no important data is uncovered to the assailant. Additionally, the hubs putting away the sections are isolated with certain separation by method for diagram T-shading to restrict an assailant of speculating the areas of the sections. Moreover, the DROPS procedure does not depend on the customary cryptographic procedures for the information security; in this way alleviating the arrangement of computationally costly approaches. We demonstrate that the likelihood to find and bargain the greater part of the hubs putting away the sections of a solitary record is to a great degree low. We likewise analyze the execution of the DROPS system with ten different plans. The more elevated amount of security with slight execution overhead was watched.
Maintaining Data Confidentiality in Association Rule Mining in Distributed En...IJSRD
The data in real world applications is distributed at multiple locations, and the owner of the databases may be different people. Thus to perform mining task, the data needs to be kept at central location which causes threat to the privacy of corporate data. Hence the key challenge is to applying mining on distributed source data with preserving privacy of corporate data. The system addresses the problem of incrementally mining frequent itemsets in dynamic environment. The assumption made here is that, after initial mining the source undergoes into small changes in each time. The privacy of data should not be threatened by an adversary i.e. the miner and target database owner should not be able to recover original data from transformed data.
Simulation of Z-Source Inverter Fed Three Phase Induction Motor DriveIJSRD
This paper presents performance characteristics of Z-source inverter (ZSI) fed Induction Motor (IM) drives. Z-Source inverter is a single stage converter which performs both buck-boost energy conversions using the LC impedance network. This reduces the voltage range of the capacitors used and also the cost of the proposed topology which is in turn used to control the speed of an induction motor which is used in many valuable industrial applications. The Z Source inverter is a combined inverter with an additional buck-boost feature and the proposed topology increases the efficiency of the circuit by reducing the voltage stress across the capacitors. The z-source inverter is very advantageous over traditional inverters and we can be employed all ac and dc power conversion applications. Z-source inverter can boost dc input voltage with no requirement of dc to dc boost converter or step up transformer hence overcoming output voltage limitation of voltage source inverter as well as lower cost. A comparison among conventional PWM inverter dc to dc boost PWM inverter and control circuit cost which are the main a power electronics system.
An Improved Energy Efficiency Algorithm in Wireless Sensor Network Using Quer...IJSRD
Wireless Sensor Networks (WSN) is an essential guide foe anyone interested in wireless communications for sensor networks, home networking, environment monitoring, target tracking, and surveillance. In wireless sensor network sensor nodes have very limited supply of energy, and also should be available in function for extremely long time (e.g. a couple of years) without being recharged. So consider the energy resource of sensor node and the life time of the sensors, to optimize the query plan, based on user specified accuracy for wireless sensor network. This proposed method aims at optimization of periodical query, with careful consideration of accuracy, along with energy consumption in data communication. User may specify a value/time accuracy constraint, according to which an optimized query plan can be created to minimize the energy consumption. The main objective is to propose an energy efficient algorithm to reduce data transmission and to increase the life time of wireless sensor network.
A Review on Pattern Recognition with Offline Signature Classification and Tec...IJSRD
Pattern recognition gets renowned and come in touch with us since 1960’s and it get lots of attention from all over the world by their outstanding characteristics. In this paper Pattern recognition was presented, including idea, system, application and incorporation. In the meantime, ten descriptions and also more than ten techniques, for example- recognition was compressed. At the end, grouping of PR and structure and its associated fields and also application ranges were presented at point of interest. PR has researcher’s attention attracted in the last few decades as an approach of machine learning because of its areas of extensive spread application. The application area contains business, speech recognition, data mining, communications, military intelligence, automations, medicine, Bioinformatics, document classification and various others. In this review paper many Pattern Recognition approaches have been reviewed and also their pros/cons, application particular paradigm has been presented. The signature Recognition and check framework is used to aware and confirm individual's written hand signature. Presently transcribed mark is a standout amongst the most commonly acknowledged individual traits for personal attributes. Signature verification gives approval in money related and business exchange. Signature confirmation finds its uses in the field of net keeping money, travel permit check framework, gives validation to a hopefuls in broad daylight examination from their marks, charge cards, bank checks.
COMPARISON OF DIFFERENT APPROXIMATIONS OF FUZZY NUMBERSWireilla
ABSTRACT
The notions of interval approximations of fuzzy numbers and trapezoidal approximations of fuzzy numbers have been discussed. Comparisons have been made between the close-interval approximation, valueambiguity interval approximation and distinct approximation with the corresponding crisp and trapezoidal fuzzy numbers. A numerical example is included to justify the above mentioned notions.
Optimization of Fuzzy Matrix Games of Order 4 X 3IJERA Editor
In this paper, we consider a solution for Fuzzy matrix game with fuzzy pay offs. The Solution of Fuzzy matrix games with pure strategies with maximin – minimax principle is discussed. A method takes advantage of the relationship between fuzzy sets and fuzzy matrix game theories can be offered for multicriteria decision making. Here, m x n pay off matrix is reduced to 4 x 3 pay off matrix.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular
fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to
aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of
triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A
comparison has been made betweenapproximation of triangular fuzzy systems and the corresponding fuzzy
triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular
fuzzy numbers are also found.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular
fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to
aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of
triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A
comparison has been made betweenapproximation of triangular fuzzy systems and the corresponding fuzzy
triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular
fuzzy numbers are also found.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular
fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to
aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of
triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A
comparison has been made betweenapproximation of triangular fuzzy systems and the corresponding fuzzy
triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular
fuzzy numbers are also found.
Aggregation of Opinions for System Selection Using Approximations of Fuzzy Nu...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A comparison has been made betweenapproximation of triangular fuzzy systems and the corresponding fuzzy triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular fuzzy numbers are also found.
In this article, we propose a new approach to solve intuitionistic fuzzy assignment
problem. Classical assignment problem deals with deterministic cost. In practical
situations it is not easy to determine the parameters. The parameters can be modeled
to fuzzy or intuitionistic fuzzy parameters. This paper develops an approach based on
diagonal optimal algorithm to solve an intuitionistic fuzzy assignment problem. A new
ranking procedure based on combined arithmetic mean is used to order the
intuitionistic fuzzy numbers so that Diagonal optimal algorithm [22] can be applied to
solve the intuitionistic fuzzy assignment problem. To illustrate the effectiveness of the
algorithm numerical examples were given..
Intuitionistic Fuzzification of T-Ideals in Bci-Algebrasiosrjce
The notions of intuitionistic fuzzy T-ideals in BCI-algebras are introduced.Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy T-idealare provided. Using a collection of T-ideals, intuitionistic fuzzy T-ideals areestablished.
The Fuzzy set Theory has been applied in many fields such as Management, Engineering etc. In this paper a new operation on Hexagonal Fuzzy number is defined where the methods of addition, subtraction, and multiplication has been modified with some conditions. The main aim of this paper is to introduce a new operation for addition, subtraction and multiplication of Hexagonal Fuzzy number on the basis of alpha cut sets of fuzzy numbers
Pseudo Bipolar Fuzzy Cosets of Bipolar Fuzzy and Bipolar Anti-Fuzzy HX Subgroupsmathsjournal
In this paper, we introduce the concept of pseudo bipolar fuzzy cosets, pseudo bipolar fuzzy double cosets of a bipolar fuzzy and bipolar anti-fuzzy subgroups. We also establish these concepts to bipolar fuzzy and bipolar anti-fuzzy HX subgroups of a HX group with suitable examples. Also we discuss some of their relative properties.
Some Unbiased Classes of Estimators of Finite Population Meaninventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
Maintaining Data Confidentiality in Association Rule Mining in Distributed En...IJSRD
The data in real world applications is distributed at multiple locations, and the owner of the databases may be different people. Thus to perform mining task, the data needs to be kept at central location which causes threat to the privacy of corporate data. Hence the key challenge is to applying mining on distributed source data with preserving privacy of corporate data. The system addresses the problem of incrementally mining frequent itemsets in dynamic environment. The assumption made here is that, after initial mining the source undergoes into small changes in each time. The privacy of data should not be threatened by an adversary i.e. the miner and target database owner should not be able to recover original data from transformed data.
Performance and Emission characteristics of a Single Cylinder Four Stroke Die...IJSRD
The current trends in CI engine are to use Water-diesel emulsion as alternative fuel. It can be employed directly to the existing CI Engine system with no additional modifications. This system helps in reduction of NOx as well as PM, which in turn improve the combustion efficiency of the engine. However there are still investigations have to be done. The current work mainly concentrated on diesel engine run on water-diesel emulsions and its effect on engine performance and emissions were studied. The various loads were applied on a constant speed diesel engine run on water-diesel emulsions of varying ratios of 0.2:1, 0.3:1. 0.4:1 and 0.5:1. Emission and performance characteristics were measured and were compared with base diesel operation. The emissions like NOx and smoke density were found to decrease greatly and brake thermal efficiency was found to increase at high loads. Smoke level was 4.2 BSU and 3 BSU for base diesel and water diesel emulsion of 0.4. The ignition delay was found to increase with water diesel emulsions. This also increased the maximum rate of pressure rise and peak pressure. The engine was found to run rough with water-diesel emulsions. The optimal water-diesel ratio was found to be 0.4:1 by weight. HC and CO emissions were found to increase with water diesel emulsions.
Preclusion of High and Low Pressure In Boiler by Using LABVIEWIJSRD
Pressure is an important physical parameter to be controlled in process boiler, heat exchanger, nuclear reactor and steam carrying pipeline. In the article the issue has been face in boiler operation due to pressure is handled. In boiler, the problem is due to maximum and minimum range of pressure. Due to the issues there is a chance to causes the hazop. To avoid such the problem the high and low pressure in boiler has to control. In the paper such the problem has sorted out by implementing ON-OFF control. Here the proposed control action for pressure control is implemented with the help of LabVIEW (Laboratory Virtual Instrument Engineering Workbench) software and NI ELVIS hardware. In the idea the boiler’s low range and high is monitored and controlled valve desirably. And also the high range and low range of pressure in the boiler is signified to plant operator by alarm signal.
Prevention and Detection of Man in the Middle Attack on AODV ProtocolIJSRD
In this paper it is discuss about AODV protocol and security attacks and man in the middle attack in detail. AODV Protocol is use to find route and very important protocol for communication in wireless network. So AODV protocol should be Secured and it is a big challenge. There are various attacks that occur on it. Here in this paper it discussed about the detection and preventions of man-in-the-middle attack in detail.
Comparative Analysis of PAPR Reduction Techniques in OFDM Using Precoding Tec...IJSRD
In this modern era, Orthogonal Frequency Division Multiplexing (OFDM) has been proved to be an explicit promising technique for wired and wireless systems because of its several advantages like high spectral efficiency, robustness against frequency selective fading, relatively simple receiver implementation etc. Besides having a number of advantages OFDM suffers from few disadvantages like high Peak to Average Power Ratio (PAPR), Intercarrier Interference (ICI), Intersymbol Interference (ISI) etc. These detrimental effects, if not compensated properly and timely, can result in system performance degradation. This paper mainly concentrates on reduction of PAPR.A comparisons have been made between various precoding techniques against conventional OFDM.
Evaluation the Effect of Machining Parameters on MRR of Mild SteelIJSRD
Today’s life is totally based on Internet. Now a days people cannot imagine life without Internet. Information and communication technology plays vital role in today’s online networked society. In today’s life, we are very close to the online social networks. Online social networks are used for posting and sharing information across various social networking sites. But user’s privacy is not maintained by online social networks. For maintaining users sensitive information’s privacy online social networks provides little or no support. For filtering unwanted messages we propose a system using machine learning (ML). Using machine learning in soft classifier content based filtering performed. In proposed system filtering rules (FR’s) are provided for content independent filtering.. Blacklists are used for more flexibility by which filtering choices are increased. Proposed system provides security to the Online Social Networks.
Filter unwanted messages from walls and blocking nonlegitimate user in osnIJSRD
Today’s life is totally based on Internet. Now a days people cannot imagine life without Internet. Information and communication technology plays vital role in today’s online networked society. In today’s life, we are very close to the online social networks. Online social networks are used for posting and sharing information across various social networking sites. But user’s privacy is not maintained by online social networks. For maintaining users sensitive information’s privacy online social networks provides little or no support. For filtering unwanted messages we propose a system using machine learning (ML). Using machine learning in soft classifier content based filtering performed. In proposed system filtering rules (FR’s) are provided for content independent filtering.. Blacklists are used for more flexibility by which filtering choices are increased. Proposed system provides security to the Online Social Networks.
Keystroke Dynamics Authentication with Project Management SystemIJSRD
Generally user authentication is done using username and password that is called as login process. This login process is not more secure because, however a login session is still unprotected to impersonator when the user leaves his computer without logging off. Keystroke dynamics methods can be made useful to verify a user by extracting some typing features then, after the authentication process has successfully ended. From the last decade several studies proposed the use of keystroke dynamics as a behavioral biometric tool to verify users. We propose a new method, for representing the keystroke patterns by joining similar pairs of consecutive keystrokes. The above proposed method is used to consider clustering the di-graphs which are based on their temporal features. In this project, authentication system is provide to project management system that make more Secure management system without acknowledging unauthorized user. The Project Management System addresses the management of software projects. It provides the framework for organizing and managing resources in such a way that these resources deliver all the work required to complete a software project within defined scope, time and cost constraints. The system applies only to the management of software projects and is a tool that facilitates decision making.
Diagnosing lungs cancer Using Neural NetworksIJSRD
Artificial Neural Networks is the new technology. It is the branch of Artificial Intelligence and also it is an accepted new technology. Now a days Neural Networks Plays a Vital role in Medicine, Particularly in some fields such as cardiology, oncology etc. And also it has many applications in many areas like Science and Technology, Education, Business, Business and Manufacturing, etc. Neural Networks is most useful for making the decision more Effective. In this Paper, by the use of Neural Networks how the severe disease Lungs Cancer has been diagnosed more effectively. This Paper discussed about how the Lungs cancer can be identified effectively in earlier stages and diagnosed using Neural Networks and some devices. The Neural Networks has been successfully applied in Carcinogenesis. The main aim of this research is by the use of Neural Networks the Carcinogenesis can be diagnosed more cost-effective, easy to use techniques and methods. This Paper discussed about how the Lungs cancer can be identified effectively in earlier stages and diagnosed using Neural Networks and some devices. Sputum Cytology is used to detect the Lungs Cancer in Early stages.
A Survey on Sentiment Analysis and Opinion MiningIJSRD
In Today’s world, the social media has given web users a place for expressing and sharing their thoughts and opinions on different topics or events. For this purpose, the opinion mining has gained the importance. Sentiment classification and Opinion Mining is the study of people’s opinion, emotions, attitude towards the product, services, etc. Sentiment Analysis and Opinion Mining are the two interchangeable terms. There are various approaches and techniques exist for Sentiment Analysis like Naïve Bayes, Decision Trees, Support Vector Machines, Random Forests, Maximum Entropy, etc. Opinion mining is a useful and beneficial way to scientific surveys, political polls, market research and business intelligence, etc. This paper presents a literature review of various techniques used for opinion mining and sentiment analysis.
A Defect Prediction Model for Software Product based on ANFISIJSRD
Artificial intelligence techniques are day by day getting involvement in all the classification and prediction based process like environmental monitoring, stock exchange conditions, biomedical diagnosis, software engineering etc. However still there are yet to be simplify the challenges of selecting training criteria for design of artificial intelligence models used for prediction of results. This work focus on the defect prediction mechanism development using software metric data of KC1.We have taken subtractive clustering approach for generation of fuzzy inference system (FIS).The FIS rules are generated at different radius of influence of input attribute vectors and the developed rules are further modified by ANFIS technique to obtain the prediction of number of defects in software project using fuzzy logic system.
Experimental Investigation of Granulated Blast Furnace Slag ond Quarry Dust a...IJSRD
In this experimental work ninety nine cubes has been prepared having dimension 70.7x70.7x70.7 mm are cast as per IS:4031 (2000). In this experimental investigation cement mortar mix 1:3 by volume were selected for 0%, 20%, 40%, 60%, 80% and 100% partially replacement of natural sand (NS) by Granulated blast furnace slag (GBFS) and quarry dust (QD) [3 cubes on each parameter respectively] for W/C ratio of 0.55 respectively. All the cubes were tested under compressive testing machine. To compare the average compressive strength of natural sand (NS) with granulated blast furnace slag (GBFS) and quarry dust (QD).
Product Quality Analysis based on online ReviewsIJSRD
Customers satisfaction is the most important criteria before buying any product. Technology today has grown to such an extent that every smallest possible query is found on internet. An individual can express his reviews towards a product through Internet. This allows others to have a brief idea about the product before buying one for them. In this paper, we take into account all the challenges and limitations encountered while reading the online reviews and time being consumed in understanding quality of the product from the reviews. We include several methods and algorithms that help the consumer to understand the Quality of the product in better way.
Solving Fuzzy Matrix Games Defuzzificated by Trapezoidal Parabolic Fuzzy NumbersIJSRD
The matrix game theory gives a mathematical background for dealing with competitive or antagonistic situations arise in many parts of real life. Matrix games have been extensively studied and successfully applied to many fields such as economics, business, management and e-commerce as well as advertising. This paper deals with two-person matrix games whose elements of pay-off matrix are fuzzy numbers. Then the corresponding matrix game has been converted into crisp game using defuzzification techniques. The value of the matrix game for each player is obtained by solving corresponding crisp game problems using the existing method. Finally, to illustrate the proposed methodology, a practical and realistic numerical example has been applied for different defuzzification methods and the obtained results have been compared
Study of Clustering of Data Base in Education Sector Using Data MiningIJSRD
Data mining is a technology used in different disciplines to search for significant relationships among variables in n number of data sets. Data mining is frequently used in all types’ areas as well as applications. In this paper the application of data mining is attached with the field of education. The relationship between student’s university entrance examination results and their success was studied using cluster analysis and k-means algorithm techniques.
Fault Tolerance in Big Data Processing Using Heartbeat Messages and Data Repl...IJSRD
Big data is a popular term used to define the exponential evolution and availability of data, includes both structured and unstructured data. The volatile progression of demands on big data processing imposes heavy burden on computation, communication and storage in geographically distributed data centers. Hence it is necessary to minimize the cost of big data processing, which also includes fault tolerance cost. Big Data processing involves two types of faults: node failure and data loss. Both the faults can be recovered using heartbeat messages. Here heartbeat messages acts as an acknowledgement messages between two servers. This paper depicts about the study of node failure and recovery, data replication and heartbeat messages.
Investigation of Effect of Process Parameters on Maximum Temperature during F...IJSRD
In case of friction stir welding, the maximum temperature along the weld line within appropriate range at tool workpiece interface is responsible for quality of welded joint. Through this paper, an attempt is made to establish a relationship between the input process parameters and the maximum temperature along the weld line during friction stir welding of aluminium alloy AA-7075. The design of pre-experimental simulation has been performed in accordance with full factorial technique. The simulation of friction stir welding has been performed by varying input parameters, tool rotational speed and welding speed. The analysis of variance (ANOVA) is used to investigate the effect of input parameters on maximum temperature during friction stir welding. A correlation was established between input parameters and maximum temperature by multiple regression lines. This study indicates that the tool rotational speed is the main input parameter that has high statistical influence on maximum temperature along the weld line during friction stir welding of aluminium alloy AA-7075.
Review Paper on Computer Aided Design & Analysis of Rotor Shaft of a RotavatorIJSRD
The intent of this paper is to study the various forces and stress acting on a rotor shaft of a standard rotavator which is subjected to transient loading. The standard models of rotavator, having a progressive cutting sequence was considered for the study and analysis. The study was extended to various available models having different cutting blade arrangement. The study was carried on different papers and identifies the various forces acting on a Rotor shaft of a rotavator. The positions of the torque and forces applied are varied according to the model considered. The response was obtained by considering the angle of twist and equivalent stress on the rotor shaft. This paper presented a methodology for conducting transient analysis of rotor shaft of a rotavator,
Studies on Physico - Mechanical Properties of Chloroprene Rubber Vulcanizate ...IJSRD
Among the vulcanized elastomers, the chloroprene rubber (Neoprene) possesses a good performance being one of the most used in the current days. Compounding was carried out in a two-roll mill and vulcanized at 150°C. However, this kind of polymer is seriously playing a vital role for the manufacture of power transmission belts in the automotive industry. A worldwide method that has been used and that is an important tool in the rubber vulcanization in hydraulic press curing at high temperature in which the chloroprene compound has virtual physical and mechanical properties. In this work, the chloroprene samples were prepared according to ASTM standards. The Rheological and the physico-mechanical properties of CR vulcanizate were studied.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Solving Fuzzy Matrix Games Defuzzificated by Trapezoidal Parabolic Fuzzy Numbers
1. IJSRD - International Journal for Scientific Research & Development| Vol. 3, Issue 10, 2015 | ISSN (online): 2321-0613
All rights reserved by www.ijsrd.com 1006
Solving Fuzzy Matrix Games Defuzzificated by Trapezoidal Parabolic
Fuzzy Numbers
Mr.T.Stalin1 Mr. Dr.M.Thirucheran2
1
Research Scholar 2
Associate Professor
1,2,3
Department of Mathematics
1,2
L.N. Govt.College Ponneri, Madras University, chennai-5
Abstract— The matrix game theory gives a mathematical
background for dealing with competitive or antagonistic
situations arise in many parts of real life. Matrix games have
been extensively studied and successfully applied to many
fields such as economics, business, management and e-
commerce as well as advertising. This paper deals with two-
person matrix games whose elements of pay-off matrix are
fuzzy numbers. Then the corresponding matrix game has
been converted into crisp game using defuzzification
techniques. The value of the matrix game for each player is
obtained by solving corresponding crisp game problems
using the existing method. Finally, to illustrate the proposed
methodology, a practical and realistic numerical example
has been applied for different defuzzification methods and
the obtained results have been compared
.Key words: Fuzzy number, trapezoidal fuzzy number,
probabilic fuzzy number, Fuzzy payoff, Defuzzification ,
game theory , two-person matrix games
I. INTRODUCTION
In many real world practical problems with competitive
situation, it is required to take the decision where there are
two or more opposite parties with conflicting interests and
the action of one depends upon the action which is taken by
the opponent. A great variety of competitive situation is
commonly seen in everyday life viz., in military battles,
political campaign, elections economics, business,
management and e-commerce, etc. Game theory is a
mathematical way out for finding of conflicting interests
with competitive situations, which includes players or
decision makers who select different strategies from the set
of admissible strategies.
In this paper, we have treated imprecise parameters
considering fuzzy sets/fuzzy numbers. To handle the
problem with such types of imprecise parameters, generally
stochastic, fuzzy and fuzzy-stochastic approaches are
applied and the corresponding problems are converted into
deterministic problems for solving them. In the last few
years, several attempts have been made in the existing
literature for solving game problem with fuzzy payoff. .
Fuzziness in game problem has been well discussed by
Campos [1]. Sakawa and Nishizaki [2] introduced max-min
solution procedure for multi-objective fuzzy games. Based
on fuzzy duality theory [3, 4, 5], Bector et al. [6, 7], and
Vijay et al. [8] proved that a two person zero-sum matrix
game with fuzzy goals and fuzzy payoffs is equivalent to a
pair of linear programming problems. [9] Vahidi, J. and
Rezvani, S.: 2013, Arithmetic operations on trapezoidal
fuzzy numbers, Jounal Nonlinear Analysis and Applications
2013, Article ID jnaa–00111, In this paper, two person
matrix games have taken into consideration. The element of
payoff matrix is considered to be fuzzy number [10]. Then
the corresponding problem has been converted into crisp
equivalent two person matrix game using different
defuzzification methods [11]. . Finally, to illustrate the
methodology, a numerical example has been applied for
different defuzzification methods and the computed results
have been compared.
II. DEFINITION AND PRELIMINARIES
A. Definition 2.1:
Let be a non-empty set. A fuzzy set A
~
is defined as the set
of pairs, XxxxA A
:)(,
~
~ where 1,0:)(~ xA
is
a mapping and )(~ xA
is called the membership function of
A
~
. The value )(~ xA
=0 is used to represent for complete
non-membership, whereas )(~ xA
=1 is used to represent
for complete membership. The values in between zero and
one are used to represent intermediate degrees of
membership.
B. Definition 2. 2:
A fuzzy set A
~
is called convex if for all Xxx 21
, such
that )(),(min))1(( 2
~
1
~
21
~ xxxx AAA
,where 1,0 .
C. Definition 2.3:
The set of elements that belong to the fuzzy set A
~
at least
to the degree is called the -level set or -cut and is
given by )(:
~
~ xXxA A
. If
)(:
~
~ xXxA A
, it is called strong -level
set or strong -cut.
D. Definition 2.4:
A fuzzy set A
~
is called a normal fuzzy set if there exist at
least one Xx such that .1)(~ xA
E. Definition 2.5:
A fuzzy number is a fuzzy set on the real line R , must
satisfy the following conditions.
1) There exists at least one Rx 0
for which
.1)( 0
~ xA
.
2) )(~ xA
is pair wise continuous.
3) A
~
must be convex and normal.
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F. Definition 2.6:
A trapezoidal fuzzy fuzzy number (TrFN) A
~
is a normal
fuzzy number represented by the quadruplet ),,,( dcba
where dcba are real numbers and its membership
function 1,0:)(~ XxA
is given below
else
dxcif
dc
dx
cxbif
bxaif
ab
ax
xA
,0
,
,1
,
)(~
G. Definition 2.7:
A trapezoidal parabolic fuzzy number (TrPFN) A
~
is a
normal fuzzy number represented by the quadruplet
),,,( dcba where dcba are real numbers and its
membership function 1,0:)(~ XxA
is given below
else
dxcif
cd
cx
cxbif
bxaif
ab
xb
xA
,0
,1
,1
,1
)( 2
2
~
III. FUZZY GAME MATHEMATICAL MODELING
A. Payoff Matrix:
Let mi
AAAAAA ,....,,,, 4321
be a pure strategy
available for player A and nj
BBBBBB ,....,,,, 4321
be a pure strategy available for player B. When player A
chooses a pure strategy i
A and the player B chooses a pure
strategy j
B ,then ij
g is the payoff for player A and - ij
g be
the payoff for the player B. The two-person zero-sum matrix
game G can be represented as a pay-off matrix
nmij
gG
.
B. Fuzzy Payoff Matrix:
Let mi
AAAAAA ,....,,,, 4321
be a pure strategy
available for player A and nj
BBBBBB ,....,,,, 4321
be a pure strategy available for player B. Here, it is assumed
that each player has his/her choices from amongst the pure
strategies. Also, it is assumed that player A is always the
gainer and player B is always the loser. That is, all payoffs
are assumed in terms of player A. Let ij
g~ be the fuzzy
payoff which is the gain of player A from player B if player
A chooses strategy i
A where as player B chooses j
B .Then
the fuzzy payoff matrix of player A and B is
nmij
gG
~~
.
C. Mixed Strategy:
Let us consider the fuzzy matrix game whose payoff matrix
is nmij
gG
~~
. The mixed strategy for the player-A, is
denoted by m
xxxx ,....,, 321
, where
mixi
,....3,2,1,0 , and 1 i
x . It is to be noted
that ,)0,...0,1,0,...0(
m
i
e mixi
,....3,2,1,0
represent the pure strategy for the player-A and
m
i
i
m
i
xe
1
. If
m
i
iim
xxS
1
1,0: then
.mm
ES
Similarly, The mixed strategy for the player-B, is denoted
by n
yyyy ,....,, 321
, where
njy j
,....3,2,1,0 , and 1 j
y . It is to be noted
that ,)0,...0,1,0,...0(
n
j
e njy j
,....3,2,1,0
represent the pure strategy for the player-B and
n
j
j
n
j
ye
1
. If
n
j
jjn
yyS
1
1,0: then
.nn
ES Where m
S and n
S are the spaces of mixed
strategies for the player-A and player-B respectively.
D. Maximin-Minimax Principle or Maximin-Minimax
Criteria of Optimality for Fuzzy Payoff Matrix:
Let the player A’s payoff matrix be nmij
g
. If player A
takes the strategy i
A then surely he/she will get at least
mi ,....3,2,1 for taking any strategy by the opponent
player B . Thus by the maximin-minimax criteria of
optimality, the player A will choose that strategy which
corresponds to the best of these worst outcomes
)~(min),.....~(min),~(min 21 mj
j
j
j
j
j
gDFVgDFVgDFV .Thus
the maximin value for player A is given by
)~(minmax ij
ji
gDFV .Similarly, player B will choose that
strategy which corresponds to the best (minimum) of the
worst outcomes (maximum losses)
)~(max),.....~(max),~(max 21 in
i
i
i
i
i
gDFVgDFVgDFV . Thus the
maximin value for player B is given by
)~(maxmin ij
ij
gDFV .Here , )~( ij
gDFV represents
defuzzified value of the fuzzy number ij
g~
1) Theorem 1:
If a matrix game possesses a saddle point, it is necessary and
sufficient that
)~(minmax ij
ji
gDFV = )~(maxmin ij
ij
gDFV .
a) Definition 3.1:
A pair , of mixed strategies for the players in a matrix
game is called a situation in mixed strategies. In a situation
, of mixed strategies each usual situation (i, j) in pure
strategies becomes a random event occurring with
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probabilities ., ji
yx Since in the situation (i, j), player-A
receives a payoff )~( ij
gDFV , the mathematical
expectation of his payoff under , is equal to
m
i
n
j
jiij
yxgDFVE
1 1
)(),( .
2) Theorem 2;
Let ),( E be such that both ),(maxmin
E
mn SS
and
),(minmax
E
nm SS
exist, then
),(maxmin
E
mn SS
),(minmax
E
nm SS
.
E. Saddle Point Of A Function:
Let ),( E be a function of two variables (vectors) and
in m
S and n
S respectively. The
point 00
, , m
S0
, n
S0
is said to be the saddle
point of the function ),( E if
),( 0
E ),( 00
E ),( 0
E .
1) Theorem 3:
Let ),( E be a function of two variables m
S and
n
S such that ),(minmax
E
nm SS
and
),(maxmin
E
mn SS
exist. Then the necessary and sufficient
condition for the existence of a saddle point 00
, of
),( E is that
),( 00
E = ),(minmax
E
nm SS
= ),(maxmin
E
mn SS
.
F. Value Of A Matrix Game:
The common value of ),(minmax
E
nm SS
and
),(maxmin
E
mn SS
is called the value of the matrix game
with payoff matrix nmij
gG
~~
and denoted by v(G) or
simply v.
1) Definition 3.2:
Thus if , is an equilibrium situation in mixed
strategies of the game ESS nm
,, , then
*
,
*
are the
optimal strategies for the players A and B respectively in the
matrix game with fuzzy payoff matrix nmij
gG
~~
. Hence
*
,
*
are optimal strategies for the players A and B
respectively iff
),(
*
E ),(
**
E ),(
*
E nm
SS , .
2) Definition 3.3:
),(),(max),(minmax),(),(min
****
EEEEE
),(),(min),(maxmin),(),(max
****
EEEEE
a) Theorem4;
,(maxmin,(minmax iEjEv
ij
and the outer
extrema are attained at optimal strategies of players.
b) Theorem5:
)~(minmax ij
ji
gDFV v )~(maxmin ij
ij
gDFV .
Proof: By the theorem 4, we have
m
j
SjEv
,(minmax . But
m
jj
SjEjE
),(min,(minmax .Therefore Letting
m
i
e we have )~(min),(min),(min ij
jj
m
i
j
gDFVjiEjeEv
and we get v )~(min ij
j
gDFV .The left side v is independent
of i so that taking maximum with respect to i, we obtain
v
)~(minmax ij
ji
gDFV . Proof of the second part is
similar.
c) Theorem 6;
If player-A possesses a pure optimal strategy
*
i , then
)~(min)~(minmax *
jij
ij
ji
gDFVgDFVv
(ii). If player-B possesses a pure optimal strategy
*
j
,then )~(max)~(maxmin *
iji
ij
ij
gDFVgDFVv
Proof:
),(min),(minmax * jeEjEv
m
ijj
as
m
i
e *
*
is
optimal. Proof of the rest is similar.
G. Solution Of Fuzzy Matrix Game:
Let us consider a 22 Matrix game whose fuzzy payoff
matrix G
~
is given by
2221
1211
~~
~~
~
gg
gg
G
If G
~
has no saddle point, then the value of the game is
))~()~(())~()~((
)~()~()~()~(
21122211
21122211
gDFVgDFVgDFVgDFV
gDFVgDFVgDFVgDFV
v
,provided
0))~()~(())~()~(( 21122211
gDFVgDFVgDFVgDFV .
It can be proved that
0))~()~(())~()~(( 21122211
gDFVgDFVgDFVgDFV implies
that G
~
has a saddle point.
IV. SOME DEFUZZIFICATION TECHNIQUES
Defuzzification is the process of producing a quantifiable
result in fuzzy logic, given the fuzzy sets and the
corresponding degrees of membership. There are several
Defuzzification techniques available in the existing
literature. Here two general techniques are taken and
compared. The techniques are Centre of Area of Fuzzy
Number (COA of Fuzzy Number) and Bisector of Area of
Fuzzy Number (BOA of Fuzzy Number).
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A. Centre of Area Of Fuzzy Number (COA Of Fuzzy
Number):
This defuzzification can be expressed as
x
A
x
A
COA
dxx
dxxx
x
)(
)(
where COA
x is the crisp output,
)(xA
is the membership function corresponding to the
fuzzy number and x is the output variable. This method is
also known as center of gravity or centroid defuzzification
method.
Defuzzified values for Centre of Area of Fuzzy Number for
trapezoidal fuzzy fuzzy number (TrFN) is
3
)(
)(
abcd
abcd
dcba
xCOA
.
Defuzzified values for Centre of Area of Fuzzy Number for
trapezoidal parabolic fuzzy number (TrPFN) is
)22(4
)2233(
2222
cbad
cdabbcad
xCOA
.
B. Bisector Of Area Of Fuzzy Number (BOA Of Fuzzy
Number):
The bisector of area is the vertical line that divides the
region into two sub-regions of equal area. The formula for
COA
x is given by
d
x
A
x
a
A
BOA
BOA
dxxdxx )()( .It is
sometimes, but not always coincident with the centroid line.
Defuzzified values for Bisector of Area of Fuzzy Number
for trapezoidal fuzzy fuzzy number (TrFN) is
4
)( dcba
xBOA
.
Defuzzified values for Bisector of Area of Fuzzy Number
for trapezoidal parabolic fuzzy number (TrPFN) is
6
)22( cbda
xBOA
.
V. NUMERICAL EXAMPLE
Suppose that there are two firms X and Y to enhance the
market share of a new product by competing in advertising.
The two firms are considering two different strategies to
increase market share: strategy I (adv. by pamphlets), II
(adv. by road banners). Here it is assumed that the targeted
market is fixed, i.e. the market share of the one firm
increases while the market share of the other firm decreases
and also each company puts all its advertisements in one.
The above problem may be regarded as matrix game.
Namely, the firm X and Y are considered as players X and
Y respectively.The marketing research department of firm X
establishes the following pay-off matrix
)165,160,155,140()80,70,60,50(
)145,135,125,120()165,160,150,145(~
G
Where the element in the matrix indicates that the sales
amount of the X increase by “about 160” units when the
firm X and Y use the strategy I (adv. by pamphlets)
simultaneously. The other elements in the matrix can be
explained similarly.
Defuzzification
Methods
Defuzzified
Pay of Matrix
Value of
the game
COA - TrFN
44.15465
43.131155~
G 23.136v
COA - TrPFN
86.15465
77.131155~
G 35.136v
BOA - TrFN
15565
25.131155~
G 21.136v
BOA - TrPFN
16.15465
66.131155~
G 23.136v
The computational game value results have been shown in
the above table for different parametric values. Due to the
choices of decision makers’, the payoff value in a zero sum
game might be imprecise rather than precise value. The
optimal solution sets, as obtained by the defuzzification
approach, are consistent with those obtained by standard
existing approach under fuzzy set up. Thus, it can be
claimed that the defuzzification approach attempted in this
work well to handle the matrix game with fuzzy payoff.
VI. CONCLUSION
In this paper, a method of solving fuzzy game problem using
two fuzzy Defuzzification techniques of fuzzy numbers has
been considered. A Numerical example is presented to
illustrate the proposed methodology. Due to the choices of
decision makers’, the payoff value in a zero sum game
might be imprecise rather than precise value. This
impreciseness may be represented by various ways. In this
paper, we have represented this by fuzzy number. Then the
fuzzy game problem has been converted into crisp game
problem after Defuzzification in which all the payoff values
are crisp valued. Here, two Defuzzification techniques have
been used to solve the fuzzy game and the corresponding
crisp games with their strategies and value of the game have
been presented and compared.
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fuzzy matrix games, Fuzzy Sets and Systems 32(3)
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[3] C.R. Bector, S. Chandra, On duality in linear
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