Fuzzy soft set is one of the recent topics developed for dealing with the uncertainties present
in most of our real life situations. The parameterization tool of soft set theory enhances the flexibility of
its application. In this paper, we have studied membership grade, power set,
-cut set , strong fuzzy
-
cut set ,some standard operation fuzzy soft set, degree of subset hood and proposed some results with
examples.
In this paper, we define the new notion of interval-valued Pythagorean fuzzy ideals in semigroups and established the properties of its with suitable examples. Also, we introduce the concept of interval valued Pythagorean fuzzy sub-semigroup, interval valued Pythagorean fuzzy left (resp. right) ideal, interval valued Pythagorean fuzzy bi-ideal, interval valued Pythagorean fuzzy interior ideal and homomorphism of an interval valued Pythagorean fuzzy ideal in semigroups with suitable illustration. We show that every interval valued Pythagorean fuzzy left (resp. right) ideal is an interval valued Pythagorean fuzzy bi-ideal.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
In this paper we introduce the notions of Fuzzy Ideals in BH-algebras and the notion
of fuzzy dot Ideals of BH-algebras and investigate some of their results.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A Study on Intuitionistic Multi-Anti Fuzzy Subgroups mathsjournal
For any intuitionistic multi-fuzzy set A = { < x , µA(x) , νA(x) > : x∈X} of an universe set X, we study the set [A](α, β) called the (α, β)–lower cut of A. It is the crisp multi-set { x∈X : µi(x) ≤ αi , νi(x) ≥ βi , ∀i } of X. In this paper, an attempt has been made to study some algebraic structure of intuitionistic multi-anti fuzzy subgroups and their properties with the help of their (α, β)–lower cut sets
In this paper, we define the new notion of interval-valued Pythagorean fuzzy ideals in semigroups and established the properties of its with suitable examples. Also, we introduce the concept of interval valued Pythagorean fuzzy sub-semigroup, interval valued Pythagorean fuzzy left (resp. right) ideal, interval valued Pythagorean fuzzy bi-ideal, interval valued Pythagorean fuzzy interior ideal and homomorphism of an interval valued Pythagorean fuzzy ideal in semigroups with suitable illustration. We show that every interval valued Pythagorean fuzzy left (resp. right) ideal is an interval valued Pythagorean fuzzy bi-ideal.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
In this paper we introduce the notions of Fuzzy Ideals in BH-algebras and the notion
of fuzzy dot Ideals of BH-algebras and investigate some of their results.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A Study on Intuitionistic Multi-Anti Fuzzy Subgroups mathsjournal
For any intuitionistic multi-fuzzy set A = { < x , µA(x) , νA(x) > : x∈X} of an universe set X, we study the set [A](α, β) called the (α, β)–lower cut of A. It is the crisp multi-set { x∈X : µi(x) ≤ αi , νi(x) ≥ βi , ∀i } of X. In this paper, an attempt has been made to study some algebraic structure of intuitionistic multi-anti fuzzy subgroups and their properties with the help of their (α, β)–lower cut sets
In this paper, we introduce the concept of residual quotient of intuitionistic fuzzy subsets of ring and module and then define the notion of residual quotient intuitionistic fuzzy submodules , residual quotient intuitionistic fuzzy ideals. We study many properties of residual quotient relating to union, intersection, sum of intuitionistic fuzzy submodules (ideals). Using the concept of residual quotient, we investigate some important characterization of intuitionistic fuzzy annihilator of subsets of ring and module. We also study intuitionistic fuzzy prime submodules with the help of intuitionistic fuzzy annihilators. Many related properties are defined and discussed.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Part of Lecture series on EE646, Fuzzy Theory & Applications delivered by me during First Semester of M.Tech. Instrumentation & Control, 2012
Z H College of Engg. & Technology, Aligarh Muslim University, Aligarh
Reference Books:
1. T. J. Ross, "Fuzzy Logic with Engineering Applications", 2/e, John Wiley & Sons,England, 2004.
2. Lee, K. H., "First Course on Fuzzy Theory & Applications", Springer-Verlag,Berlin, Heidelberg, 2005.
3. D. Driankov, H. Hellendoorn, M. Reinfrank, "An Introduction to Fuzzy Control", Narosa, 2012.
Please comment and feel free to ask anything related. Thanks!
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.
Fixed Point Results In Fuzzy Menger Space With Common Property (E.A.)IJERA Editor
This paper presents some common fixed point theorems for weakly compatible mappings via an implicit relation in Fuzzy Menger spaces satisfying the common property (E.A)
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.
Mechanical Characterization of Biodegradable Linen Fiber CompositesIJMER
The conventional materials like iron, mild steel, cast iron etc are having good mechanical properties. Hence they are widely used in structural engineering applications. These conventional materials have some defects like formation of rust, low weight to strength ratio, high production cost. To
overcome these defects, engineers started fabricating composite materials. Composites exhibit peculiar
properties like different strengths in different directions, rust resistant, high strength to weight ratio, but
they pollute the environment. Now the natural fibre composites are widely used in automobile industry.
The natural fibres and resins are used to fabricate an eco friendly composite material. Lack of resources
and increasing environmental pollution has evoked great interest in the research of materials that are
friendly to our health and environment. Bio polymer composites fabricated from natural fibres is currently
the most promising area in polymer sciences. This is designed to assess the possibility of fibre as
reinforcing material in composites. Epoxy resin was made a stiffened panel to conduct tensile test. In this
paper it is aimed to explain all possible ways to use natural composites in automobile components. The
main advantages of using natural fibers are their degradability and light weight. They are environment
friendly and also increase the fuel economy
Stability of Simply Supported Square Plate with Concentric CutoutIJMER
The finite element method is used to obtain the elastic buckling loads for simply supported isotropic square plate containing circular, square and rectangular cutouts. ANSYS finite element software had been used in the study. The applied inplane loads considered are uniaxial and biaxial compressions. In all the cases the load is distributed uniformly along the plate outer edges. The effects of the size and shape of concentric cutouts with different plate thickness ratios and having all-round simply supported boundary condition on the plate buckling strength have been considered in the analysis. It is found that cutouts have considerable influence on the buckling load factor k and the effect is larger when cutout ratios greater than 0.3 and for thickness ratio greater than 0.15.
In this paper, we introduce the concept of residual quotient of intuitionistic fuzzy subsets of ring and module and then define the notion of residual quotient intuitionistic fuzzy submodules , residual quotient intuitionistic fuzzy ideals. We study many properties of residual quotient relating to union, intersection, sum of intuitionistic fuzzy submodules (ideals). Using the concept of residual quotient, we investigate some important characterization of intuitionistic fuzzy annihilator of subsets of ring and module. We also study intuitionistic fuzzy prime submodules with the help of intuitionistic fuzzy annihilators. Many related properties are defined and discussed.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Part of Lecture series on EE646, Fuzzy Theory & Applications delivered by me during First Semester of M.Tech. Instrumentation & Control, 2012
Z H College of Engg. & Technology, Aligarh Muslim University, Aligarh
Reference Books:
1. T. J. Ross, "Fuzzy Logic with Engineering Applications", 2/e, John Wiley & Sons,England, 2004.
2. Lee, K. H., "First Course on Fuzzy Theory & Applications", Springer-Verlag,Berlin, Heidelberg, 2005.
3. D. Driankov, H. Hellendoorn, M. Reinfrank, "An Introduction to Fuzzy Control", Narosa, 2012.
Please comment and feel free to ask anything related. Thanks!
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.
Fixed Point Results In Fuzzy Menger Space With Common Property (E.A.)IJERA Editor
This paper presents some common fixed point theorems for weakly compatible mappings via an implicit relation in Fuzzy Menger spaces satisfying the common property (E.A)
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.
Mechanical Characterization of Biodegradable Linen Fiber CompositesIJMER
The conventional materials like iron, mild steel, cast iron etc are having good mechanical properties. Hence they are widely used in structural engineering applications. These conventional materials have some defects like formation of rust, low weight to strength ratio, high production cost. To
overcome these defects, engineers started fabricating composite materials. Composites exhibit peculiar
properties like different strengths in different directions, rust resistant, high strength to weight ratio, but
they pollute the environment. Now the natural fibre composites are widely used in automobile industry.
The natural fibres and resins are used to fabricate an eco friendly composite material. Lack of resources
and increasing environmental pollution has evoked great interest in the research of materials that are
friendly to our health and environment. Bio polymer composites fabricated from natural fibres is currently
the most promising area in polymer sciences. This is designed to assess the possibility of fibre as
reinforcing material in composites. Epoxy resin was made a stiffened panel to conduct tensile test. In this
paper it is aimed to explain all possible ways to use natural composites in automobile components. The
main advantages of using natural fibers are their degradability and light weight. They are environment
friendly and also increase the fuel economy
Stability of Simply Supported Square Plate with Concentric CutoutIJMER
The finite element method is used to obtain the elastic buckling loads for simply supported isotropic square plate containing circular, square and rectangular cutouts. ANSYS finite element software had been used in the study. The applied inplane loads considered are uniaxial and biaxial compressions. In all the cases the load is distributed uniformly along the plate outer edges. The effects of the size and shape of concentric cutouts with different plate thickness ratios and having all-round simply supported boundary condition on the plate buckling strength have been considered in the analysis. It is found that cutouts have considerable influence on the buckling load factor k and the effect is larger when cutout ratios greater than 0.3 and for thickness ratio greater than 0.15.
A ZVS Interleaved Boost AC/DC Converter Using Super Capacitor Power for Hybri...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
An Amalgamation-Based System for Micro aneurysm Detection and Diabetic Retino...IJMER
We propose an ensemble-based framework to improve microaneurysm detection. Unlike
the well-known approach of considering the output of multiple classifiers, we propose a combination of
internal components of microaneurysm detectors, namely preprocessing methods and candidate
extractors. We have evaluated our approach for microaneurysm detection in an online competition,
where this algorithm is currently ranked as first, and also on two other databases.
Orientation Effects of Stress Concentrators on the Material Deformation Behav...IJMER
Present investigation pertains to carry out to experimental work to generate data in order to
establish the mode of material deformation and fracture in AISI 316 stainless steel strips of 1.70mm thickness in
the presence of elliptical notches at the center of the specimen whose major axis were designed to incline to the
tensile axis at an angle of 0o
, 45o
and 90o
and the same happens to be the axis of rolling. An elliptical hole of
8.00mm (major axis) with 5.0mm (minor axis) were machined in each specimen so as to correspond to the above
angles of 0o
45o
and90o
and one specimen without any elliptical hole as a notch for comparative analysis of the
experimental data. These flat specimens with and without stress concentrators were tested under tension using
Hounsfield Tcnsomctcr and the changes in notch geometry have been recorded at various loadings. Further, the
visual appearance of the cracks initiation have been continuously observed and recorded. The effect of stress
ratio factors and the strain ratio parameters on the mode of fracture on material deformation in and around the
stress concentrator has been thoroughly analyzed and it has been established that the crack initiation began
either at the inner tips of the minor or the major axis of the elliptical stress concentrator, but, always
perpendicular to the direction of loading irrespective of the rolling direction and the orientations of the stress
concentrators. However, the changes in the rotation of the major and the minor axis of the elliptical stress
concentrators were found to alter, and, this alteration in fact assisted in estimating the strains along the major as
well as the minor axis of the stress concentrators. Relation between a plastic strain ratio with respect to the ratio
between the major and the minor strains was observed to be of extremely complex nature. The overall
observation in the present investigation has indicated that thin strips or sheet specimens containing a single or
multiple or a combined type of stress concentrators will create a keen interest in the research approach of the
investigators and make them aware of the seriousness of the presence of the stress concentrators and caution
them to incorporate any possible design notifications in order to avoid any catastrophic failure (s).
Integrating Environmental Accounting in Agro-Allied and Manufacturing Indust...IJMER
ONLY WHEN THE LAST TREE IS CUT, ONLY WHEN THE LAST RIVER IS POLLUTED, ONLY WHEN THE LAST FISH IS CAUGHT, ONLY THEN WILL THEY REALIZE THAT YOU CANNOT EAT MONEY’ American proverb
Due to growing awareness and concern on the impact of human activity on the ecosystem, there is an
increasing trend to judge organizations in relation to the community in which it operates. The impact of the activities on the environment with regard to pollution of water, air, land and abuse of natural resources are coming under scrutiny of governments, stakeholders and citizens. Education is considered the key to effective development strategies and TVET institutions then must be the master
key that can alleviate poverty, promote peace, conserve the environment, improve the quality of life
for all and help achieve sustainable development. Unless proper accounting work is done, it cannot be determined that both have been fulfilling their responsibilities. The aim of the study was to explore whether distinctive processes of environmental accounting are possible in agro-allied and
manufacturing industries with a view to enhancing sustainability. To accomplish this aim, this research explores environmental accountability practices in TVET institutions. This paper is in part of an exploratory research project and it is limited in that it attempts to be illuminative and theoretically driven. The paper aims to prove that environmental reporting and disclosure will
enable in agro-allied and manufacturing industries undertake a major transformation that includes
approaches that harmonize economic prosperity, environmental conservation and social well-being.
However, while strategies for achieving this goal are not widespread, a range of international experiences is beginning to suggest ways forward. These initiatives include national TVET policy reforms, green campus, green curriculum, green community, green research and green culture. The paper includes suggested templates that can be useful in agro-allied and manufacturing industries
Cross Spectral Density Analysis for Various Codes Suitable for Spread Spectru...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
Multistage interconnection networks (MIN) are among the most efficient switching architectures for the number of switching Element (SE). Optical crosstalk in optical multistage interconnection network on the omega network topology Switches are arranged in multiple stages. These switches also referred to as switching element (SEs) have two input and two output ports, interconnected to the neighboring stages in a shuffle exchange connected pattern message routing in such a network is determined by the interstate connection pattern.
Optical Multistage interconnection networks (OMIN) are advanced version of MINs. The main Problem with OMIN is crosstalk. The main purpose of this paper is to Present crosstalk free modified omega network, which is based on time domain approach. This paper presents the source and destination based Algorithm (SDBA) .SDBA does the scheduling for source and their respective destination addresses for the message routing. SDBA is compared with the crosstalk modified omega network (CFMON).CFMON also Minimizes the crosstalk. This paper is the modified form of the omega network.
Implementation of Multiple Touch Gesture Using Depth InformationIJMER
In this paper, we propose a method of implementing a multiple touch gesture using the
depth information. We obtain the depth information using depth camera and determine gesture type using
it. Using this method, it is possible to provide an event according to this gesture and to implement the
application supporting multiple touch gesture at low costs. In addition, user can control unit instinctively
in shooting game by applying this method to the screen of large size.
Development of Algorithm for Voice Operated Switch for Digital Audio Control ...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
Experimental Investigation on Effect of Particle Sizes of Molybdenum Disulphi...IJMER
In the present work, experimental investigation has been carried out to identify the
effectiveness of employing three different particle sizes of MoS2 (Nano-particles: 40 nm size, Technical
superfine grade: 1.75 μm size and Technical grade: 53 μm size) in varying quantities (0.5, 1.0 and 1.5% by
weight) on the wear of the sliding surfaces. The experiments were conducted on a conformal block and
disk test setup. The running-in distance required to achieve steady state wear was determined
experimentally. The wear of the block is measured as its weight loss after the test. The results of the
experiments are reported
Comparing: Routing Protocols on Basis of sleep modeIJMER
The architecture of ad hoc wireless network consists of mobile nodes for communication
without the use of fixed-position routers. The communication between them takes place without
centralized control. Routing is a very crucial issue, so to deal with this routing algorithms must deliver
the packet in significant delay. There are different protocols for handling the mobile environment like
AODV, DSR and OLSR. But this paper will focus on performance of AODV and OLSR routing protocols.
The performance of these protocols is analyzed on two metrics: time and throughput
In this paper we present a new concept called “generalized neutrosophic soft set”. This concept
incorporates the beneficial properties of both generalized neutrosophic set introduced by A.A.Salama [7]
and soft set techniques proposed by Molodtsov [4]. We also study some properties of this concept. Some
definitions and operations have been introduced on generalized neutrosophic soft set. Finally we present
an application of generalized neuutrosophic soft set in decision making problem.
International Journal of Computer Science, Engineering and Information Techno...ijcseit
In this paper we present a new concept called “generalized neutrosophic soft set”. This concept
incorporates the beneficial properties of both generalized neutrosophic set introduced by A.A.Salama [7]
and soft set techniques proposed by Molodtsov [4]. We also study some properties of this concept. Some
definitions and operations have been introduced on generalized neutrosophic soft set. Finally we present
an application of generalized neuutrosophic soft set in decision making problem.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A fusion of soft expert set and matrix modelseSAT Journals
Abstract
The purpose of this paper is to define different types of matrices in the light of soft expert sets. We then propose a decision making
model based on soft expert set.
Keywords: Soft set, soft expert set, Soft Expert matrix.
In this paper, we introduce the concept of residual quotient of intuitionistic fuzzy subsets of ring and module and then define the notion of residual quotient intuitionistic fuzzy submodules , residual quotient intuitionistic fuzzy ideals. We study many properties of residual quotient relating to union, intersection, sum of intuitionistic fuzzy submodules (ideals). Using the concept of residual quotient, we investigate some important characterization of intuitionistic fuzzy annihilator of subsets of ring and module. We also study intuitionistic fuzzy prime submodules with the help of intuitionistic fuzzy annihilators. Many related properties are defined and discussed
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
An approach to Fuzzy clustering of the iris petals by using Ac-meansijsc
This paper proposes a definition of a fuzzy partition element based on the homomorphism between type-1 fuzzy sets and the three-valued Kleene algebra. A new clustering method
based on the C-means algorithm, using the defined partition, is presented in this paper, which will
be validated with the traditional iris clustering problem by measuring its petals.
In this paper, the notion α -anti fuzzy new-ideal of a PU-algebra are defined and discussed. The homomorphic images (pre images) ofα -anti fuzzy new-ideal under homomorphism of a PU-algebras has been obtained. Some related result have been derived.
In this paper, the notion a -anti fuzzy new-ideal of a PU-algebra are defined and discussed. The
homomorphic images (pre images) ofa -anti fuzzy new-ideal under homomorphism of a PU-algebras has
been obtained. Some related result have been derived.
A Study on Intuitionistic Multi-Anti Fuzzy Subgroupsmathsjournal
For any intuitionistic multi-fuzzy set A = { < x , µA(x) , νA(x) > : x∈X} of an universe set X, we study the set [A](α, β) called the (α, β)–lower cut of A. It is the crisp multi-set { x∈X : µi(x) ≤ αi ,νi(x) ≥ βi , ∀i } of X. In this paper, an attempt has been made to study some algebraic structure of intuitionistic multi-anti fuzzy subgroups and their properties with the help of their (α, β)–lower cut sets.
An Application of Interval Valued Fuzzy Soft Matrix In Medical Diagnosisiosrjce
: Today is a world of uncertainty with its associated problems, which can be well handled by soft set
theory. In this paper, we extend sanchez`s approach for medical diagnosis using the representation of an
interval valued fuzzy soft matrices. we introduce the definition of union and intersection of Interval valued fuzzy
soft matrices with examples.Finally, we extend our approach in application of these matrices in medical
Diagnosis.
In real life situations, there are many issues in which we face uncertainties, vagueness, complexities and unpredictability. Neutrosophic sets are a mathematical tool to address some issues which cannot be met using the existing methods. Neutrosophic soft matrices play a crucial role in handling indeterminant and inconsistent information during decision making process. The main focus of this article is to discuss the concept of neutrosophic sets, neutrosophic soft sets and neutrosophic soft matrices theory which are very useful and applicable in various situations involving uncertainties and imprecisions. Thereafter our intention is to find a new method for constructing a decision matrix using neutrosophic soft matrices as an application of the theory. A neutrosophic soft matrix based algorithm is considered to solve some problems in the diagnosis of a disease from the occurrence of various symptoms in patients. This article deals with patient-symptoms and symptoms-disease neutrosophic soft matrices. To come to a decision, a score matrix is defined where multiplication based on max-min operation and complementation of neutrosophic soft matrices are taken into considerations.
On Fuzzy - Semi Open Sets and Fuzzy - Semi Closed Sets in Fuzzy Topologic...IOSR Journals
Abstract: The aim of this paper is to introduce the concept of fuzzy - semi open and fuzzy - semi closed sets of a fuzzy topological space. Some characterizations are discussed, examples are given and properties are established. Also, we define fuzzy - semi interior and fuzzy - semi closure operators. And we introduce fuzzy
- t-set, -SO extremely disconnected space analyse the relations between them.
MSC 2010: 54A40, 03E72.
A Study on Translucent Concrete Product and Its Properties by Using Optical F...IJMER
- Translucent concrete is a concrete based material with light-transferring properties,
obtained due to embedded light optical elements like Optical fibers used in concrete. Light is conducted
through the concrete from one end to the other. This results into a certain light pattern on the other
surface, depending on the fiber structure. Optical fibers transmit light so effectively that there is
virtually no loss of light conducted through the fibers. This paper deals with the modeling of such
translucent or transparent concrete blocks and panel and their usage and also the advantages it brings
in the field. The main purpose is to use sunlight as a light source to reduce the power consumption of
illumination and to use the optical fiber to sense the stress of structures and also use this concrete as an
architectural purpose of the building
Developing Cost Effective Automation for Cotton Seed DelintingIJMER
A low cost automation system for removal of lint from cottonseed is to be designed and
developed. The setup consists of stainless steel drum with stirrer in which cottonseeds having lint is mixed
with concentrated sulphuric acid. So lint will get burn. This lint free cottonseed treated with lime water to
neutralize acidic nature. After water washing this cottonseeds are used for agriculter purpose
Study & Testing Of Bio-Composite Material Based On Munja FibreIJMER
The incorporation of natural fibres such as munja fiber composites has gained
increasing applications both in many areas of Engineering and Technology. The aim of this study is to
evaluate mechanical properties such as flexural and tensile properties of reinforced epoxy composites.
This is mainly due to their applicable benefits as they are light weight and offer low cost compared to
synthetic fibre composites. Munja fibres recently have been a substitute material in many weight-critical
applications in areas such as aerospace, automotive and other high demanding industrial sectors. In
this study, natural munja fibre composites and munja/fibreglass hybrid composites were fabricated by a
combination of hand lay-up and cold-press methods. A new variety in munja fibre is the present work
the main aim of the work is to extract the neat fibre and is characterized for its flexural characteristics.
The composites are fabricated by reinforcing untreated and treated fibre and are tested for their
mechanical, properties strictly as per ASTM procedures.
Hybrid Engine (Stirling Engine + IC Engine + Electric Motor)IJMER
Hybrid engine is a combination of Stirling engine, IC engine and Electric motor. All these 3 are
connected together to a single shaft. The power source of the Stirling engine will be a Solar Panel. The aim of
this is to run the automobile using a Hybrid engine
Fabrication & Characterization of Bio Composite Materials Based On Sunnhemp F...IJMER
The present day technology demands eco-friendly developments. In this era the
composite material are playing a vital roal in different field of Engineering .The composite materials
are using as a principle materials. Nowaday the composite materials are utilizing as a important
component of engineering field .Where as the importance of the applications of composites is well
known, but thrust on the use of natural fibres in it for reinforcement has been given priority for some
times. But changing from synthetic fibres to natural fibres provides only half green-composites. A
partial green composite will be achieved if the matrix component is also eco-friendly. Keeping this in
view, a detailed literature surveyed has been carried out through various issues of the Journals
related to this field. The material systems used are sunnhemp fibres. Some epoxy and hardener has
been also added for stability and drying of the bio-composites. Various graphs and bar-charts are
super-imposed on each other for comparison among themselves and Graphs is plotted on MAT LAB
and ORIGIN 6.0 software. To determining tensile strengths, Various properties for different biocomposites
have been compared among themselves. Comparison of the behaviour of bio-composites of
this work has been also compare with other works. The bio-composites developed in this work are
likely to get applications in fall ceilings, partitions, bio-degradable packagings, automotive interiors,
sports things (e.g. rackets, nets, etc.), toys etc.
Geochemistry and Genesis of Kammatturu Iron Ores of Devagiri Formation, Sandu...IJMER
The Greenstone belts of Karnataka are enriched in BIFs in Dharwar craton, where Iron
formations are confined to the basin shelf, clearly separated from the deeper-water iron formation that
accumulated at the basin margin and flanking the marine basin. Geochemical data procured in terms of
major, trace and REE are plotted in various diagrams to interpret the genesis of BIFs. Al2O3, Fe2O3 (T),
TiO2, CaO, and SiO2 abundances and ratios show a wide variation. Ni, Co, Zr, Sc, V, Rb, Sr, U, Th,
ΣREE, La, Ce and Eu anomalies and their binary relationships indicate that wherever the terrigenous
component has increased, the concentration of elements of felsic such as Zr and Hf has gone up. Elevated
concentrations of Ni, Co and Sc are contributed by chlorite and other components characteristic of basic
volcanic debris. The data suggest that these formations were generated by chemical and clastic
sedimentary processes on a shallow shelf. During transgression, chemical precipitation took place at the
sediment-water interface, whereas at the time of regression. Iron ore formed with sedimentary structures
and textures in Kammatturu area, in a setting where the water column was oxygenated.
Experimental Investigation on Characteristic Study of the Carbon Steel C45 in...IJMER
In this paper, the mechanical characteristics of C45 medium carbon steel are investigated
under various working conditions. The main characteristic to be studied on this paper is impact toughness
of the material with different configurations and the experiment were carried out on charpy impact testing
equipment. This study reveals the ability of the material to absorb energy up to failure for various
specimen configurations under different heat treated conditions and the corresponding results were
compared with the analysis outcome
Non linear analysis of Robot Gun Support Structure using Equivalent Dynamic A...IJMER
Robot guns are being increasingly employed in automotive manufacturing to replace
risky jobs and also to increase productivity. Using a single robot for a single operation proves to be
expensive. Hence for cost optimization, multiple guns are mounted on a single robot and multiple
operations are performed. Robot Gun structure is an efficient way in which multiple welds can be done
simultaneously. However mounting several weld guns on a single structure induces a variety of
dynamic loads, especially during movement of the robot arm as it maneuvers to reach the weld
locations. The primary idea employed in this paper, is to model those dynamic loads as equivalent G
force loads in FEA. This approach will be on the conservative side, and will be saving time and
subsequently cost efficient. The approach of the paper is towards creating a standard operating
procedure when it comes to analysis of such structures, with emphasis on deploying various technical
aspects of FEA such as Non Linear Geometry, Multipoint Constraint Contact Algorithm, Multizone
meshing .
Static Analysis of Go-Kart Chassis by Analytical and Solid Works SimulationIJMER
This paper aims to do modelling, simulation and performing the static analysis of a go
kart chassis consisting of Circular beams. Modelling, simulations and analysis are performed using 3-D
modelling software i.e. Solid Works and ANSYS according to the rulebook provided by Indian Society of
New Era Engineers (ISNEE) for National Go Kart Championship (NGKC-14).The maximum deflection is
determined by performing static analysis. Computed results are then compared to analytical calculation,
where it is found that the location of maximum deflection agrees well with theoretical approximation but
varies on magnitude aspect.
In récent year various vehicle introduced in market but due to limitation in
carbon émission and BS Séries limitd speed availability vehicle in the market and causing of
environnent pollution over few year There is need to decrease dependancy on fuel vehicle.
bicycle is to be modified for optional in the future To implement new technique using change in
pedal assembly and variable speed gearbox such as planetary gear optimise speed of vehicle
with variable speed ratio.To increase the efficiency of bicycle for confortable drive and to
reduce torque appli éd on bicycle. we introduced epicyclic gear box in which transmission done
throgh Chain Drive (i.e. Sprocket )to rear wheel with help of Epicyclical gear Box to give
number of différent Speed during driving.To reduce torque requirent in the cycle with change in
the pedal mechanism
Integration of Struts & Spring & Hibernate for Enterprise ApplicationsIJMER
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the EJB model, Spring Framework assert that ordinary java beans(POJO) can be utilize with minimal
modifications. This modular framework can be used to develop the application faster and can reduce
complexity. This paper will highlight the design overview of Spring Framework along with its features that
have made the framework useful. The integration of multiple frameworks for an E-commerce system has
also been addressed in this paper. This paper also proposes structure for a website based on integration of
Spring, Hibernate and Struts Framework.
Microcontroller Based Automatic Sprinkler Irrigation SystemIJMER
Microcontroller based Automatic Sprinkler System is a new concept of using
intelligence power of embedded technology in the sprinkler irrigation work. Designed system replaces
the conventional manual work involved in sprinkler irrigation to automatic process. Using this system a
farmer is protected against adverse inhuman weather conditions, tedious work of changing over of
sprinkler water pipe lines & risk of accident due to high pressure in the water pipe line. Overall
sprinkler irrigation work is transformed in to a comfortableautomatic work. This system provides
flexibility & accuracy in respect of time set for the operation of a sprinkler water pipe lines. In present
work the author has designed and developed an automatic sprinkler irrigation system which is
controlled and monitored by a microcontroller interfaced with solenoid valves.
On some locally closed sets and spaces in Ideal Topological SpacesIJMER
In this paper we introduce and characterize some new generalized locally closed sets
known as
δ
ˆ
s-locally closed sets and spaces are known as
δ
ˆ
s-normal space and
δ
ˆ
s-connected space and
discussed some of their properties
Intrusion Detection and Forensics based on decision tree and Association rule...IJMER
This paper present an approach based on the combination of, two techniques using
decision tree and Association rule mining for Probe attack detection. This approach proves to be
better than the traditional approach of generating rules for fuzzy expert system by clustering methods.
Association rule mining for selecting the best attributes together and decision tree for identifying the
best parameters together to create the rules for fuzzy expert system. After that rules for fuzzy expert
system are generated using association rule mining and decision trees. Decision trees is generated for
dataset and to find the basic parameters for creating the membership functions of fuzzy inference
system. Membership functions are generated for the probe attack. Based on these rules we have
created the fuzzy inference system that is used as an input to neuro-fuzzy system. Fuzzy inference
system is loaded to neuro-fuzzy toolbox as an input and the final ANFIS structure is generated for
outcome of neuro-fuzzy approach. The experiments and evaluations of the proposed method were
done with NSL-KDD intrusion detection dataset. As the experimental results, the proposed approach
based on the combination of, two techniques using decision tree and Association rule mining
efficiently detected probe attacks. Experimental results shows better results for detecting intrusions as
compared to others existing methods
Natural Language Ambiguity and its Effect on Machine LearningIJMER
"Natural language processing" here refers to the use and ability of systems to process
sentences in a natural language such as English, rather than in a specialized artificial computer
language such as C++. The systems of real interest here are digital computers of the type we think of as
personal computers and mainframes. Of course humans can process natural languages, but for us the
question is whether digital computers can or ever will process natural languages. We have tried to
explore in depth and break down the types of ambiguities persistent throughout the natural languages
and provide an answer to the question “How it affects the machine translation process and thereby
machine learning as whole?” .
Today in era of software industry there is no perfect software framework available for
analysis and software development. Currently there are enormous number of software development
process exists which can be implemented to stabilize the process of developing a software system. But no
perfect system is recognized till yet which can help software developers for opting of best software
development process. This paper present the framework of skillful system combined with Likert scale. With
the help of Likert scale we define a rule based model and delegate some mass score to every process and
develop one tool name as MuxSet which will help the software developers to select an appropriate
development process that may enhance the probability of system success.
Material Parameter and Effect of Thermal Load on Functionally Graded CylindersIJMER
The present study investigates the creep in a thick-walled composite cylinders made
up of aluminum/aluminum alloy matrix and reinforced with silicon carbide particles. The distribution
of SiCp is assumed to be either uniform or decreasing linearly from the inner to the outer radius of
the cylinder. The creep behavior of the cylinder has been described by threshold stress based creep
law with a stress exponent of 5. The composite cylinders are subjected to internal pressure which is
applied gradually and steady state condition of stress is assumed. The creep parameters required to
be used in creep law, are extracted by conducting regression analysis on the available experimental
results. The mathematical models have been developed to describe steady state creep in the composite
cylinder by using von-Mises criterion. Regression analysis is used to obtain the creep parameters
required in the study. The basic equilibrium equation of the cylinder and other constitutive equations
have been solved to obtain creep stresses in the cylinder. The effect of varying particle size, particle
content and temperature on the stresses in the composite cylinder has been analyzed. The study
revealed that the stress distributions in the cylinder do not vary significantly for various combinations
of particle size, particle content and operating temperature except for slight variation observed for
varying particle content. Functionally Graded Materials (FGMs) emerged and led to the development
of superior heat resistant materials.
Energy Audit is the systematic process for finding out the energy conservation
opportunities in industrial processes. The project carried out studies on various energy conservation
measures application in areas like lighting, motors, compressors, transformer, ventilation system etc.
In this investigation, studied the technical aspects of the various measures along with its cost benefit
analysis.
Investigation found that major areas of energy conservation are-
1. Energy efficient lighting schemes.
2. Use of electronic ballast instead of copper ballast.
3. Use of wind ventilators for ventilation.
4. Use of VFD for compressor.
5. Transparent roofing sheets to reduce energy consumption.
So Energy Audit is the only perfect & analyzed way of meeting the Industrial Energy Conservation.
An Implementation of I2C Slave Interface using Verilog HDLIJMER
The focus of this paper is on implementation of Inter Integrated Circuit (I2C) protocol
following slave module for no data loss. In this paper, the principle and the operation of I2C bus protocol
will be introduced. It follows the I2C specification to provide device addressing, read/write operation and
an acknowledgement. The programmable nature of device provide users with the flexibility of configuring
the I2C slave device to any legal slave address to avoid the slave address collision on an I2C bus with
multiple slave devices. This paper demonstrates how I2C Master controller transmits and receives data to
and from the Slave with proper synchronization.
The module is designed in Verilog and simulated in ModelSim. The design is also synthesized in Xilinx
XST 14.1. This module acts as a slave for the microprocessor which can be customized for no data loss.
Discrete Model of Two Predators competing for One PreyIJMER
This paper investigates the dynamical behavior of a discrete model of one prey two
predator systems. The equilibrium points and their stability are analyzed. Time series plots are obtained
for different sets of parameter values. Also bifurcation diagrams are plotted to show dynamical behavior
of the system in selected range of growth parameter
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)
Some New Operations on Fuzzy Soft Sets
1. International
OPEN ACCESS Journal
Of Modern Engineering Research (IJMER)
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss. 4 | Apr. 2014 | 65 |
Some New Operations on Fuzzy Soft Sets
Kumud Borgohain1
, Chittaranjan Gohain2
1,
Deptt. of Mathematics, Dhemaji College, Assam, India
2,
Deptt. of Mathematics, Duliajan College, Assam, India
I. Introduction
In many complicated problems arising in the fields of engineering, social science, economics,
environment, medical science etc. have various uncertainties. Fuzzy soft sets are very useful structures arising in
many areas of mathematics and computer science. The theory soft sets was initiated by Molodtsov[4] in 1999
for modeling uncertainty present in real life. Roughly speaking a soft set is a parameterized classification of the
objects of the universe. He has shown several applications of soft sets in different areas like integration, decision
making etc. In 2003, Maji, Biswas and Ray [5] studied the theory of soft sets initiated by Molodtsov. They
defined equality of two soft sets, subset and super set of a set, complement of a soft set , null soft set and
absolute soft set with examples. Soft binary operations like AND, OR and also the operations of union,
intersection were also defined. In 2005, Pie and Miao [10] and Chen et al [2] improved the work of Maji et al
[5]. In 2012, Borah, Neog and Sut [9] studied the theory of soft sets initiated by Molodtsov [4] and put
forwarded some more propositions regarding fuzzy soft set. In this paper, an analysis has been made to discuss
about some properties related to fuzzy soft sets along with examples and proofs of certain results.
II. Preliminaries
Definition 2.1[1]
Let U be an initial universal set and E be a set of parameters. Let P (U) denote the power set of U. A
pair (F, A) is called a soft set over U if F is a mapping given by F: A (U) ,Where A E
Definition 2.2[6]
Let U be a universe and E a set of attributes. Then the pair (U, E) denotes the collection of all fuzzy
soft sets on U with attributes from E and is called a fuzzy soft class.
Definition 2.3[6]
For two fuzzy soft sets (F, A) and (G,B) over a common universe U , we say that (F,A) is a fuzzy soft
subset of (G,B) if
i) A B
ii) For all ε Є A, F(ε) is a sub set G(ε) and is written as F(A) (G,B)
Definition 2.4[6]
For two fuzzy soft sets (F, A) and (G, B) over a common universe U are said to be soft set equal if
(F,A) is a soft subset of (G,B) and (G,B) is a soft subset of (F,A)
Definition 2.6[6]
Intersection of two fuzzy soft sets (F,A) and (G,B) over a common universe U is a fuzzy soft set (H,C),
Where C= ε Є C, H(ε )= F(ε) G(ε) and is written as (F,A) (G,B) = (H,C)
III. Main Result
Definition3.1
let X={x} be a collection of objects denoted by x than a fuzzy soft set Ă in X is a set of ordered pairs Ă
= {x, µĂ(x):x X}, where µĂ(x) is called the membership grade of x in Ă.
Abstract: Fuzzy soft set is one of the recent topics developed for dealing with the uncertainties present
in most of our real life situations. The parameterization tool of soft set theory enhances the flexibility of
its application. In this paper, we have studied membership grade, power set, -cut set , strong fuzzy -
cut set ,some standard operation fuzzy soft set, degree of subset hood and proposed some results with
examples.
Keywords: Fuzzy set, Soft sets, fuzzy soft class, standard union fuzzy soft set, standard intersection fuzzy
soft set
2. Some new operations on fuzzy soft sets
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss. 4 | Apr. 2014 | 66 |
Example 3.1
Let X= {p, q ,r, s} and A:X I defined A(p)=o.1 A(q)=0.2 ,A(r)= 0.3 A(s)=0.4. Then fuzzy soft set A
can be written as A= {(p, 0.1),(q,0.2),(r,0.3)(s,0.4)}
Definition3.2
Let X be a domain. Then set of all fuzzy soft subsets of X is called the fuzzy soft power set.
Example 3.2 Let X= {a, b} be a fuzzy soft set Then fuzzy soft power set is { ,[a],[b],[a, b]}
Definition 3.3
A fuzzy soft set a is defined on X .The -cut set A
is made up of members X. Whose members
grade is not less than ,therefore A
= { xx, A(x) } Where [0,1]
Example3.3 Let x={p, q, r, s} and fuzzy soft set A=
0.9
p
+
1.0
q
+
0.2
r
+
0.1
s
and -cut set for
=0.1,0.2,0.9,1.0 than
1.0
A={q},
0.9
A=[p, q},
0.2
A={p, q, r},
0.1
A={p, q, r, s}=X
Definition 3.4
Let A be a fuzzy soft set on X. Then strong fuzzy soft -cut set A
is made up of member of X.
whose membership grade is greater than i. e A
={xX, A(x) ˃ } where
[0, 1]
Example 3.4 In Examle3.3 the strong -cut set is
1.0
A
={q],
0.9
A
={q],
0.2
A
=[p,q},
0.1
A
={p,q,r}
Definition3.5
The set of all levels [0,1] that represents distinct -cut set of a given fuzzy soft set A is called a
fuzzy soft level set of A then Ʌ(A) ={ : A(x)= for all xX}
Example3.5 Let X= {a, b, c, d} and fuzzy soft set A =
0.1 0.4 0.3 0.5 0.3
a b c d e
then fuzzy soft level set
of A= {0.1, 0.3, 0.4, 0.5}
Definition3.6
The support of a fuzzy soft set A over the universal set X is the crisp set that contains all the elements
that have non-zero membership grades in A and is denoted by Supp(A) i.e. Supp(A)={ xX, A(x) ˃0}
Definition3.7
Let A be a fuzzy soft set over universal set X. than the set of all those elements of X whose
membership grade is 1 called core of fuzzy soft set A and is denoted by core(A) i. e core(A) ={ xX, A(x) =1}
Definition3.8
Let A be a fuzzy soft set over a universal set X. Then the height of A is the largest membership grade
obtained by any element in that set and is denoted by h(A) i.e h(A) =suppxXA(x)
Example3.6 If A= {0,0.2,0.8} than h(A)=0.8
Definition3.9
A fuzzy soft set A of a classical set X is called fuzzy soft normal if there exists an xX such that A(x)
=1
Example3.7 If a= {0, 0.1, 0.2, 1.0} than A(x) =1
IV. Standard Operation Of Fuzzy Soft Set
Definition4.1
Let A be a fuzzy soft subset of a nonempty set X. Then the complement of A is denoted by A and is
denoted by A = 1-A(x) xX
Definition4.2
Let A and B are two fuzzy soft subset over nonempty set X. Then the standard union of A and B are
denoted by ( )( ) max[ ( ), ( )]A B x A x B x x X
Definition4.3
Let A and B are two fuzzy soft subset over nonempty set X. Then the standard intersection of A and B
are denoted by ( )( ) min[ ( ), ( )]A B x A x B x x X
Proposition 4.1 Let A, B be fuzzy soft sets over a universal set X then A B A B A B
3. Some new operations on fuzzy soft sets
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss. 4 | Apr. 2014 | 67 |
Pr : max[ ( ), ( )]
x X
oof A B A x B x
min[ ( ), ( )]
x X
A B A x B x
max[ ( ), ( )] min[ ( ), ( )]
x X x X
A B A B A x B x A x B x
= [ ( ) ( )]
x X
A x B x
or [ ( ) ( )]
x X
B x A x
= ( ) ( )
x X x X
A x B x
= A B
Definition4.4
Let A be a fuzzy soft subset over a finite set X then scalar cardinality is denoted by ( )
x X
A A x
Example4.4 If A= {0.1, 0.2, 0.3} be a fuzzy soft set then A 0.1+0.2+0.3+0.6
Definition4.5
Let A be a fuzzy soft set over a finite set X is obtained by computing the magnitude of fuzzy soft set A
with the universal set X and is denoted by
A
A
X
Example4.4 If A= {0.1, 0.2, 0.8, 0.3} be a fuzzy soft set then A 0.1+0.2+0.8+0.3=1.4
4x , therefore
A
A
X
=
1.4
.35
4
V. Degree Of Subset Hood
Definition5.1
The support of a fuzzy soft set A over a finite universal set X is the crisp set that contains all elements
of X that have non zero membership grades in A i.e. supp(A) ={ xX, A(x) ˃0}
Definition5.2
The height of a fuzzy soft set A is the largest membership grades obtained by any element in that set
and is denoted by h(A)=sup(A)
Definition5.3
Let A and B are two fuzzy soft sets of universal set X. Then degree of subset hood denoted by S(A,B)
is defined as
1
( , ) [ max[0, ( ) ( )]
x X
S A B A A x B x
A
Preposition 5.13 Let A and B are two fuzzy soft sets of universal set X . Then degree of subset hood denoted by
S(A,B) is defined as
1
( , ) [ max[0, ( ) ( )]
x X
S A B A A x B x
A
or ( , )
A B
S A B
A
Proof:
1
( , ) [ max[0, ( ) ( )]
x X
S A B A A x B x
A
…………………………….(1)
We have [ max[0, ( ) ( )]]
x X
A A x B x
=[ ( ) max[0, ( ) ( )]]
x X x X
A x A x B x
= [ ( ) max[0, ( ) ( )]]
x X
A x A x B x
= min[ ( ) 0, ( ) { ( ) ( )}]
x X
A x A x A x B x
4. Some new operations on fuzzy soft sets
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 4 | Iss. 4 | Apr. 2014 | 68 |
= min[ ( ), ( )]
x X
A x B x
= A B ……………………………………………………………………(2)
From (1) and (2), we get ( , )
A B
S A B
A
VI. Conclusion
In this paper, we have given definitions of power soft set, core of fuzzy soft set, strong fuzzy -cut
set, standard operations of fuzzy soft set and illustrate with some examples. We have introduced the concept
fuzzy soft set, degree of subset hood. It is hoped that our findings will help enhancing this study on fuzzy soft
sets for the researchers.
REFERENCES
[1] Borah M.J, Neog. T.J, Sut. D.K. „Fuzzy Soft Matrix Theory and its Decision Making‟ International Journal of
Modern Engineering Research. Vol.-2 Issue.2 March-April, pp121-127,2012
[2] Chen,D. Tsang,E.C.C, Yeung.D.S, Wang.X “The parameterization reduction of soft sets and its Applications”Vol.49,
No.-5-6,pp757-763,2005
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