The document summarizes research on complex fuzzy sets. Complex fuzzy sets extend traditional fuzzy sets by allowing membership functions to range over the unit circle in the complex plane rather than just [0,1]. The paper defines complex fuzzy sets and operations like union, intersection, and complement. It presents examples and properties of these operations. It also introduces a probabilistic interpretation of complex fuzzy sets to distinguish them from probability.
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.
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.
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
The numerical solution of Huxley equation by the use of two finite difference methods is done. The first one is the explicit scheme and the second one is the Crank-Nicholson scheme. The comparison between the two methods showed that the explicit scheme is easier and has faster convergence while the Crank-Nicholson scheme is more accurate. In addition, the stability analysis using Fourier (von Neumann) method of two schemes is investigated. The resulting analysis showed that the first scheme
is conditionally stable if, r ≤ 2 − aβ∆t , ∆t ≤ 2(∆x)2 and the second
scheme is unconditionally stable.
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.
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.
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
The numerical solution of Huxley equation by the use of two finite difference methods is done. The first one is the explicit scheme and the second one is the Crank-Nicholson scheme. The comparison between the two methods showed that the explicit scheme is easier and has faster convergence while the Crank-Nicholson scheme is more accurate. In addition, the stability analysis using Fourier (von Neumann) method of two schemes is investigated. The resulting analysis showed that the first scheme
is conditionally stable if, r ≤ 2 − aβ∆t , ∆t ≤ 2(∆x)2 and the second
scheme is unconditionally stable.
Bayesian system reliability and availability analysis underthe vague environm...ijsc
Reliability modeling is the most important discipline of reliable engineering. The main purpose of this paper is to provide a methodology for discussing the vague environment. Actually we discuss on Bayesian system reliability and availability analysis on the vague environment based on Exponential distribution
under squared error symmetric and precautionary asymmetric loss functions. In order to apply the Bayesian approach, model parameters are assumed to be vague random variables with vague prior distributions. This approach will be used to create the vague Bayes estimate of system reliability and availability by introducing and applying a theorem called “Resolution Identity” for vague sets. For this purpose, the original problem is transformed into a nonlinear programming problem which is then divided up into eight subproblems to simplify computations. Finally, the results obtained for the subproblems can
be used to determine the membership functions of the vague Bayes estimate of system reliability. Finally, the sub problems can be solved by using any commercial optimizers, e.g. GAMS or LINGO.
A class of coupled neural networks with different internal time-delays and coupling delays is
investigated, which consists of nodes of different dimensions. By constructing suitable Lyapunov
functions and using the linear matrix inequality, the criteria of exponential stabilization for the coupled
dynamical system are established, and formulated in terms of linear matrix inequality. Finally, numerical
examples are presented to verify the feasibility and effectiveness of the proposed theoretical results.
EXACT SOLUTIONS OF A FAMILY OF HIGHER-DIMENSIONAL SPACE-TIME FRACTIONAL KDV-T...cscpconf
In this paper, based on the definition of conformable fractional derivative, the functional
variable method (FVM) is proposed to seek the exact traveling wave solutions of two higherdimensional
space-time fractional KdV-type equations in mathematical physics, namely the
(3+1)-dimensional space–time fractional Zakharov-Kuznetsov (ZK) equation and the (2+1)-
dimensional space–time fractional Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony
(GZK-BBM) equation. Some new solutions are procured and depicted. These solutions, which
contain kink-shaped, singular kink, bell-shaped soliton, singular soliton and periodic wave
solutions, have many potential applications in mathematical physics and engineering. The
simplicity and reliability of the proposed method is verified.
On Fuzzy Soft Multi Set and Its Application in Information Systems ijcax
Research on information and communication technologies have been developed rapidly since it can be applied easily to several areas like computer science, medical science, economics, environments, engineering, among other. Applications of soft set theory, especially in information systems have been found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with respect to these newly defined operations. In this paper, we extend their work and study some more basic properties of their defined operations. Also, we define some basic supporting tools in information system also application of fuzzy soft multi sets in information system are presented and discussed. Here we define the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy soft multi set is a fuzzy multi valued information system.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
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
In this paper, we study the cartesian product of intuitionistic fuzzy soft normal subgroup structure over snorm. By using s-norm of S, we characterize some basic results of intuitionistic S-fuzzy soft subgroup of normal subgroup. Also, we define the relationship between intuitionistic S-fuzzy soft subgroup and intuitionistic S-fuzzy soft normal subgroup. Finally we prove some basic properties
VALIDATION METHOD OF FUZZY ASSOCIATION RULES BASED ON FUZZY FORMAL CONCEPT AN...cscpconf
In order to treat and analyze real datasets, fuzzy association rules have been proposed. Several
algorithms have been introduced to extract these rules. However, these algorithms suffer from
the problems of utility, redundancy and large number of extracted fuzzy association rules. The
expert will then be confronted with this huge amount of fuzzy association rules. The task of
validation becomes fastidious. In order to solve these problems, we propose a new validation
method. Our method is based on three steps. (i) We extract a generic base of non redundant
fuzzy association rules by applying EFAR-PN algorithm based on fuzzy formal concept analysis.
(ii) we categorize extracted rules into groups and (iii) we evaluate the relevance of these rules
using structural equation model.
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.
LATTICE-CELL : HYBRID APPROACH FOR TEXT CATEGORIZATIONcscpconf
In this paper, we propose a new text categorization framework based on Concepts Lattice and cellular automata. In this framework, concept structure are modeled by a Cellular Automaton for Symbolic Induction (CASI). Our objective is to reduce time categorization caused by the Concept Lattice. We examine, by experiments the performance of the proposed approach and compare it with other algorithms such as Naive Bayes and k nearest neighbors. The results show performance improvement while reducing time categorization.
On Fuzzy Soft Multi Set and Its Application in Information Systems ijcax
Research on information and communication technologies have been developed rapidly since it can be
applied easily to several areas like computer science, medical science, economics, environments,
engineering, among other. Applications of soft set theory, especially in information systems have been
found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft
multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with
respect to these newly defined operations. In this paper, we extend their work and study some more basic
properties of their defined operations. Also, we define some basic supporting tools in information system
also application of fuzzy soft multi sets in information system are presented and discussed. Here we define
the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy
soft multi set is a fuzzy multi valued information system.
On Fuzzy Soft Multi Set and Its Application in Information Systems ijcax
Research on information and communication technologies have been developed rapidly since it can be
applied easily to several areas like computer science, medical science, economics, environments,
engineering, among other. Applications of soft set theory, especially in information systems have been
found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft
multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with
respect to these newly defined operations. In this paper, we extend their work and study some more basic
properties of their defined operations. Also, we define some basic supporting tools in information system
also application of fuzzy soft multi sets in information system are presented and discussed. Here we define
the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy
soft multi set is a fuzzy multi valued information system.
Bayesian system reliability and availability analysis underthe vague environm...ijsc
Reliability modeling is the most important discipline of reliable engineering. The main purpose of this paper is to provide a methodology for discussing the vague environment. Actually we discuss on Bayesian system reliability and availability analysis on the vague environment based on Exponential distribution
under squared error symmetric and precautionary asymmetric loss functions. In order to apply the Bayesian approach, model parameters are assumed to be vague random variables with vague prior distributions. This approach will be used to create the vague Bayes estimate of system reliability and availability by introducing and applying a theorem called “Resolution Identity” for vague sets. For this purpose, the original problem is transformed into a nonlinear programming problem which is then divided up into eight subproblems to simplify computations. Finally, the results obtained for the subproblems can
be used to determine the membership functions of the vague Bayes estimate of system reliability. Finally, the sub problems can be solved by using any commercial optimizers, e.g. GAMS or LINGO.
A class of coupled neural networks with different internal time-delays and coupling delays is
investigated, which consists of nodes of different dimensions. By constructing suitable Lyapunov
functions and using the linear matrix inequality, the criteria of exponential stabilization for the coupled
dynamical system are established, and formulated in terms of linear matrix inequality. Finally, numerical
examples are presented to verify the feasibility and effectiveness of the proposed theoretical results.
EXACT SOLUTIONS OF A FAMILY OF HIGHER-DIMENSIONAL SPACE-TIME FRACTIONAL KDV-T...cscpconf
In this paper, based on the definition of conformable fractional derivative, the functional
variable method (FVM) is proposed to seek the exact traveling wave solutions of two higherdimensional
space-time fractional KdV-type equations in mathematical physics, namely the
(3+1)-dimensional space–time fractional Zakharov-Kuznetsov (ZK) equation and the (2+1)-
dimensional space–time fractional Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony
(GZK-BBM) equation. Some new solutions are procured and depicted. These solutions, which
contain kink-shaped, singular kink, bell-shaped soliton, singular soliton and periodic wave
solutions, have many potential applications in mathematical physics and engineering. The
simplicity and reliability of the proposed method is verified.
On Fuzzy Soft Multi Set and Its Application in Information Systems ijcax
Research on information and communication technologies have been developed rapidly since it can be applied easily to several areas like computer science, medical science, economics, environments, engineering, among other. Applications of soft set theory, especially in information systems have been found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with respect to these newly defined operations. In this paper, we extend their work and study some more basic properties of their defined operations. Also, we define some basic supporting tools in information system also application of fuzzy soft multi sets in information system are presented and discussed. Here we define the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy soft multi set is a fuzzy multi valued information system.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
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
In this paper, we study the cartesian product of intuitionistic fuzzy soft normal subgroup structure over snorm. By using s-norm of S, we characterize some basic results of intuitionistic S-fuzzy soft subgroup of normal subgroup. Also, we define the relationship between intuitionistic S-fuzzy soft subgroup and intuitionistic S-fuzzy soft normal subgroup. Finally we prove some basic properties
VALIDATION METHOD OF FUZZY ASSOCIATION RULES BASED ON FUZZY FORMAL CONCEPT AN...cscpconf
In order to treat and analyze real datasets, fuzzy association rules have been proposed. Several
algorithms have been introduced to extract these rules. However, these algorithms suffer from
the problems of utility, redundancy and large number of extracted fuzzy association rules. The
expert will then be confronted with this huge amount of fuzzy association rules. The task of
validation becomes fastidious. In order to solve these problems, we propose a new validation
method. Our method is based on three steps. (i) We extract a generic base of non redundant
fuzzy association rules by applying EFAR-PN algorithm based on fuzzy formal concept analysis.
(ii) we categorize extracted rules into groups and (iii) we evaluate the relevance of these rules
using structural equation model.
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.
LATTICE-CELL : HYBRID APPROACH FOR TEXT CATEGORIZATIONcscpconf
In this paper, we propose a new text categorization framework based on Concepts Lattice and cellular automata. In this framework, concept structure are modeled by a Cellular Automaton for Symbolic Induction (CASI). Our objective is to reduce time categorization caused by the Concept Lattice. We examine, by experiments the performance of the proposed approach and compare it with other algorithms such as Naive Bayes and k nearest neighbors. The results show performance improvement while reducing time categorization.
On Fuzzy Soft Multi Set and Its Application in Information Systems ijcax
Research on information and communication technologies have been developed rapidly since it can be
applied easily to several areas like computer science, medical science, economics, environments,
engineering, among other. Applications of soft set theory, especially in information systems have been
found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft
multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with
respect to these newly defined operations. In this paper, we extend their work and study some more basic
properties of their defined operations. Also, we define some basic supporting tools in information system
also application of fuzzy soft multi sets in information system are presented and discussed. Here we define
the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy
soft multi set is a fuzzy multi valued information system.
On Fuzzy Soft Multi Set and Its Application in Information Systems ijcax
Research on information and communication technologies have been developed rapidly since it can be
applied easily to several areas like computer science, medical science, economics, environments,
engineering, among other. Applications of soft set theory, especially in information systems have been
found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft
multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with
respect to these newly defined operations. In this paper, we extend their work and study some more basic
properties of their defined operations. Also, we define some basic supporting tools in information system
also application of fuzzy soft multi sets in information system are presented and discussed. Here we define
the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy
soft multi set is a fuzzy multi valued information system.
On Fuzzy Soft Multi Set and Its Application in Information Systems ijcax
Research on information and communication technologies have been developed rapidly since it can be
applied easily to several areas like computer science, medical science, economics, environments,
engineering, among other. Applications of soft set theory, especially in information systems have been
found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft
multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with
respect to these newly defined operations. In this paper, we extend their work and study some more basic
properties of their defined operations. Also, we define some basic supporting tools in information system
also application of fuzzy soft multi sets in information system are presented and discussed. Here we define
the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy
soft multi set is a fuzzy multi valued information system.
On Fuzzy Soft Multi Set and Its Application in Information Systems ijcax
Research on information and communication technologies have been developed rapidly since it can be
applied easily to several areas like computer science, medical science, economics, environments,
engineering, among other. Applications of soft set theory, especially in information systems have been
found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft
multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with
respect to these newly defined operations. In this paper, we extend their work and study some more basic
properties of their defined operations. Also, we define some basic supporting tools in information system
also application of fuzzy soft multi sets in information system are presented and discussed. Here we define
the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy
soft multi set is a fuzzy multi valued information system.
On Fuzzy Soft Multi Set and Its Application in Information Systems ijcax
Research on information and communication technologies have been developed rapidly since it can be applied easily to several areas like computer science, medical science, economics, environments, engineering, among other. Applications of soft set theory, especially in information systems have been found paramount importance. Recently, Mukherjee and Das defined some new operations in fuzzy soft multi set theory and show that the De-Morgan’s type of results hold in fuzzy soft multi set theory with
respect to these newly defined operations. In this paper, we extend their work and study some more basic properties of their defined operations. Also, we define some basic supporting tools in information system also application of fuzzy soft multi sets in information system are presented and discussed. Here we define
the notion of fuzzy multi-valued information system in fuzzy soft multi set theory and show that every fuzzy soft multi set is a fuzzy multi valued information system.
A Mixed Binary-Real NSGA II Algorithm Ensuring Both Accuracy and Interpretabi...IJECEIAES
In this work, a Neuro-Fuzzy Controller network, called NFC that implements a Mamdani fuzzy inference system is proposed. This network includes neurons able to perform fundamental fuzzy operations. Connections between neurons are weighted through binary and real weights. Then a mixed binaryreal Non dominated Sorting Genetic Algorithm II (NSGA II) is used to perform both accuracy and interpretability of the NFC by minimizing two objective functions; one objective relates to the number of rules, for compactness, while the second is the mean square error, for accuracy. In order to preserve interpretability of fuzzy rules during the optimization process, some constraints are imposed. The approach is tested on two control examples: a single input single output (SISO) system and a multivariable (MIMO) system.
The Positive Effects of Fuzzy C-Means Clustering on Supervised Learning Class...Waqas Tariq
Selection of inputs is one of the most substantial components of classification algorithms for data mining and pattern recognition problems since even the best classifier will perform badly if the inputs are not selected very well. Big data and computational complexity are main cause of bad performance and low accuracy for classical classifiers. In other words, the complexity of classifier method is inversely proportional with its classification efficiency. For this purpose, two hybrid classifiers have been developed by using both type-1 and type-2 fuzzy c-means clustering with cascaded a classifier. In this proposed classifier, a large number of data points are reduced by using fuzzy c-means clustering before applied to a classifier algorithm as inputs. The aim of this study is to investigate the effect of fuzzy clustering on well-known and useful classifiers such as artificial neural networks (ANN) and support vector machines (SVM). Then the role of positive effects of these proposed algorithms were investigated on applied different data sets.
The Positive Effects of Fuzzy C-Means Clustering on Supervised Learning Class...CSCJournals
Selection of inputs is one of the most substantial components of classification algorithms for data mining and pattern recognition problems since even the best classifier will perform badly if the inputs are not selected very well. Big data and computational complexity are main cause of bad performance and low accuracy for classical classifiers. In other words, the complexity of classifier method is inversely proportional with its classification efficiency. For this purpose, two hybrid classifiers have been developed by using both type-1 and type-2 fuzzy c-means clustering with cascaded a classifier. In this proposed classifier, a large number of data points are reduced by using fuzzy c-means clustering before applied to a classifier algorithm as inputs. The aim of this study is to investigate the effect of fuzzy clustering on well-known and useful classifiers such as artificial neural networks (ANN) and support vector machines (SVM). Then the role of positive effects of these proposed algorithms were investigated on applied different data sets.
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.
Improvement of the Shell Element Implemented in FEASTSMTiosrjce
The paper deals with shear locking problem in shell element. Shear locking does not mean complete
rigidity, it refers to unwanted high-stiffness behavior that influences the solution but does not over whelm it, so
that convergence with mesh refinement is slowed but not prevented. In the present study the Bilinear
Degenerated Shell (BDS) element model is improved based on the bubble function for membrane strain energy
and selective integration for the shear energy. After formulation of the shell element, implementation is carried
out in FEASTSMT (FINITE ELEMENT ANALYSIS OF STRUCTURES). Result of the shell element without any
bubble function terms showed sensitivity to shear locking problem. Use of bubble functions and selective
integration greatly improves the element performance. The results were compared with those available in
literatures.
ANALYSIS OF EXISTING TRAILERS’ CONTAINER LOCK SYSTEMS IJCSEIT Journal
Trailers carry large containers to various destinations in the world. These are manually locked on to
trailers as they move through these long distances. Security mainly refers to the safety of a state,
organization, property, and individuals against criminal activity. The study was made to analyze the
existing trailer locks and the insecurity being experienced currently. The study also focused on creating a
background to building an automated lock system for auto-mobiles. Findings showed that there are various
container types like the General Purpose containers, the Hard-Top containers and the Open-Top among
others. Similarly, the twist locks were the ones revised for this study. The study also discussed the
weaknesses of the twist locks, most especially the non-notification on unsecured locks. This causes leads to
accidents and wastage of lives and property. The study finally proposed an automated lock system to
overcome these weaknesses to some good extent.
A MODEL FOR REMOTE ACCESS AND PROTECTION OF SMARTPHONES USING SHORT MESSAGE S...IJCSEIT Journal
The smartphone usage among people is increasing rapidly. With the phenomenal growth of smartphone
use, smartphone theft is also increasing. This paper proposes a model to secure smartphones from theft as
well as provides options to access a smartphone through other smartphone or a normal mobile via Short
Message Service. This model provides option to track and secure the mobile by locking it. It also provides
facilities to receive the incoming call and sms information to the remotely connected device and enables the
remote user to control the mobile through SMS. The proposed model is validated by the prototype
implementation in Android platform. Various tests are conducted in the implementation and the results are
discussed.
BIOMETRIC APPLICATION OF INTELLIGENT AGENTS IN FAKE DOCUMENT DETECTION OF JOB...IJCSEIT Journal
The Job selection process in today’s globally competitive economy can be a daunting task for prospective
employees no matter their experience level. Although many years of research has been devoted to job
search and application resulting in good integration with information technology including the internet and
intelligent agent-based architectures, there are still many areas that need to be enhanced. Two such areas
include the quality of jobs associated with applicants in the job search by profiling the needs of employers
against the needs of prospective employees and the security and verifications schemes integrated to reduce
the instances of fraud and identity theft. The integration of mobile, intelligent agent, and cryptography
technologies provide benefits such as improved accessibility wirelessly, intelligent dynamic profiling, and
increased security. With this in mind we propose the intelligent mobile agents instead of human agents to
perform the Job search using fuzzy preferences which is been published elsewhere and application
operations incorporating the use of agents with a trust authority to establish employer trust and validate
applicant identity and accuracy. Our proposed system incorporates design methodologies to use JADELEAP
and Android to provide a robust, secure, user friendly solution.
FACE RECOGNITION USING DIFFERENT LOCAL FEATURES WITH DIFFERENT DISTANCE TECHN...IJCSEIT Journal
A face recognition system using different local features with different distance measures is proposed in this
paper. Proposed method is fast and gives accurate detection. Feature vector is based on Eigen values,
Eigen vectors, and diagonal vectors of sub images. Images are partitioned into sub images to detect local
features. Sub partitions are rearranged into vertically and horizontally matrices. Eigen values, Eigenvector
and diagonal vectors are computed for these matrices. Global feature vector is generated for face
recognition. Experiments are performed on benchmark face YALE database. Results indicate that the
proposed method gives better recognition performance in terms of average recognized rate and retrieval
time compared to the existing methods.
BIOMETRICS AUTHENTICATION TECHNIQUE FOR INTRUSION DETECTION SYSTEMS USING FIN...IJCSEIT Journal
Identifying attackers is a major apprehension to both organizations and governments. Recently, the most
used applications for prevention or detection of attacks are intrusion detection systems. Biometrics
technology is simply the measurement and use of the unique characteristics of living humans to distinguish
them from one another and it is more useful as compare to passwords and tokens as they can be lost or
stolen so we have choose the technique biometric authentication. The biometric authentication provides the
ability to require more instances of authentication in such a quick and easy manner that users are not
bothered by the additional requirements. In this paper, we have given a brief introduction about
biometrics. Then we have given the information regarding the intrusion detection system and finally we
have proposed a method which is based on fingerprint recognition which would allow us to detect more
efficiently any abuse of the computer system that is running.
PERFORMANCE ANALYSIS OF FINGERPRINTING EXTRACTION ALGORITHM IN VIDEO COPY DET...IJCSEIT Journal
A video fingerprint is a recognizer that is derived from a piece of video content. The video fingerprinting
methods obtain unique features of a video that differentiates one video clip from another. It aims to identify
whether a query video segment is a copy of video from the video database or not based on the signature of
the video. It is difficult to find whether a video is a copied video or a similar video, since the features of the
content are very similar from one video to the other. The main focus of this paper is to detect that the query
video is present in the video database with robustness depending on the content of video and also by fast
search of fingerprints. The Fingerprint Extraction Algorithm and Fast Search Algorithms are adopted in
this paper to achieve robust, fast, efficient and accurate video copy detection. As a first step, the
Fingerprint Extraction algorithm is employed which extracts a fingerprint through the features from the
image content of video. The images are represented as Temporally Informative Representative Images
(TIRI). Then, the second step is to find the presence of copy of a query video in a video database, in which
a close match of its fingerprint in the corresponding fingerprint database is searched using inverted-filebased
method. The proposed system is tested against various attacks like noise, brightness, contrast,
rotation and frame drop. Thus the performance of the proposed system on an average shows high true
positive rate of 98% and low false positive rate of 1.3% for different attacks.
Effect of Interleaved FEC Code on Wavelet Based MC-CDMA System with Alamouti ...IJCSEIT Journal
In this paper, the impact of Forward Error Correction (FEC) code namely Trellis code with interleaver on
the performance of wavelet based MC-CDMA wireless communication system with the implementation of
Alamouti antenna diversity scheme has been investigated in terms of Bit Error Rate (BER) as a function of
Signal-to-Noise Ratio (SNR) per bit. Simulation of the system under proposed study has been done in M-ary
modulation schemes (MPSK, MQAM and DPSK) over AWGN and Rayleigh fading channel incorporating
Walsh Hadamard code as orthogonal spreading code to discriminate the message signal for individual
user. It is observed via computer simulation that the performance of the interleaved coded based proposed
system outperforms than that of the uncoded system in all modulation schemes over Rayleigh fading
channel.
FUZZY WEIGHTED ASSOCIATIVE CLASSIFIER: A PREDICTIVE TECHNIQUE FOR HEALTH CARE...IJCSEIT Journal
In this paper we extend the problem of classification using Fuzzy Association Rule Mining and propose the
concept of Fuzzy Weighted Associative Classifier (FWAC). Classification based on Association rules is
considered to be effective and advantageous in many cases. Associative classifiers are especially fit to
applications where the model may assist the domain experts in their decisions. Weighted Associative
Classifiers that takes advantage of weighted Association Rule Mining is already being proposed. However,
there is a so-called "sharp boundary" problem in association rules mining with quantitative attribute
domains. This paper proposes a new Fuzzy Weighted Associative Classifier (FWAC) that generates
classification rules using Fuzzy Weighted Support and Confidence framework. The naïve approach can be
used to generating strong rules instead of weak irrelevant rules. where fuzzy logic is used in partitioning
the domains. The problem of Invalidation of Downward Closure property is solved and the concept of
Fuzzy Weighted Support and Fuzzy Weighted Confidence frame work for Boolean and quantitative item
with weighted setting is generalized. We propose a theoretical model to introduce new associative classifier
that takes advantage of Fuzzy Weighted Association rule mining.
GENDER RECOGNITION SYSTEM USING SPEECH SIGNALIJCSEIT Journal
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presented. A typical gender recognition system can be divided into front-end system and back-end system.
The task of the front-end system is to extract the gender related information from a speech signal and
represents it by a set of vectors called feature. Features like power spectrum density, frequency at
maximum power carry speaker information. The feature is extracted using First Fourier Transform (FFT)
algorithm. The task of the back-end system (also called classifier) is to create a gender model to recognize
the gender from his/her speech signal in recognition phase. This paper also presents the digital processing
of a speech signals (pronounced “A” and “B”) which are taken from 10 persons, 5 of them are Male and
the rest of them are Female. Power Spectrum Estimation of the signal is examined .The frequency at
maximum power of the English Phonemes is extracted from the estimated power spectrum. The system uses
threshold technique as identification tool. The recognition accuracy of this system is 80% on average.
DETECTION OF CONCEALED WEAPONS IN X-RAY IMAGES USING FUZZY K-NNIJCSEIT Journal
Scanning baggage by x-ray and analysing such images have become important technique for detecting
illicit materials in the baggage at Airports. In order to provide adequate security, a reliable and fast
screening technique is needed for baggage examination.This paper aims at providing an automatic method
for detecting concealed weapons, typically a gun in the baggage by employing image segmentation method
to extract the objects of interest from the image followed by applying feature extraction methods namely
Shape context descriptor and Zernike moments. Finally the objects are classified using fuzzy KNN as illicit
or non-illicit object.
META-HEURISTICS BASED ARF OPTIMIZATION FOR IMAGE RETRIEVALIJCSEIT Journal
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feedback and a modified stochastic algorithm. A visual feature database is constructed from the image
database, using combined feature vector. Very few fast-computable features are included in this step. The
user selects the query image, and based on that, the system ranks the whole dataset. The nearest images are
retrieved and the first automatic relevance feedback is generated. The combined similarity of textual and
visual feature space using Latent Semantic Indexing is evaluated and the images are labelled as relevant or
irrelevant. The feedback drives a feature re-weighting process and is routed to the particle swarm
optimizer. Instead of classical swarm update approach, the swarm is split, for each swarm to perform the
search in parallel, thereby increasing the performance of the system. It provides a powerful optimization
tool and an effective space exploration mechanism. The proposed approach aims to achieve the following
goals without any human interaction - to cluster relevant images using meta-heuristics and to dynamically
modify the feature space by feeding automatic relevance feedback.
ERROR PERFORMANCE ANALYSIS USING COOPERATIVE CONTENTION-BASED ROUTING IN WIRE...IJCSEIT Journal
In Wireless Ad hoc network, cooperation of nodes can be achieved by more interactions at higher protocol
layers, particularly the MAC (Medium Access Control) and network layers play vital role. MAC facilitates
a routing protocol based on position location of nodes at network layer specially known as Beacon-less
geographic routing (BLGR) using Contention-based selection process. This paper proposes two levels of
cross-layer framework -a MAC network cross-layer design for forwarder selection (or routing) and a
MAC-PHY for relay selection. Wireless networks suffers huge number of communication at the same time
leads to increase in collision and energy consumption; hence focused on new Contention access method
that uses a dynamical change of channel access probability which can reduce the number of contention
times and collisions. Simulation result demonstrates the best Relay selection and the comparative of direct
mode with the cooperative networks. And also demonstrates the Performance evaluation of contention
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M-FISH KARYOTYPING - A NEW APPROACH BASED ON WATERSHED TRANSFORMIJCSEIT Journal
Karyotyping is a process in which chromosomes in a dividing cell are properly stained, identified and
displayed in a standard format, which helps geneticist to study and diagnose genetic factors behind various
genetic diseases and for studying cancer. M-FISH (Multiplex Fluorescent In-Situ Hybridization) provides
color karyotyping. In this paper, an automated method for M-FISH chromosome segmentation based on
watershed transform followed by naive Bayes classification of each region using the features, mean and
standard deviation, is presented. Also, a post processing step is added to re-classify the small chromosome
segments to the neighboring larger segment for reducing the chances of misclassification. The approach
provided improved accuracy when compared to the pixel-by-pixel approach. The approach was tested on
40 images from the dataset and achieved an accuracy of 84.21 %.
Steganography is the technique of hiding a confidential message in an ordinary message and the extraction
of that secret message at its destination. Different carrier file formats can be used in steganography.
Among these carrier file formats, digital images are the most popular. For this work, digital images are
used. Here steganography is done on the skin portion of an image. First skin portion of an image is
detected. Random pixels are selected from that detected region using a pseudo-random number generator.
The bits of the secret message will be embedded on the LSB of these random pixels. An analysis is done to
check the efficiency and robustness of the proposed method. The aim of this work is to show that
steganography done using random pixel selection is less prone to outside attacks.
A NOVEL WINDOW FUNCTION YIELDING SUPPRESSED MAINLOBE WIDTH AND MINIMUM SIDELO...IJCSEIT Journal
In many applications like FIR filters, FFT, signal processing and measurements, we are required (~45 dB)
or less side lobes amplitudes. However, the problem is usual window based FIR filter design lies in its side
lobes amplitudes that are higher than the requirement of application. We propose a window function,
which has better performance like narrower main lobe width, minimum side lobe peak compared to the
several commonly used windows. The proposed window has slightly larger main lobe width of the
commonly used Hamming window, while featuring 6.2~22.62 dB smaller side lobe peak. The proposed
window maintains its maximum side lobe peak about -58.4~-52.6 dB compared to -35.8~-38.8 dB of
Hamming window for M=10~14, while offering roughly equal main lobe width. Our simulated results also
show significant performance upgrading of the proposed window compared to the Kaiser, Gaussian, and
Lanczos windows. The proposed window also shows better performance than Dolph-Chebyshev window.
Finally, the example of designed low pass FIR filter confirms the efficiency of the proposed window.
CSHURI – Modified HURI algorithm for Customer Segmentation and Transaction Pr...IJCSEIT Journal
Association rule mining (ARM) is the process of generating rules based on the correlation between the set
of items that the customers purchase.Of late, data mining researchers have improved upon the quality of
association rule mining for business development by incorporating factors like value (utility), quantity of
items sold (weight) and profit. The rules mined without considering utility values (profit margin) will lead
to a probable loss of profitable rules.
The advantage of wealth of the customers’ needs information and rules aids the retailer in designing his
store layout[9]. An algorithm CSHURI, Customer Segmentation using HURI, is proposed, a modified
version of HURI [6], finds customers who purchase high profitable rare items and accordingly classify the
customers based on some criteria; for example, a retail business may need to identify valuable customers
who are major contributors to a company’s overall profit. For a potential customer arriving in the store,
which customer group one should belong to according to customer needs, what are the preferred functional
features or products that the customer focuses on and what kind of offers will satisfy the customer, etc.,
finds the key in targeting customers to improve sales [9], which forms the base for customer utility mining.
AN EFFICIENT IMPLEMENTATION OF TRACKING USING KALMAN FILTER FOR UNDERWATER RO...IJCSEIT Journal
The exploration of oceans and sea beds is being made increasingly possible through the development of
Autonomous Underwater Vehicles (AUVs). This is an activity that concerns the marine community and it
must confront the existence of notable challenges. However, an automatic detecting and tracking system is
the first and foremost element for an AUV or an aqueous surveillance network. In this paper a method of
Kalman filter was presented to solve the problems of objects track in sonar images. Region of object was
extracted by threshold segment and morphology process, and the features of invariant moment and area
were analysed. Results show that the method presented has the advantages of good robustness, high
accuracy and real-time characteristic, and it is efficient in underwater target track based on sonar images
and also suited for the purpose of Obstacle avoidance for the AUV to operate in the constrained
underwater environment.
USING DATA MINING TECHNIQUES FOR DIAGNOSIS AND PROGNOSIS OF CANCER DISEASEIJCSEIT Journal
Breast cancer is one of the leading cancers for women in developed countries including India. It is the
second most common cause of cancer death in women. The high incidence of breast cancer in women has
increased significantly in the last years. In this paper we have discussed various data mining approaches
that have been utilized for breast cancer diagnosis and prognosis. Breast Cancer Diagnosis is
distinguishing of benign from malignant breast lumps and Breast Cancer Prognosis predicts when Breast
Cancer is to recur in patients that have had their cancers excised. This study paper summarizes various
review and technical articles on breast cancer diagnosis and prognosis also we focus on current research
being carried out using the data mining techniques to enhance the breast cancer diagnosis and prognosis.
FACTORS AFFECTING ACCEPTANCE OF WEB-BASED TRAINING SYSTEM: USING EXTENDED UTA...IJCSEIT Journal
Advancement in information system leads organizations to apply e-learning system to train their employees
in order to enhance its performance. In this respect, applying web based training will enable the
organization to train their employees quickly, efficiently and effectively anywhere at any time. This
research aims to extend Unified Theory of Acceptance and Use Technology (UTAUT) using some factors
such flexibility of web based training system, system interactivity and system enjoyment, in order to explain
the employees’ intention to use web based training system. A total of 290 employees have participated in
this study. The findings of the study revealed that performance expectancy, facilitating conditions, social
influence and system flexibility have direct effect on the employees’ intention to use web based training
system, while effort expectancy, system enjoyment and system interactivity have indirect effect on
employees’ intention to use the system.
ALGORITHMIC AND ARCHITECTURAL OPTIMIZATION OF A 3D RECONSTRUCTION MEDICAL IMA...IJCSEIT Journal
This paper presents an optimization of an FPGA circuit implementation of 3D reconstruction algorithm of
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Marching Cubes » has been carried out. The repetitive property of the algorithm has been exploited, as
much as possible, by means of the methodology “Adequacy Algorithm Structures”.
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Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
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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.
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Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
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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.
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Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Gen AI Study Jams _ For the GDSC Leads in India.pdf
PROBABILISTIC INTERPRETATION OF COMPLEX FUZZY SET
1. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
DOI : 10.5121/ijcseit.2012.2204 31
PROBABILISTIC INTERPRETATION OF COMPLEX
FUZZY SET
Nilambar Sethi1
, S. K. Das2
and D.C. Panda3
1
Department of Information Technology
Gandhi Institute of Engineering & Technology, Gunupur, Orissa
nilambar_sethi@rediffmail.com
2
Department of Computer Science, Berhampur University, Berhampur, Orissa
dr.dassusanta@yahoo.co.in
3
Department of Electronics & Communication Engineering
Jagannath Institute of Technology & Management, Paralakhemundi, Orissa
d_c_panda@yahoo.com
ABSTRACT
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.
KEY WORD
Complex fuzzy set, Complex fuzzy relation, complement of complex fuzzy relation, δ -equality, probability.
1. INTRODUCTION
The concept of the fuzzy set was first introduced by Zadeh in a seminal paper in 1965 [7]. This is
the generalization of script Set in terms of membership function. The notion of the fuzzy set A on
the universe of discourse U is the set of order pair {(x, µA(x)), x ε U} with a membership function
µA(x), taking the value on the interval [0,1]. Ramot et al [5], extended the fuzzy set to complex
fuzzy set with membership function, ( )siw x
sz r e= where 1i = − , which ranges in the interval [0,
1] to a unit circle. Ramot et al [4], also introduced different fuzzy complex operations and
relations, like union, intersection, complement etc., Still it is necessary to determine the
membership functions correctly, which will give the appropriate or approximate result for real life
applications. The membership function defined for the complex fuzzy set ( )siw x
sz r e= , which
compromise an amplitude term rs(x) and phase term ws. The amplitude term retains the idea of
“fuzziness” and phase term signifies declaration of complex fuzzy set, for which the second
dimension of membership is required. The complex fuzzy set allows extension of fuzzy logic that
2. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
32
is i to continue with one dimension gradeness of membership. Xin Fu et al [8] defined the fuzzy
complex membership function of the form z=a+ib, where x, y are two fuzzy numbers with
membership function µA(x), µB(x) respectively. If b does not exist, z degenerates to a fuzzy
number.
Xin Fu et al [8], also discussed a complex number in cartesian form where a= rscos(x) and
b=rssin(x), which are in polar forms defined in [4]. The fuzzy number is created by interpolating
complex number in the support of fuzzy set ([1], [2], [3][6]).The member ship function are
usually difficult to determine accurately and one may argue of accurate or precise membership
function are necessary in reality. In order to characterized in accurate membership function in
more general Cai(1995) proposed and discussed δ-equality of the fuzzy set.
Following the above resent development the fuzzy set theory Zhang et al (2004) studies δ-
equality of complex fuzzy set. This is the logical development since a complex membership
function should more difficult that a real membership function to be determine in practice.
Complex fuzzy set is a unique framework over the advantage of traditional fuzzy set .The support
of complex fuzzy set is unrestricted, may include any kind of object such as number, name etc,
which is off course a complex number. The notion of T-norm and T-conorm are used through out
this paper [4].
This paper is organized in the following order. The review of complex fuzzy set and operations
on it are discussed in section 2 and section 3 the -Equalities of complex Fuzzy Relations A
novel idea to probabilistic interpretation are studied in section 4 followed by summary and
suggestion for future work are given in section 5.
2. COMPLEX FUZZY SET AND RELATION
2.1. Concept & Operations
Complex fuzzy set is the basis for complex fuzzy logic [7]. The formal definition of complex
fuzzy set was provided in [7] followed by a discussion and interpretation of the moral concept. In
addition, several set theoretic operations on complex fuzzy set were discussed with several
examples, which illustrate the potential applications of complex fuzzy set in information
processing.
2.2. Definition of Complex Fuzzy Set
A complex fuzzy set S, defined on a universe of discourse U, is characterized by a membership
function ( )xsµ , which can assign any element x∈U as a complex valued grade of membership in
S. The value of ( )xsµ lies in a unit circle in the complex plane and in the form ( )siw x
sz r e= ,
where 1−=i and rs ∈ [0,1].
The complex fuzzy set S, may be defined as the set of order pair given by
( ){ }, ( ) :sS x x x Uµ= ∈ (1)
3. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
33
2.3. Complex Fuzzy Union
2.3.1. Definition ([6,7])
In the traditional fuzzy logic, union for two fuzzy set A and B on U denoted as A∪B is specified
by a function µ , where [ ] [ ] [ ]1,01,01,0: →×µ . (2)
The membership function µ (A∪B), may be defined as one of followings.
(i) Standard Union ( ) ( ) ( )max ,AUB A Bx x xµ µ µ= (3)
(ii) Algebraic Sum ( ) ( ) ( ) ( ) ( ).AUB A B A Bx x x x xµ µ µ µ µ= + − (4)
(iii)Bound Sum ( ) ( ) ( )min 1,AUB A Bx x xµ µ µ= + (5)
The fuzzy union must satisfy the definition 2.2 and is equivalent to the proposed T-Co norms [9].
2.3.2. Properties
The Complex fuzzy union is defined by a set of axioms. These axioms represent properties of
complex fuzzy union functions that must satisfy in order to intuitively acceptable values.
(a) Complex fuzzy union does not satisfy the closure property.
In the algebraic sum union function does not satisfy the closure property for complex fuzzy set,
which can be realized from the following example.
Example 2.3.1. ( ) ( ) ixx BA == µµ
( ) ( )
i
x
B
x
A
x
B
x
A
x
BA 21.
)()()(
+=−+=⇒ µµµµµ U
It shows that the membership function lies outside of the unit circle. i.e. 2 2
1 2+ = 5 >1.
(b) Complex Fuzzy union must be monotonic
Since complex number is not linearly order, monotonicity of the complex numbers is required.
Example 2.3.2. Suppose ( ) ( ), ,b d a b a dµ µ≤ ⇒ ≤ using definition2.3.1 (2)
Similarly the max and min operators used in (3) & (5) are not applicable to complex valued
grades of membership. Here we can apply traditional fuzzy definition of union by keeping same
approach to complex part and different approach to phase may be defined in the following way.
2.3.3. Definition ([6, 7])
Suppose A and B be two complex fuzzy set on U with complex valued membership
function ( ) ( )xx Bn µµ , respectively. Then complex fuzzy union A∪B may be defined as
( ) ( ) ( ) ( )
( )
A Biw x
A B A Bx r x r x eµ ∪
∪ = ⊕ (7)
where ⊕ represents the T-Conorm and BAW ∪ is defined as follows.
4. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
34
a) (Sum) BABA WWW +=∪ (8)
b) (Max ) ( )BABA WWW ,max=∪ (9)
c) (Min) ( )BABA WWW −=∪ min (10)
and
d) (Winner takes all)
A A B
AUB
B B A
W if r r
W
W if r r
>
=
≥
(11)
To illustrate the above, consider the following example.
Example 2.3.3: Suppose
i×0 i π iπ/2
1 e 0.4 e 0.8 e
, ,
-1 0 1
A
=
and
i3π/4 i 2π i π/5
0.2 e 0.3 e 1e
, ,
-1 0 1
B
=
Then
0 π iπ i π/5
1e 0.4e 1e
, ,
-1 0 1
A B
∪ =
Here the union operation is (1) of definition 2.3.1.
2.4. Fuzzy Complex Intersection
It should be noted that the derivation of fuzzy complex intersection closely related to complex
fuzzy union, which clear from the following definition.
2.4.1. Definition([6,7])
The intersection for two complex fuzzy set A and B on U defined as
( ) ( ) ( )
* A Bi w x
A BA B r x r x e ∩
∩ = (12)
where * is denoted as T–norm.
Example 2.4.1. From the example 2.3.3, we can find the fuzzy intersection of the two complex
fuzzy sets A and B as follows.
i3π/4 i 2 π i5π/2
0.2e 0.3e 0.8 e
, ,
-1 0 1
A B
∩ =
Note: The fuzzy union and intersection are not unique, As this depend on the type of functions
used in T-Conorm and T-norms.
2.5. Complex Fuzzy Complement
We known that the complement of a fuzzy set A on U with membership function ( )xAµ is
defined as, ( ( )xAµ−1 .) (13)
The similar concept can be applied to the complex fuzzy set. But it is not always true for some
cases. To illustrate this, consider the following example.
Example 2.5.1. Suppose the membership function of a complex fuzzy set is ( ) 1 i
s x e π
µ = .
5. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
35
That is, ( ) 1 i
s x e π
µ = [ ]ππ sincos1 i+= = −1
So the complement of ( ) 1 i
s x e π
µ = is ( ) 1 ( 1) 2s xµ = − − = , which is outside of the unit circle.
This is violating of the closure properties of Fuzzy complex number.
2.5.1. Definition ([6, 7]). Suppose A is a fuzzy set defined as U. The complex fuzzy complement
for the fuzzy set A is defined as ( )(1 )A xµ− ,
where ( ) ( )[ ])(sin)(cos xwxwxrx sssA +=µ (14)
This form of complex fuzzy complement does not reduce to its traditional fuzzy logic,
if ( ) 0=xws . That is,
when ( ) 0s xµ = , ( )( ) [ ]1 ( )s sC x r x iµ = − + which is again a complex number.
Hence we can write ( )( ) ( )( ) ( )
. sic wx
s sC x C r x eµ = (15)
Consider the function C: [0, 1] → [0, 1], if ( ) ( )( )s sx C xµ µ= then the equation (13) holds. So
we need ( ) ( )( )xCxC ss µµ =. to satisfy the equation (13). This can be achieved by adding π
to ( )sw x .
Hence the complement of ( )sw x will be ( )sw x π+ that is ( ) ( )( )s sC x C xµ µ π= + . (16)
2.6. Operation on Complex Fuzzy numbers [8]
Let 1z a ib= + %%% and 2z c id= + %%% be two complex fuzzy numbers where ,a b%% , ,c d%% are fuzzy
number with membership function ( )a xµ% , ( )b
xµ% , ( )c xµ% , ( )d
xµ%
respectively. The basic arithmetic operation on 1z% and 2z% are defined as follows.
2.6.1.Addition
( ) ( ),
~~~~~~
21 dbicazz +++=+ (17)
Where dbandca
~~~~ ++ are newly derived fuzzy numbers with the following membership
functions:
( ) ( ) ( )( )2~1~~~
21
xxVy ca
xxy
ca µµµ ∧=
+=
+
( ) ( ) ( )( ).2~1~~~
21
xxVy dbxxydb
µµµ ∧=
+=+ (18)
2.6.2.Subtraction
( ) ( ),
~~~~~~
21 dbicazz −+−=− (19)
Where dbandca
~~~~ −− are newly derived fuzzy numbers with the following membership
functions :
6. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
36
( ) ( ) ( )( )2~1~~~
21
xxVy ca
xxy
ca µµµ ∧=
−=
−
( ) ( ) ( )( ).2~1~~~
21
xxVy dbxxydb
µµµ ∧=
−=− (20)
2.6.3.Multiplication
( ) ( ),
~~~~~~~~~~
21 dacbidbcazz ++−=× (21)
Where dacbanddbca
~~~~~~~~ −− are newly derived fuzzy numbers with the following
membership functions.
( ) ( ) ( ) ( ) ( )( )4~3~2~1~~~~~
4321
xxxxVy dbca
xxxxydbca
µµµµµ ∧∧∧=
−=−
( ) ( ) ( ) ( ) ( )( )4~3~2~1~~~~~
4321
xxxxVy dacbxxxxydacb
µµµµµ ∧∧∧=
+=− (22)
2.6.4.Division
+
−
+
+
+
= 2222
2
1
~~
~~~~
~~
~~~~
~
~
dc
dacb
i
dc
dbca
z
z
(23)
For notational simplicity, let 221 ~~
~~~~
~
dc
dbca
t
+
+
= and 222 ~~
~~~~
~
dc
dacb
t
+
+
= where 1
~
t and 2
~
t are newly derived
fuzzy numbers with the following membership functions:
( ) ( ) ( ) ( ) ( )( )4~3~2~1~
0
4
2
3
2
,
4
2
3
2
~
4231
1
xxxxVy dcba
xx
xx
xxxx
y
t µµµµµ ∧∧∧=
≠+
+
+
=
( ) ( ) ( ) ( ) ( )( )4~3~2~1~
0
4
2
3
2
,
4
2
3
2
~
4132
2
xxxxVy dcba
xx
xx
xxxx
y
t µµµµµ ∧∧∧=
≠+
+
−
=
(24)
2.6.7. Modulus
Given ,
~~~
1 biaz += the modulus of 1
~z is defined:
22
1
~~~ baz += (25)
It is obvious that 1
~z is a newly derived fuzzy number with the following membership function:
( ) ( ) ( )( )1 2 2
1 2
1 2
az b
x x
y
y V x xµ µ µ
= +
= ∧ %%% (26)
7. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
37
2.7. COMPLEX FUZZY RELATION
In this section, the complex fuzzy relation is introduced. Here discussion is limited to the relation
between two complex fuzzy set.
2.7.1. Definition (Complex Fuzzy Relation) ([10]): Let A and B be two complex fuzzy sets
defined on U. Then
( ) ( ) ( )
( ) ( ) ( )
. a n d .A Biw x iw x
A A B Bx r x e x r x eµ µ= =
are their corresponding membership values. We can say A B≤ if and only if both amplitude and
phase of A and B are A B≤ that is ( )Ar x ≤ ( )Br x and ( )Aw x ≤ ( )Bw x .
A complex fuzzy relation R (U,V) is a complex fuzzy subset of the product space U x V.
The relation R(U,V) is characterized by a complex membership function
( ), , ,R x y x U y Vµ ∈ ∈ (27)
Where ( ) ( ) ( ) ( ){ }, ( , , , ) ,RR U V x y x y x y U Vµ= ∀ ∈ ×
Here the membership function ( ),R x yµ has the value within an unit circle in the complex plane
with the from ( ) ( ) ( )yxwi
R eyxryx ,
.,, =µ
where ( )yxwi
e ,
is a periodic function defined as ( ) ( ), , 2 , 0, 1, 2w x y w x y k kπ= + = ± ± (28)
2.7.2. Definition ([10])
Let X, Y and Z be three different Universes. Suppose A be a complex fuzzy relation defined from
X to Y and B be a complex fuzzy relation defined from Y to Z. Then composition of A and B
denoted on AoB is a complex fuzzy relation defined from X to Z which can be represented as
( ) ( ) ( )
( ) ( )( )
( ) ( )( )sup(inf , , ,
,
, , . sup inf , , , .
A B
yAoB
i w x y w y z
i w x z
AoB AoB A B
y
x z r x z e r x y r y z eµ ∀
∀
= = (29)
2.7.3. Definition (Complex Fuzzy Union Relation) ([10])
Let A and B be two complex fuzzy relations defined on U × V. The corresponding membership
functions of A and B are defined as
( ) ( ) ( ),
, , . Ai w x y
A Ax y r x y eµ = and ( ) ( ) ( ),
, , . Bi w x y
B Bx y r x y eµ = respectively.
The complex fuzzy union relation of A and B is defined as A∪B by membership function
( ),A B x yµ ∪ where
( ) ( ) ( ),
, , . AUBi w x y
A B AUBx y r x y eµ ∪ = ( ) ( )( ) ( ) ( )max ( , , , )
max , , , . A Bi w x y w x y
A Br x y r x y e= (30)
where ( ),A Br x y∪ is a relation valued function on [0,1] and ( ),A B x yi w
e ∪
is a periodic function
defined in (18)
8. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
38
2.7.4. Definition (Complex Fuzzy Intersection Relation) ([10])
Let A and B be two complex fuzzy sets defined on U x V with their corresponding membership
functions as
( ) ( ) ( )
( ) ( ) ( ), ,
, , and , , ,A Bi w x y i w x y
A A B Bx y r x y e x y r x y eµ µ= =
respectively. The complex fuzzy intersection relation of A and B is defined as A∩B by
membership function ( ),A B x yµ ∩
where ( ) ( ) ( ),
, , . A Bi w x y
A B A Bx y r x y eµ ∩
∩ ∩=
( ) ( )( ) ( ) ( )min( , , , )
min , , , . A Bi w x y w x y
A Br x y r x y e= (31)
Here ( )yxr BA ,∩ is a relation valued function on [0,1] and ( ),A B x yi w
e ∩
is a periodic function.
3. -EQUALITIES OF COMPLEX FUZZY RELATION [8]
This section introduces δ-equalities of complex fuzzy relation and discusses associated theories.
Also introduces implication operators of fuzzy rules and exams complex fuzzy inference in the
framework of δ-equalities of complex fuzzy relations.
Definition 3.1 A distance of complex fuzzy sets is a function
( ) ( )( ) [ ]1,0,: **
→×× VUFVUFρ with the properties: for any A, B, C ∈F*
(U×V)
(1) ( ) ( ) 0,,0, =≥ BABA ρρ If and only if A = B,
(2) ( ) ( ),,, ABBA ρρ =
(3) ( ) ( ) ( ).,,, BCCABA ρρρ +≤
In the following, we introduce a function d, which plays a key role in the rest of paper. We define
( ) ( ) ( ) ( )( ),,,supmax, , yxryxrBAd BAVUyx −= ×∈
( ) ( ) ( ) ),
1
sup , ,
2
A Bx y U V
x y x yω ω
π ∈ ×
− (32)
Obviously, this function d (., .) is closure for any relations between two complex fuzzy sets
defined is Section 2, for example, Complex fuzzy union and complex fuzzy intersection, etc.
Example 3.1 Let
1.2 2 1.6
0.6 1.0 0.8 0.5
1 0 1 2
i i i i
e e e e
A
π π π π
= + + +
−
1.4 2 1.2 0.8
0.7 1.0 0.6 0.4
1 0 1 2
i i i i
e e e e
A
π π π π
′ = + + +
−
We see
( )
( ) ( ) 2.0,,sup
,
=− ′
×∈
yxryxr AA
VUyx
and
( )
( ) ( )
,
1
sup , , 0.2.
2
A A
x y U V
x y x yω ω
π
′
∈ ×
− = Therefore
d ( A, A’
) = 0.2
It is easy to see that, if A and B are two real fuzzy sets on U×V, then
9. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
39
( )
( ) ( )
,
( , ) sup , , .A B
x y U V
d A B x y x yµ µ
∈ ×
−
Definition 3.2 [ Cai 1995] Let U be a universe of discourse. Let A and B be two fuzzy sets on U,
and ( ) ( )xandx BA µµ their membership functions, respectively. Then A and B are said to be δ-
equal, denoted by A = (δ) B, if any only if
( ) ( ) .10,1sup ≤≤−≤−
∈
δδµµ xx BA
Ux
(33)
In this way, we say A and B construct an δ-equality.
Lemma 3.1 Let
( ) .1,0;1,0max 212121 ≤≤−+=∗ δδδδδδ (34)
Then
(1) [ ],1,0;00 11 ∈∀=∗ δδ
(2) [ ],1,0;1 111 ∈∀=∗ δδδ
(3) [ ],1,0,;10 2121 ∈∀≤∗≤ δδδδ
(4) [ ],1,0,,; 2
'
1121
'
1211
'
11 ∈∀∗≤∗⇒≤ δδδδδδδδδ
(5) [ ],1,0,,; 211221 ∈∀∗=∗ δδδδδδ
(6) ( ) ( ) [ ].1,0,,; 321321321 ∈∀∗∗=∗∗ δδδδδδδδδ
Lemma 3.2 Let f, g be bounded real valued functions on a set U. Then
( ) ( ) ( ) ( )xgxfxgxf
UxUxUx
−≤−
∈∈∈
supsupsup
( ) ( ) ( ) ( )xgxfxgxf
UxUxUx
−≤−
∈∈∈
supinfinf
Definition 3.3 [Zhang et al. 2004) Let A and B be two complex fuzzy sets on U, and
( ) ( ) ( )
. Ai x
A Ax r x e
ω
µ = and ( ) ( ) ( )
. Bi x
B Bx r x e
ω
µ = their membership functions,
respectively. Then A and B are said to be δ-equal, denoted by ( ) ,BA δ= if and only if
( ) .10;1, ≤≤−≤ δδBAd (35)
Theorem 3.1 Let A, A’
be complex fuzzy sets defined on U, and B, B’
be complex fuzzy sets
defined on V. If A = ( ) '
1 Aδ and B =( ) '
2 Bδ , then ( )( BABA ′⊕′=⊕ 21 ,min δδ .
Theorem 3.2 Let A, A’
be complex fuzzy sets defined on U, and B, B’
be complex fuzzy sets
defined on V. If A = ( ) '
1 Aδ and B = ( ) '
2 Bδ , then ( )( )1 2min ,A B A Bδ δ ′ ′⊗ = ⊗ .
Theorem 3.3 Suppose Dienes-Rescher implication operator is applied to the fuzzy rule ‘If X is A
then Y is B’, that is ( ) BABAI ⊕=, or
( ) ( ) ( ) ( )( ) ( ) ( )( )max 2 ,
1 ,
, max 1 , . A Bi x y
A BA B
x y r x r y e
π ω ω
µ
−
= − . Further, let A’ and B’
be two complex fuzzy sets with ( ) ( ) ,'' 21 BBandAA δδ == then
10. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
40
( ) ( )( ) ( )''
21 ,,min,1 BAIBA δδ=
Theorem 3.4 Suppose Lukasiewicz implication operator is applied to the fuzzy rule ‘If X is A
then Y is B’, that is BABAI ∗=),( or
( ) ( ) ( ) ( )( ) ( ) ( )( )
1 ,
, . A Bi x y
A BA B
x y r x r y e
ω ω
µ
∗
= ∗
Further, let A’ and B’ be two complex fuzzy sets with ( ) ( ) ,'' 21 BBandAA δδ == then
( ) ( ) ( )''
21 ,,1 BAIBA δδ ∗=
Where
( ) ( )
( ) ( )2 max 0, 1
2 2
A B
A B
x y
x y
ω ω
ω ω π
π π
∗ = + −
Theorem 3.5 Suppose Zadeh implication operator is applied to the fuzzy rule ‘If X is A then Y is
B’, that is ( )BAABAI ⊗⊕=),( or
( ) ( ) ( ) ( ) ( )( )( ) ( ) ( ) ( )( )( )max 2 ,min ,
1 ,
, max 1 ,min , . A A Bi x x y
A A BA B
x y r x r x r y e
π ω ω ω
µ
−
= −
Further, let A’ and B’ be two complex fuzzy sets with ( ) ( ) ,'' 21 BBandAA δδ == then
( ) ( )( ) ( )''
21 ,,min,1 BAIBA δδ=
Theorem 3.6 Suppose Godel implication operator is applied to the fuzzy rule ‘If X is A then Y is
B’, that is I (A, B) = AΘB
Or ( ) ( ) ( ) ( ) ( ) ( )1 , ,
1 , 1 ,
, , A Bi x y
A B A B
x y r x y e
ω
µ = , where
( ) ( ) ( )
( ) ( )
{1
1 , ,
, A B
B
if r x r y
A B r y otherwise
r x y
≤
=
( ) ( ) ( )
( ) ( )
{2
1 ,
., A B
B
if x y
A B y otherwise
x y π ω ω
ωω ≤
=
Further, let A’ and B’ be two complex fuzzy sets with ( ) ( ) ,'' 21 BBandAA δδ == then
( ) ( ) ( )',', BAIBAI δ=
Where
( ) ( )( ) ( ) (( )( )
( ) ( )( ) ( ) (( )( )
'
' '
max inf ,inf inf min , ,
max
1
max inf ,inf inf min ,
2
B B B B
y y y V
B B B B
y y y V
r y r y r y r y
y y y y
δ
ω ω ω ω
π
∈
∈
∗
=
∗
And
( ) ( )
( ) ( )2 max 0, 1
2 2
A B
A B
x y
x y
ω ω
ω ω π
π π
∗ = + −
From the above operation δ is not exactly related to '( ), ( )A A
x xµ µ but is exactly related to
'( ), ( )B B
x xµ µ .
Realistic interpretation in complex fuzzy set
11. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
41
4. PROBABILITY OF COMPLEX FUZZY SET.
A lot of criticism of a fuzzy logic has come from the probability theory community. Due to the
some confusion is caused by complicated relation ship between the CFL and probability. They
are similar is certain respect, yet different in some other respect. Here we are reveal this
mysterious relationship between CFL and probability. It is important that we understand their
relationship clearly so that we can not clarity confusion such as CFL is a clever disguise of
probability theory but also to learn use both technique appropriately such as benefit will
maximized.
4.1. Definition: The probability of a complex fuzzy event A is a generalization of probability
theory.
P (A) = ( ) ( )A xx p x dxµ ×∫ (36)
If X is continuous or
P (A) = ( ) ( )A i x i
i
x p x dxµ ×∑ (37)
If X is discrete PX denotes the probability distribution function of X. and ( )A ixµ be characterized
by the membership function of the form ( )siw x
sz r e= on a unit circle.
More over let two event A and B of a sample Space .We know probability theory
P(A∪B)=P(A)+P(B)-P(A∩B). Does the Relationship hold for Complex Fuzzy event? Answer
depends upon choice of complex fuzzy union.
4.2. Definition (Conditional probability)
Suppose A and B are two event of a Sample Space The conditional probability A given B defined
as P(A/B)=
( )
( )
P A B
P B
∩
(38)
4.3. Definition
Let A and B are two Complex Fuzzy Event of a Sample Space S. The Probability of both the
Complex Fuzzy event defined by
( )P A B∩ = ( ) ( ) ( )A B x
x S
x x p xµ µ
∈
× ×∑ (39)
The member ship function may be defined by (21) and (22).
Where ( ) ( )A Bx xµ µ× ( ) ( ),ac bd i bc ad= − + +% % % %%% % % if ( )A x a ibµ = + and ( )B x c idµ = + .
As the probability is coming on the form of complex number we can evaluate modulo to
get the final result defined by (19).
12. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
42
4.4. Definition
If A and B are any two complex fuzzy event in a sample space S and P (A)≠0 The conditional
probability A given B, P(A/B)=
( )
( )
P A B
P B
∩
(40)
Or
( ) ( / ) ( )P A B P A B P B∩ = ×
4.5. Probabilistic Interpretation of CFS
It is possible to give complex Fuzzy set a probabilistic interpretation viewing the membership
degree of x in a complex fuzzy set A as a conditional probability of A given x. ( ) ( / )A x P A xµ =
Such probabilistic interpretation is consistent with a compliment operation of Complex Fuzzy set
as
( ) ( / )c
c
A
x P A xµ = (41)
Which may be calculated by (16).
How ever the probabilistic interpretation does not help us in calculation the intersection or union
of complex fuzzy set.
( ) ( / )A B x P A B xµ ∩ = ∩ (42)
( ) ( / )A B x P A B xµ ∪ = ∪ (43)
From the probability theory
( / ) ( / ) ( / ) ( / )P A B x P A x P B x P A B x∪ = + − ∪
( ) ( / )A B x P A B xµ ∪ = ∪
Here we only established constraints between union and intersection. If A and B conditionally
independent of x we get
( / ) ( / ) ( / )P A B x P A x P B x∪ = × (44)
If one is Subset of others
( / )
( / )
( / )
P A x if A B
P A B x
P B x if B A
⊆
∩ =
⊂
(45)
Or
(( / ) m i n ( ( / ) , ( / ) )P A B x P A x P B x∩ = (46)
Theorem 4.1
If A1 A2…….. Ak. are complex Fuzzy event of U such that
1
( ) 1Ai
n
i
x x Uµ
=
= ∀ ∈∑
P(Ai) ≠0 i=1,2,..,k and B is the complex Fuzzy event of U,P(B) ≠0
13. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.2, No.2, April 2012
43
1
( / ) ( )
( / )
( / ) ( )
j j
j k
i i
i
P B A P A
P A B
P B A P A
=
×
=
×∑
Proof:
P (A/B)=
( )
( )
P A B
P B
∩
By Defininition(4.4)
In order to show the right hand side of the equation we can expand the denominator of (46).
1
( / ) ( )
k
i i
i
P B A P A
=
×∑
=
1
( )
k
i
i
P A B
=
∩∑
=
1
( ) ( ) ( )i
k
k
A k B k k
i x
x x P xµ µ
=
× ×∑∑
= ( ) ( ) ( )i
k
B k k A k
x
x P x xµ µ
× ×
∑ ∑
= ( ) ( )
k
B k k
x
x P xµ ×∑
=P(B)
Since P(B/Aj)×P(Aj)=P(Aj ∩ B)
Theorem is thus proved.
5. CONCLUSION
The work presented in this paper is the novel frame work of complex fuzzy relation. In this paper
the various properties and operation of complex fuzzy set as well as complex fuzzy relation are
investigated. We also presented the complement of complex fuzzy relation as well probabilistic
interpretation is presented. A further study is required to implement these notions in real life
applications such as knowledge representation and information retrieval in a Complex plan
corresponding of two variables which is not suitable for traditional fuzzy logic. Also it can be do
the complex fuzzy measure to more general class as well as complex fuzzy inference rule.
REFERENCE
[1] Buckley J.J (1987) “Fuzzy Complex Number” in Proceedings of ISFK, Gaungzhou, China, pp.597-
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[2] Buckley J.J (1989) “Fuzzy Complex Number”, Fuzzy Sets &Systems, vol33, pp 333-345.
[3} Buckley J.J (1991) “Fuzzy Complex Analysis I: Differentiation”, Fuzzy Sets &Systems, Vol 4l, pp.
269-284.
[4] Jang J.S.R, Sun C.T, Mizutani E, (2005) “Neuro-Fuzzy And Soft Computing”, PHI, New Delhi.
[5] Pedrycz and Gomide F, (2004) “Introduction To Fuzzy Set Analysis And Design”, PHI, New
Delhi.
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[6] Ramot Daniel, Menahem Friedman, Gideon Langholz and Abraham Kandel (2003) “Complex Fuzzy
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Authors
Mr. Nilambar Sethi is working as an Associate Professor in the Department of
Information Technology, Gandhi Institute of Engineering & Technology (GIET),
Gunupur, Orissa, India. He is under the supervision of Dr. S.K. Das and Dr. D. C.
Panda for his Doctoral degree in the field of Complex fuzzy sets and its applications.
He is a life member of ISTE. He has the research interests in the fields of Computer
Security, Algorithm Analysis and Fuzzy Logic.
Dr. S. K. Das is working as a Reader (Associate Professor) and Head of the
Department of Computer Science, Berhampur University, Berhampur, Orissa, India.
He has more than 17 research publications in National and International Journals and
conferences. He has supervised three Ph.D. scholars and more than 10 scholars are
under supervision. He is a life member of IEEE, ISTE, SGAT, CSI and OITS. He has
the research interests in the fields of Data Communication and Computer Networks,
Computer Security, Internet and Web Technologies, Database Management Systems,
Mobile Ad Hoc Networking and Applications.
Dr. D. C. Panda is working as an Assistant Professor in the Department of
Electronics and Communication Engineering, Jagannath Institute of Technology and
Management (JITM), Paralakhemundi, Orissa, India. He has more than 33 research
publications in National and International Journals and conferences. He attended
Several QIP of different Universities and Institutions of India. He is a reviewer of
IEEE Antenna and Wave Propagation Letters and Magazine. He published a book
“Electromagnetic Field Theory Simplified:- A New Approach for Beginners”, which is
under review. He is an exposure in Computational Electromagnetic Tools. He has the
research interests in the fields of Soft Computing Techniques, Computational
Electromagnetic, Microwave Engineering and MIMO Wireless Networks.