Complex Intuitionistic Fuzzy Sets Research Articles

Some results on information measures for complex intuitionistic fuzzy sets

Some results on information measures for complex intuitionistic fuzzy sets

Exponential, Logarithmic and Compensative Generalized Aggregation Operators Under Complex Intuitionistic Fuzzy Environment

This manuscript presents some new exponential, logarithmic and compensative exponential of logarithmic operational laws based on t-norm and co-norm for complex intuitionistic fuzzy (CIF) numbers. The prevailing extensions of fuzzy set theory handle the uncertain data by representing the satisfaction and dissatisfaction degrees as real values and can deal with only one-dimensional problems due to which some important information may be lost in some situations. A modification to these, CIF sets are characterized by complex-valued degrees of satisfaction and dissatisfaction and handle two dimensional data simultaneously in one set using additional terms, called phase terms, which generally give information related with periodicity. Motivated by the characteristics of CIF model, we present some new operational laws and compensative operators namely generalized CIF compensative weighted averaging and generalized CIF compensative weighted geometric. Some properties related to proposed operators are discussed. In light of the developed operators, a group decision-making method is put forward in which weights are determined objectively and is illustrated with the aid of an example. The reliability of the presented decision-making method is explored by comparing it with several prevailing studies. The influence of the parameters used in exponential and logarithmic operations on CIF numbers is also discussed.

Similarity Measures between Temporal Complex Intuitionistic Fuzzy Sets and Application in Pattern Recognition and Medical Diagnosis

This work addresses the issue of similarity measures between two temporal complex Atanassov’s intuitionistic fuzzy sets, many measures of similarity between complex Atanassov’s intuitionistic fuzzy sets. What was proposed before did not consider the abstention group influence, which may lead to counterintuitive results in some cases. A new structure of temporal complex Atanassov’s intuitionistic fuzzy sets is obtained. This set is formally generalized from a conventional Atanassov’s intuitionistic complex fuzzy sets. Here we analyze the limitations of the existing similarity measures. Then, a new similarity measure of temporal complex Atanassov’s intuitionistic fuzzy sets is proposed and several numeric examples are given to demonstrate the validity of the proposed measure. Finally, the proposed similarity measure is applied to pattern recognition and medical diagnosis.

New generalised Bonferroni mean aggregation operators of complex intuitionistic fuzzy information based on Archimedean t-norm and t-conorm

ABSTRACTThis manuscript presents aggregation operators which encapsulate the interaction among the criteria and preferences under complex intuitionistic fuzzy (CIF) conditions. The current extensions of fuzzy set theory handle the uncertain data by representing the satisfaction and dissatisfaction degrees as real values and can trade with only one-dimensional problems due to which some important knowledge may be lost in some situations. A modification to these, CIF sets are portrayed by complex-valued degrees of satisfaction and dissatisfaction and handle two-dimensional data concurrently in one set using additional terms, called phase terms, which usually give knowledge related with periodicity. Motivated by the features of the CIF model, we present some aggregation operators, namely, generalised CIF Bonferroni mean and generalised CIF weighted Bonferroni mean. Some features related to proposed operators are addressed. In light of the developed operators, a decision-making method is put forward and is drawn with the aid of an example. The reliability of the presented decision-making method is examined with the help of a validity test and by comparing the results of the example with several predominating studies.

Robust Averaging–Geometric Aggregation Operators for Complex Intuitionistic Fuzzy Sets and Their Applications to MCDM Process

This paper presents aggregation operators which encapsulate the interaction among the criteria and preferences under complex intuitionistic fuzzy (CIF) conditions. The current extensions of fuzzy set theory handle only the uncertain data by representing the satisfaction and dissatisfaction degrees as real values and hence lose some information. A modification to these, CIF sets are portrayed by complex-valued membership degrees and can handle the data concurrently using additional terms, called phase terms, which usually give knowledge related to periodicity. Motivated by the features of the CIF model, this paper studies some aggregation operators, weighted averaging and geometric, for CIF sets and investigates their properties. To ease with the possible application, we explore the decision-making (DM) process in the CIF set environment and present an algorithm to solve the multiple criteria DM problems. Finally, a practical example is presented to demonstrate the DM process based on the proposed operators and compared their performance with some similar approaches.

On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition

The concept of complex fuzzy set (CFS) and complex intuitionistic fuzzy set (CIFS) is two recent developments in the field of fuzzy set (FS) theory. The significance of these concepts lies in the fact that these concepts assigned membership grades from unit circle in plane, i.e., in the form of a complex number instead from [0, 1] interval. CFS cannot deal with information of yes and no type, while CIFS works only for a limited range of values. To deal with these kinds of problems, in this article, the concept of complex Pythagorean fuzzy set (CPFS) is developed. The novelty of CPFS lies in its larger range comparative to CFS and CIFS which is demonstrated numerically. It is discussed how a CFS and CIFS could be CPFS but not conversely. We investigated the very basic concepts of CPFSs and studied their properties. Furthermore, some distance measures for CPFSs are developed and their characteristics are studied. The viability of the proposed new distance measures in a building material recognition problem is also discussed. Finally, a comparative study of the proposed new work is established with pre-existing study and some advantages of CPFS are discussed over CFS and CIFS.

Complex Intuitionistic Fuzzy Graphs with Application in Cellular Network Provider Companies

In recent years, a mathematical approach of blending different aspects is on the way, which as a result gives a more generalized approach. Following the above mathematical approach, we combine two very powerful techniques, namely complex intuitionistic fuzzy sets and graph theory, and introduce the notion of complex intuitionistic fuzzy graphs. Then, we introduce certain notions including union, join and composition of complex intuitionistic fuzzy graphs, through which one can easily manipulate the complex intuitionistic fuzzy graphs in decision making problems. We elucidate these operations with some examples. We also describe the homomorphisms of complex intuitionistic fuzzy graphs. Finally, we provide an application in cellular network provider companies for the testing of our approach.

A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making

The objective of this work is to present novel correlation coefficient measures for measuring the relationship between the two complex intuitionistic fuzzy sets (CIFSs). In the existing studies of fuzzy and its extension, the uncertainties present in the data are handled with the help of degrees of membership which are the subset of real numbers, and may lose some useful information and hence consequently affect on the decision results. An alternative to these, complex intuitionistic fuzzy set handles the uncertainties with the degrees whose ranges are extended from real subset to the complex subset with unit disc and hence handle the two-dimensional information in a single set. Thus, motivated by this, we develop correlation and weighted correlation coefficients under the CIFS environment in which pairs of the membership degrees represent the two-dimensional information. Also, some of the desirable properties of it are investigated. Further, based on these measures, a multicriteria decision-making approach is presented under the CIFS environment. Two illustrative examples are taken to demonstrate the efficiency of the proposed approach and validate it by comparing their results with the several existing approaches’ results.

Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision‐making

AbstractThe objective of this manuscript is to present some aggregation operators for aggregating the different complex intuitionistic fuzzy (CIF) sets by considering the dependency between the pairs of its membership degrees. In the existing studies of fuzzy and its extensions, the uncertainties present in the data are handled with the help of degrees of membership that are the subset of real numbers, which may lose some useful information and hence consequently affect the decision results. A modification to these, complex intuitionistic fuzzy set handles the uncertainties with the degrees whose ranges are extended from real subset to the complex subset with unit disc and hence handle the two‐dimensional information in a single set. Thus, motivated by this, we developed some new power aggregation operators, namely, CIF power averaging, CIF weighted power averaging, CIF ordered weighted power averaging, CIF power geometric, CIF weighted power geometric, and CIF ordered weighted power geometric. Also, some of the desirable properties of these are investigated. Further, based on these operators, a multicriteria decision‐making approach is presented under the CIF set environment. An illustrative example related to the selection of the best alternative(s) is considered to demonstrate the efficiency of the proposed approach and is validated it by comparing their results with the several existing approaches results.

Some Generalized Complex Intuitionistic Fuzzy Aggregation Operators and Their Application to Multicriteria Decision-Making Process

The objective of this manuscript is to present some generalized weighted averaging aggregation operators for aggregating the different complex intuitionistic fuzzy sets using t-norm operations. In the existing studies of fuzzy and its extension, the uncertainties present in the data are handled with the help of degrees of membership which are the subset of real numbers, which may loose some useful information and hence consequently affect on the decision results. As a modification to these, complex intuitionistic fuzzy set handles the uncertainties with the degrees whose ranges are extended from real subset to the complex subset with the unit disk and hence handle the two-dimensional information in a single set. Thus, motivated by this, we developed some new averaging aggregation operators, namely complex intuitionistic fuzzy (CIF) weighted averaging, CIF ordered weighted averaging and CIF hybrid averaging in conjunction with their desirable properties. Then, we utilized these operators to propose a multicriteria decision-making approach and illustrated a numerical example to demonstrate the working of the proposed approach. Finally, the proposed results are compared with existing approaches results.

The Algebraic Structures of Complex Intuitionistic Fuzzy Soft Sets Associated with Groups and Subgroups

In recent years, the theory of complex fuzzy sets has captured the attention of many researchers, and research in this area has intensified in the past five years. However, almost all of the researchers in this area have focused on the development of various complex fuzzy based models as well as constructing decision making processes using current decision making approaches and tools. In this spirit, this paper focuses on developing the algebraic structures pertaining to groups and subgroups for the complex intuitionistic fuzzy soft set model. This paper was constructed based on the complex intuitionistic fuzzy soft set model which is characterized by a membership and a non-membership structure for both the amplitude and phase terms of the elements. This model was chosen due to its dual-membership structure that is better able to handle the uncertainties and partial ignorance that exists in most complex data, whilst retaining all the characteristics and advantages of complex fuzzy sets. Besides examining the properties and structural characteristics of the algebraic structures, the relationship between the algebraic structures introduced here and the corresponding algebraic structures in fuzzy group theory and classical group theory were also discussed and verified.

Enhanced Decision Support System Applications Based on Complex Intuitionistic Fuzzy Soft Expert Sets Theory

Decision making is one of the important milestones in the development of various real-life aspects. Decision Support System (DSS) is a computerized information system used to enhance decision-making in several areas. This study aims to improve DSS applications by extending two concepts of complex intuitionistic fuzzy sets and soft expert sets to propose the theory of complex intuitionistic fuzzy soft expert sets and defines some related concepts pertaining to this notion as well as the basic operations on this concept. Moreover, the algorithm for such concept is developed.

Interval Complex Neutrosophic Set: Formulation and Applications in Decision-Making

Neutrosophic set is a powerful general formal framework which generalizes the concepts of classic set, fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set, etc. Recent studies have developed systems with complex fuzzy sets, for better designing and modeling real-life applications. The single-valued complex neutrosophic set, which is an extended form of the single-valued complex fuzzy set and of the single-valued complex intuitionistic fuzzy set, presents difficulties to defining a crisp neutrosophic membership degree as in the single-valued neutrosophic set. Therefore, in this paper we propose a new notion, called interval complex neutrosophic set (ICNS), and examine its characteristics. Firstly, we define several set theoretic operations of ICNS, such as union, intersection and complement, and afterward the operational rules. Next, a decision-making procedure in ICNS and its applications to a green supplier selection are investigated. Numerical examples based on real dataset of Thuan Yen JSC, which is a small-size trading service and transportation company, illustrate the efficiency and the applicability of our approach.

Complex neutrosophic set

Complex fuzzy sets and complex intuitionistic fuzzy sets cannot handle imprecise, indeterminate, inconsistent, and incomplete information of periodic nature. To overcome this difficulty, we introduce complex neutrosophic set. A complex neutrosophic set is a neutrosophic set whose complex-valued truth membership function, complex-valued indeterminacy membership function, and complex-valued falsehood membership functions are the combination of real-valued truth amplitude term in association with phase term, real-valued indeterminate amplitude term with phase term, and real-valued false amplitude term with phase term, respectively. Complex neutrosophic set is an extension of the neutrosophic set. Further set theoretic operations such as complement, union, intersection, complex neutrosophic product, Cartesian product, distance measure, and ź-equalities of complex neutrosophic sets are studied here. A possible application of complex neutrosophic set is presented in this paper. Drawbacks and failure of the current methods are shown, and we also give a comparison of complex neutrosophic set to all such methods in this paper. We also showed in this paper the dominancy of complex neutrosophic set to all current methods through the graph.

On Complex Intuitionistic Fuzzy Soft Sets with Distance Measures and Entropies

We introduce the concept of complex intuitionistic fuzzy soft sets which is parametric in nature. However, the theory of complex fuzzy sets and complex intuitionistic fuzzy sets are independent of the parametrization tools. Some real life problems, for example, multicriteria decision making problems, involve the parametrization tools. In order to get their new entropies, some important properties and operations on the complex intuitionistic fuzzy soft sets have also been discussed. On the basis of some well-known distance measures, some new distance measures for the complex intuitionistic fuzzy soft sets have also been obtained. Further, we have established correspondence between the proposed entropies and the distance measures of complex intuitionistic fuzzy soft sets.