Complex Intuitionistic Fuzzy Research Articles

Multi-criteria decision making method based on Bonferroni mean aggregation operators of complex intuitionistic fuzzy numbers

Complex intuitionistic fuzzy sets (CIFSs), characterized by complex-valued grades of membership and non-membership, are a generalization of standard intuitionistic fuzzy (IF) sets that better speak to time-periodic issues and handle two-dimensional data in a solitary set. Under this environment, in this article, various mean-type operators, namely complex IF Bonferroni means (CIFBM) and complex IF weighted Bonferroni mean (CIFWBM) are presented along with their properties and numerous particular cases of CIFBM are discussed. Further, using the presented operators a decision-making approach is developed and is illustrated with the help of a practical example. Also, the reliability of the developed methodology is investigated with the aid of validity test criteria and the example results are compared with prevailing methods based on operators.

A Novel Applications of Complex Intuitionistic Fuzzy Sets in Group Theory

In this paper, we initiate the novel concept of complex intuitionistic fuzzy subgroups and prove that every complex intuitionistic fuzzy subgroup generates two intuitionistic fuzzy subgroups. We extend this ideology to define the concept of level subsets of complex intuitionistic fuzzy set and discuss its various fundamental algebraic characteristics. We also show that the level subset of the complex intuitionistic fuzzy subgroups is a subgroup. Furthermore, we investigate the homomorphic image and pre-image of complex intuitionistic fuzzy subgroup under group homomorphism. Moreover, we prove that the product of two complex intuitionistic fuzzy subgroups is also a complex intuitionistic fuzzy subgroup and develop some new results about direct product of complex intuitionistic fuzzy subgroups.

Generalized Geometric Aggregation Operators Based on T-Norm Operations for Complex Intuitionistic Fuzzy Sets and Their Application to Decision-making

Complex intuitionistic fuzzy set (CIFS) is a special intuitionistic fuzzy set where the membership and non-membership degrees are expressed by a complex-valued membership degree and can more easily describe the vagueness and uncertainty in the real world. Archimedean t-conorm and t-norm (ATT), as an important class of the t-norm (TN) and t-conorm (TC), have greater flexibility in the information fusion process. In this paper, we extend the ATT to CIFSs and present some generalized geometric aggregation operators, which can be used to handle the multiple criteria decision-making (MCDM) problems. For it, we firstly define some new operational laws of the CIFSs based on ATT, then some weighted geometric aggregation operators based on proposed operations are proposed. Further, some desirable properties and special cases of them are studied. Finally, a decision-making approach is developed for the MCDM problem with complex intuitionistic fuzzy information. A practical example is given to show the availability and advantages of the proposed method by comparison with some existing methods. The proposed aggregation operators are more generalized than the existing ones to utilize the uncertain and imprecise information. Several existing operators are considered as special cases of the proposed one. Finally, the proposed method will offer various choices to the decision-maker to access the finest alternatives.

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.

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.

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.

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.