On conjunctive complex fuzzification of Lagrange's theorem of ξ−CFSG

The application of a complex fuzzy logic system based on a linear conjunctive operator represents a significant advancement in the field of data analysis and modeling, particularly for studying physical scenarios with multiple options. This approach is highly effective in situations where the data involved is complex, imprecise and uncertain. The linear conjunctive operator is a key component of the fuzzy logic system used in this method. This operator allows for the combination of multiple input variables in a systematic way, generating a rule base that captures the behavior of the system being studied. The effectiveness of this method is particularly notable in the study of phenomena in the actual world that exhibit periodic behavior. The foremost aim of this paper is to contribute to the field of fuzzy algebra by introducing and exploring new concepts and their properties in the context of conjunctive complex fuzzy environment. In this paper, the conjunctive complex fuzzy order of an element belonging to a conjunctive complex fuzzy subgroup of a finite group is introduced. Several algebraic properties of this concept are established and a formula is developed to calculate the conjunctive complex fuzzy order of any of its powers in this study. Moreover, an important condition is investigated that determines the relationship between the membership values of any two elements and the membership value of the identity element in the conjunctive complex fuzzy subgroup of a group. In addition, the concepts of the conjunctive complex fuzzy order and index of a conjunctive complex fuzzy subgroup of a group are also presented in this article and their various fundamental algebraic attributes are explored structural. Finally, the conjunctive complex fuzzification of Lagrange's theorem for conjunctive complex fuzzy subgroups of a group is demonstrated

Bipolar complex fuzzy credibility aggregation operators and their application in decision making problem

A bipolar complex fuzzy credibility set (BCFCS) is a new approach in computational intelligence and decision-making under uncertainty. Bipolar complex fuzzy credibility (BCFC) information has been employed as a strategy for dealing with confusing and unreliable situations that arise in everyday life. In this paper, we used the concept of aggregation operators to diagnose the well-known averaging and geometric aggregation operators, as well as evaluate some properties and related results. Using described operators, an algorithm for multiple criteria group decision making is proposed. Then, a numerical example of a case study of Hospital selection is discussed. Lastly, the comparative analysis of suggested operators with existing operators are also given to discuss the rationality, efficiency and applicability of these operators

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity