No abstract

This research article is devoted to establish some general aggregation operators, based on Yager’s t-norm and t-conorm, to cumulate the Fermatean fuzzy data in decision-making environments. The Fermatean fuzzy sets (FFSs), an extension of the orthopair fuzzy sets, are characterized by both membership degree (MD) and nonmembership degree (NMD) that enable them to serve as an excellent tool to represent inexact human opinions in the decision-making process. In this article, the valuable properties of the FFS are merged with the Yager operator to propose six new operators, namely, Fermatean fuzzy Yager weighted average (FFYWA), Fermatean fuzzy Yager ordered weighted average (FFYOWA), Fermatean fuzzy Yager hybrid weighted average (FFYHWA), Fermatean fuzzy Yager weighted geometric (FFYWG), Fermatean fuzzy Yager ordered weighted geometric (FFYOWG), and Fermatean fuzzy Yager hybrid weighted geometric (FFYHWG) operators. A comprehensive discussion is made to elaborate the dominant properties of the proposed operators. To verify the importance of the proposed operators, an MADM strategy is presented along with an application for selecting an authentic lab for the COVID-19 test. The superiorities of the proposed operators and limitations of the existing operators are discussed with the help of a comparative study. Moreover, we have explained comparison between the proposed theory and the Fermatean fuzzy TOPSIS method to check the accuracy and validity of the proposed operators. The influence of various values of the parameter in the Yager operator on decision-making results is also examined.

We define the Cartesian product, composition, union and join on interval-valued fuzzy graphs and investigate some of their properties. We also introduce the notion of interval-valued fuzzy complete graphs and present some properties of self complementary and self weak complementary interval-valued fuzzy complete graphs

Group decision‐making is a process wherein multiple individuals interact simultaneously, analyze problems, evaluate the possible available alternatives, characterized by multiple conflicting criteria, and choose suitable alternative solution to the problem. Technique for establishing order preference by similarity to the ideal solution (TOPSIS) is a well‐known method for multiple‐criteria decision‐making. The purpose of this study is to extend the TOPSIS method to solve multicriteria group decision‐making problems equipped with Pythagorean fuzzy data, in which the assessment information on feasible alternatives, provided by the experts, is presented as Pythagorean fuzzy decision matrices having each entry characterized by Pythagorean fuzzy numbers. A revised closeness index is utilized to obtain the ranking of alternatives and to identify the optimal alternative. The developed Pythagorean fuzzy TOPSIS (PF‐TOPSIS) is illustrated by a flow chart. At length, practical examples interpreting the applicability of our proposed PF‐TOPSIS are solved.