Fermatean Cubic Fuzzy Aggregation Operators and Their Application in Multiattribute Decision-Making Problems

Abstract

The purpose of aggregation methods is to convert a list of objects of a set into a single object of the same set usually by an $n$ -arry function, so-called aggregation operator. The key features of this work are the aggregation operators, because they are based on a novel set called Fermatean cubic fuzzy set (F-CFS). F-CFS has greater spatial scope and can deal with more ambiguous situations where other fuzzy set extensions fail to support them. For this purpose, the notion of F-CFS is defined. F-CFS is the transformation of intuitionistic cubic fuzzy set (I-CFS), Pythagorean cubic fuzzy set (P-CFS), interval-valued cubic fuzzy set, and basic orthopair fuzzy set and is grounded on the constraint that “the cube of the supremum of membership plus nonmembership degree is $\le 1$ ”. We have analyzed some properties of Fermatean cubic fuzzy numbers (F-CFNs) as they are the alteration $$ of basic properties of I-CFS and P-CFS. We also have defined the score and deviation degrees of F-CFNs. Moreover, the distance measuring function between two F-CFNs is defined which shows the space between two F-CFNs. Based on this notion, the aggregation operators namely Fermatean cubic fuzzy-weighted averaging operator (F-CFWA), Fermatean cubic fuzzy-weighted geometric operator (F-CFWG), Fermatean cubic fuzzy-ordered-weighted averaging operator (F-CFOWA), and Fermatean cubic fuzzy-ordered-weighted geometric operator (F-CFOWG) are developed. Furthermore, the notion is applied to multiattribute decision-making (MADM) problem in which we presented our objectives in the form of F-CFNs to show the effectiveness of the newly developed strategy.