Fermatean Fuzzy Interactive Aggregation Operators and their Application to Decision-making

This article explores some interactive aggregation operators for Fermatean fuzzy sets (FFS). These operators are generalisations of those defined for intuitionistic fuzzy sets. It revises the existing operational rules for Fermatean Fuzzy Numbers (FFNs) to construct interactive aggregation operators for FFSs. The improved operational rules incorporate the effects of the membership and non-membership values of the operand FFNs on the resulting FFN. Based on the weighted arithmetic mean and weighted geometric mean, this article proposes two aggregation operators, namely, the Fermatean Fuzzy Interactive Weighted Averaging (FFIWA) operator and the Fermatean Fuzzy Interactive Weighted Geometric (FFIWG) operator. It discusses some properties of the proposed operators and develops an approach for Multi-Attribute Decision making (MADM) using these operators. A numerical example illustrates the developed approach, which is tested for validity using some evaluation criteria.