Fermatean Fuzzy Interactive Aggregation Operators with Application in MADM Problems

Abstract

Abstract In this manuscript, we give some innovative operations called interactive aggregation operators for Fermatean fuzzy numbers (FFNs). We discuss some drawbacks of the existing operational laws of FFNs, that is, all the existing aggregation operators (AggOps) in the literature for FFNs can't consider the interaction between the participation and non-participation function. We may conclude that the impacts of other degrees of participation or non-participation on a corresponding geometric or an arithmetic AggOps have no effect on the aggregation process. Additionally, the existing AggOps show that the grades of overall participation (non-participation) functions are independent of the grades of non-participation (participation) functions. As a result, under these circumstances, the results of existing models are insufficient and do not provide a realistic preference order of the possibilities. So we introduce the concept of interactive aggregation operations and then design the following several innovative Fermatean fuzzy interactive aggregation operators to address the limitations. Fermatean fuzzy interactive weighted arithmetic (FFIWA) aggregation operator, Fermatean fuzzy interactive ordered weighted arithmetic (FFIOWA) aggregation operator, Fermatean fuzzy interactive hybrid arithmetic (FFIHA) aggregation operator, Fermatean fuzzy interactive weighted geometric (FFIWG) aggregation operator, Fermatean fuzzy interactive ordered weighted geometric (FFIOWG) aggregation operator, Fermatean fuzzy interactive hybrid geometric (FFIHG) aggregation operator. The most remarkable properties of these proposed aggregation operator are studied. Furthermore, numerical examples employing the innovative Fermatean fuzzy interactive arithmetic aggregation operators and Fermatean fuzzy interactive geometric aggregation operators are used to demonstrate and validate a group decision-making issue. To demonstrate the validity of the suggested operators, a comparison of the proposed and existing operators in the literature is done.