Abstract
Fermatean fuzzy set (FFS) is a more efficient, flexible, and generalized model to deal with uncertainty, as compared to intuitionistic and Pythagorean fuzzy models. This research article presents a novel multiple-attribute decision-making (MADM) technique based on FFS. Aggregation operators (AOs), for example, Dombi, Einstein, and Hamacher, are frequently being used in the MADM process and are considered useful tools for evaluating the given alternatives. Among these, one of the most effective is the Hamacher operator. The salient feature of this operator is that it reduces the impact of negative information and provides more accurate results. Motivated by the primary characteristics of the Hamacher operator, we apply Hamacher interactive aggregation operators based on FFSs to determine the best alternative. Using Hamacher’s norm operations, we introduce some new geometric operators, namely, Fermatean fuzzy Hamacher interactive weighted geometric (FFHIWG) operator, Fermatean fuzzy Hamacher interactive ordered weighted geometric (FFHIOWG) operator, and Fermatean fuzzy Hamacher interactive hybrid weighted geometric (FFHIHWG) operator. Some important results and properties of the proposed AOs are discussed, and to achieve the optimal alternative, the proposed MADM technique is carried out in a real-life application of the medical field. An algorithm of the proposed technique is also developed. The significance of the proposed method is that Fermatean fuzzy Hamacher interactive geometric (FFHIG) operators deal with the relationship among belongingness degree (BD) and nonbelongingness degree (NBD) of the objects, which perform a crucial role in decision-making (DM). At last, to show the exactness and validity of the proposed work, a comparative analysis of the proposed model and the existing models is presented.
Highlights
Ambiguous or uncertain information is one of the greatest dilemmas dealing with the multiple-attribute decision-making (MADM) process. e uncertain information can be captured in different ways
A Fermatean fuzzy set (FFS) having emerging applications in MADM, is a more efficient technique to cope with ambiguities involved in the given data, as compared to IFSs and PFSs
E interaction between belongingness and nonbelongingness degrees has been discussed in the proposed Hamacher interactive AOs (HIAOs)
Summary
Ambiguous or uncertain information is one of the greatest dilemmas dealing with the MADM process. e uncertain information can be captured in different ways. There are some restrictions involved in all these theories, for example, FST deals with belongingness degree only, whereas IFST deals with both BD and NBD but it restricts their sum to be less or equal to 1. To overcome this issue, PFST replaces the condition of the sum to “the sum of squares of BD and NBD to be less or equal to 1.”. E notion of FFS was initiated from IFSs and PFSs, where the sum of cubes of NBD and BD is less than or equal to one. PFST replaces the condition of the sum to “the sum of squares of BD and NBD to be less or equal to 1.” Recently, a more generalized theory, namely, Fermatean fuzzy set theory (FFST), was introduced by Senapati and Yager [7]. e notion of FFS was initiated from IFSs and PFSs, where the sum of cubes of NBD and BD is less than or equal to one.
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