Multiple-Attribute Decision-Making Using Fermatean Fuzzy Hamacher Interactive Geometric Operators

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.

Multicriteria decision-making based on distance measures and knowledge measures of Fermatean fuzzy sets

“…A novel divergence measure and multi-objective optimization based on the ratio analysis with the full multiplicative form (MULTIMOORA) method in FF setting were proposed by Rani and Mishra ( 2021 ). Some Hamacher interactive geometric FF aggregation functions and their usability in medical field were given by Shahzadi et al ( 2021b ). The concept of fermatean fuzzy bipolar soft sets with their utility in MCDM was given by Ali and Ansari ( 2021 ).…”

A case study of electronic waste recycling using interval-valued Fermatean fuzzy Hamacher aggregation operators

“…Induced by the Hamacher operations and FFS, the authors proposed FF Hamacher arithmetic and geometric AOs. Shahzadi et al [37] proposed various AOs, for instance, Dombi, Einstein, and Hamacher under FFSs and utilized these AOs in the MADM process to evaluate the given alternatives. Senapati and Chen [38] introduced various novel IVPF AOs based on Hamacher trian-gular norms and discussed their application in MADM issues.…”

A Novel T-Spherical Fuzzy REGIME Method for Managing Multiple-Criteria Choice Analysis Under Uncertain Circumstances

“…In such considerations, it is evidently meaningful to constitute non-standard fuzzy configurations for modelling imprecision and murkiness in recent decades, such as advanced fuzzy models regarding intuitionistic fuzziness (Atanassov, 1986), Pythagorean fuzziness (Yager, 2013), Fermatean fuzziness Yager, 2019a, 2019b), q-rung orthopair fuzziness (Yager, 2017), picture fuzziness (Cuong, 2014), spherical fuzziness (Gündoğdu and Kahraman, 2019), and T-spherical fuzziness (Mahmood et al, 2019). As an efficacious means to expound ambiguous and equivocal information, the generalizations of fuzzy sets exhibit a mathematical strength to expatiate on the uncertainty in subjective thinking and cognitive processes for the reasoning behind intricate decisions in a logical and sensible way (Garg, 2021a;Senapati and Yager, 2019b;Shahzadi et al, 2021;Ullah et al, 2020a). After introducing the generalizations of fuzzy sets, the ordinary fuzzy version of decision models and techniques also began to attain full developments via these higher-order fuzzy sets.…”