A novel approach to MADM problems using Fermatean fuzzy Hamacher prioritized aggregation operators

Abstract

A generalized form of union and intersection on FFS can be formulated from a generalized t-norm (TN) and t-conorm (TCN). Hamacher operations such as Hamacher product and Hamacher sum, are good alternatives to produce such product and sum. The Hamacher operations can generate more ‡exible and more accurate results in decision making process due to the working parameter involved in these operations. The intuitionistic fuzzy set, brifely as; IFS and its extension involving Pythagorean fuzzy set (PFS) and Fermatean fuzzy set (FFS), are all e¤ective tools to express uncertain and incomplete cognitive information with membership, nonmembership and hesitancy degrees. The Fermatean fuzzy set (FF-set) carries out uncertain and imprecise information smartly in exercising decision-making than IFS and PFS. By adjusting the prioritization of attributes in FF-environment, in this course of this article, we …rst device new operations on FF information using prioritized attributes and by employing HTN and HTCN, we discuss the basic operations. Induced by the Hamacher operations and FF-set, we propose FF Hamacher arithmetic and also geometric aggregation operators (AOs). In the …rst section, we introduce the concepts of an FF Hamacher prioritized AO, and FF Hamacher prioritized weighted AO. In the second part, we develop FF Hamacher prioritized geometric operator (GO), and FF Hamacher prioritized weighted GO. We study essential properties and a few special cases of our newly proposed operators. Then, we make use of these proposed operators in developing tools which are key factors in solving the FF multi-attribute decision-making situations with prioritization. The university selection phenomena is considered as a direct application for analysis and to demonstrate the practicality and e¢ cacy of our proposed model. The working parameter considered in these AOs is analyzed in di¤erent existing and proposed AOs. Further, comparison analysis is conducted for the authenticity of proposed & existing operators.

Multi-attribute decision-making for electronic waste recycling using interval-valued Fermatean fuzzy Hamacher aggregation operators

“…PF interactive Hamacher power AOs to assess the express service quality using entropy weights were utilized in Wang et al (2021). Hadi et al (2021) Akram et al (2022a, b, c, d, e, f, g) and Jan et al (2021).…”

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

“…Certain Hamacher AOs based on the IVIFNs and their application to MCDM were proposed by Liu [40]. Other valuable contributions on Hamacher AOs can be seen from [41,42,43,44].…”

Fermatean Hesitant Fuzzy Prioritized Heronian Mean Operator and Its Application in Multi-Attribute Decision Making

“…By extending the Hamacher aggregation operators and the prioritized aggregation (PA) operator [30]. Jan et al [31] proposed the Fermatean fuzzy Hamacher prioritized weighted average (FFHPWA) operator and Fermatean fuzzy Hamacher prioritized weighted geometric (FFHPWG) operator. Rani et al [32,33] proposed several Fermatean fuzzy Heronian mean operators and Fermatean fuzzy Einstein information aggregation operators based on Heronian mean (HM) operators and Einstein aggregation operators, and then applied them to the choice of food waste treatment technology.…”

“…Most existing Fermatean fuzzy aggregation methods assume that the attribute weights are known. Considering that the priority relationship between attributes is often easier to obtain than the attribute weights, the prioritized aggregation (PA) operators [31] are effectively used to determine the attribute weights, which can make the decision-making results objective and fair. Chen et al [56] proposed a prioritized measure-guided aggregation operator based on the ordered weighted average (OWA) operator and the Choquet integral.…”