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

Abstract

The intuitionistic fuzzy set, briefly as; IFS and its extension involving Pythagorean fuzzy set (PFS) and Fermatean fuzzy set (FFS), are all effective tools to express uncertain and incomplete cognitive information with membership, nonmembership, and hesitancy degrees. The FFS introduced by Senapati and Yager, carries out uncertain and imprecise information smartly in exercising decision-making than IFS and PFS. A generalized form of union and intersection on FFS can be formulated from a generalized T-norm and T-conorm. Hamacher operations such as Hamacher product and Hamacher sum, are good alternatives to product and sum. In this course of this article, we first device new operations on Fermatean fuzzy information by employing Hamacher T-conorm and T-norm and discuss basic operations. Induced by the Hamacher operations and FFS, we propose Fermatean fuzzy Hamacher arithmetic and also geometric aggregation operators. In the first section, we introduce the concepts of a Fermatean fuzzy Hamacher weighted average operator, a Fermatean fuzzy Hamacher ordered weighted average operator, and a Fermatean fuzzy Hamacher hybrid weighted operator and discuss their basic properties in detail. In the second part, we develop Fermatean fuzzy Hamacher weighted geometric operator, Fermatean fuzzy Hamacher ordered 2 2 , which does not carry out the boundary condition of a PFS. However, it is clear to see (0.8) + 3 (0.7) = 0.512 + 0.343 = 0.855 < 1 3 , which is an appropriate reason for the introduction of a HADI ET AL.| 3465 new division of fuzzy set, called Fermatean fuzzy set (FFS). It is also important to mention that the class of this type of fuzzy sets has more ability to capture the uncertainties as compared with IFSs and PFSs, and are qualified to handle higher degree of vagueness. MADM has been extensively used in many area of sciences, for example, Xu and Xia 17 ; and Xu and Chen 18 introduced intuitionistic fuzzy weighted averaging (IFWA) operator and intuitionistic fuzzy ordered weighted averaging (IFOWA) operator.The fuzzy information aggregation operators are necessarily appealing in significant research areas and are given profound consideration among the scientific community.

Interval-valued fermatean fuzzy sets with multi-criteria weighted aggregated sum product assessment-based decision analysis framework

“…Here, this paper would like to take the powerfulness of the theory of Fermatean fuzziness into account to portray uncertainty, imprecision, and vagueness in a more flexible manner. The FFSs, which were initiated by [ 36 ], are characterized by BG and NG, whose cubes sum is less than or equal to one but the sum is not required to be less than one [ 11 , 31 , 36 ]. It is worth mentioning that the prime difference between FFSs, IFSs and PFSs is their distinct constraints.…”

“…In accordance with the three-phase Fermatean fuzzy group decision analysis approach, [ 34 ] formulated the tax collection issue of governments to finance a public transportation system under the FFS context. Inspired by the Hamacher operational laws, [ 11 ] defined some Hamacher AOs under the FFS context and further utilized them to introduce a novel MCDM framework for cyclone disaster assessment. [ 10 ] introduced an innovative Fermatean fuzzy MCDA technique by combining the Dempster–Shafer theory and Fermatean fuzzy entropy.…”

Fermatean fuzzy Heronian mean operators and MEREC‐based additive ratio assessment method: An application to food waste treatment technology selection

“…Next, we utilize the existing AOs namely Fermatean fuzzy weighted averaging AO (FFWAAO), 7 Fermatean fuzzy weighted geometric AO (FFWGAO), 7 Fermatean fuzzy Hamacher weighted averaging AO (FFHWAAO), 12 Fermatean fuzzy Hamacher weighted geometric AO (FFHWGAO), 12 T A B L E 8 Overall performance degree of FWTT of weighted evaluation matrix Fermatean fuzzy Einstein weighted averaging AO (FFEWAAO), 14 and Fermatean fuzzy Einstein weighted averaging AO (FFEWGAO) 14 for the same case study (Section 6). The final utility degrees and ranking order of alternatives are presented in Table 12.…”

“…Gül 11 proposed the Fermatean fuzzy extensions of simple additive weighting (SAW), additive ratio assessment (ARAS), and Vlsekriterijuska optimizacija i komoromisno resenje (VIKOR) approaches, and their applications in covering the testing facility selection for the treatment of Covid-19 disease. Inspired by Hamacher operations and FFS, Hadi et al 12 studied several Hamacher AOs for FFSs and further, discussed their enviable properties. In accordance with Hamacher's norm operations, Shahzadi et al 13 introduced a series of Fermatean fuzzy Hamacher interactive AOs and applied in multicriteria decision analysis.…”

“…Rani and Mishra 14 proposed some Fermatean fuzzy Einstein AOs and their weighted forms for aggregating the Fermatean fuzzy numbers. In a study, Hadi et al 12 generated several Hamacher AOs and their enviable properties, and employed for MCDM problems. In the recent past, these operators have successfully been applied in Fermatean fuzzy MCDM, but these AOs do not consider the interrelationships among the Fermatean fuzzy numbers during process of aggregation.…”