Year: 2026
Type: article
Abstract: Since K. T. Atanassov introduced the intuitionistic fuzzy set (IFS), numerous extensions and and methodologies have been developed and applied in practical contexts. Among these, the Fermatean fuzzy set (FFS) has been recognized as particularly adaptable for handling the uncertainty inherent in multi-criteria decision-making (MCDM) problems due to its expanded domain space. Although various aggregation operators (AOs) have been proposed for FFSs, some of them yield unreasonable or counter-intuitive results in certain situations. In this paper, a detailed review and critical analysis are conducted to reveal the shortcomings of existing approaches. To address these issues, new operational rules (ORs) for FFSs are proposed, and their desirable mathematical properties are formally established. The advantages of the proposed method are demonstrated through several numerical examples that highlight its improved behavior compared with existing approaches. Furthermore, to validate the reliability and practical relevance of the proposed method, it is applied to selected MCDM and pattern recognition problems.
Source: Scientific Reports
Author: Hoang Nguyen
Institution: Gdynia Maritime University
Language: English
Topic: Fuzzy and Soft Set Theory
Field: Decision Sciences
Domain: Social Sciences
Open Access status: gold
Estimated APC paid: $2,690
OpenAlex ID: W7204474504
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