Work

Intuitionistic fuzzy sets and some of their so-called extensions

Year: 2025

Type: article

Abstract: In the present paper we investigate the relationship between intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and some proposed extensions of fuzzy sets, intuitionistic fuzzy sets, and sets that have similar structure. In many cases we establish that the proposed concepts claiming to be extensions of the intuitionistic fuzzy sets are either incorrect in their definitions or offer nothing new compared to the already existing notions. Finally, we formulate four requirements that must be observed so that a new concept claiming to extend an existing one can be considered legitimate and viable, expanding the boundaries of the existing mathematical theory in a meaningful way.

Source: Notes on Intuitionistic Fuzzy Sets

DOI: 10.7546/nifs.2025.31.3.372-385

Authors: Krassimir Atanassov, Peter Vassilev, Vassia Atanassova

Institutions: Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering

Language: English

Topic: Fuzzy and Soft Set Theory

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: diamond

Funder: Bulgarian National Science Fund

Award: G5526119323