On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights

Abstract

In this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise information or human judgment. The intuitionistic fuzzy sets can also reflect the approval, rejection, and hesitation of decision-makers. The degrees of satisfiability and non-satisfiability and uncertainty of each alternative with respect to a set of criteria are described by membership functions, non-membership functions, and hesitancy indexes, respectively. The aggregation algorithm DIFSM is inspired by Hellwig’s method based on two reference points: ideal point (pattern) and anti-ideal point (anti-pattern), measuring distances between the alternative and ideal point and distance between the ideal and anti-ideal point. The proposed methods take into consideration the entropy-based weights of criteria. An illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach. Additionally, the comparative analysis results, using the DIFSM and the Intuitionistic Fuzzy TOPSIS-based framework, are presented.

The intuitionistic fuzzy synthetic measure in a dynamic analysis of the subjective quality of life of citizens of European cities

“…The Intuitionistic Fuzzy Synthetic Measures (IFSM) is a modification of a less-known variant of Hellwig's measure in a fuzzy environment and is defined in eight steps (Roszkowska et al, 2022).…”

“…Therefore, a new and important direction of the research addressing the measurement of the subjective quality of life refers to the methods for con-ECONOMICS AND ENVIRONMENT 1(88) • 2024 structing synthetic measures based on aggregated ordinal data, which additionally allows for conducting dynamic comparative analyses. Roszkowska et al (2022) proposed a new approach to measuring the subjective quality of life for aggregated data measured on an ordinal measurement scale. In this approach, the Intuitionistic Fuzzy Synthetic Measure (IFSM) was used.…”