Work

Analysis on Inclusion and Preference of Intuitionistic Fuzzy Sets Using Hesitation Degree and Its Application to Presidential Election in US and Korea

Year: 2026

Type: article

Abstract: Inclusion and preference relations are fundamental comparison tools in intuitionistic fuzzy set (IFS) theory and play an important role in decision analysis under uncertainty. In IFS representations, the hesitation degree reflects information that is not captured by membership and non-membership values alone. This study investigates the structural relationship between hesitation and the inclusion and preference relations of IFSs. A proposed interpretation of membership and non-membership degrees is employed to provide a geometric perspective on hesitation. Within this framework, analytical relations between hesitation inequalities and preference conditions are derived. In particular, it is shown that the hesitation inequality constitutes a necessary condition for preference, whereas inclusion relations remain compatible with a wider range of hesitation configurations. The theoretical observations are illustrated using electoral datasets from the 2002 South Korean presidential election and the 2000 United States presidential election in Florida. Regional vote shares are transformed into intuitionistic fuzzy representations to analyze the distribution of hesitation across regions. The examples demonstrate how hesitation may influence the stability of preference relations while inclusion relations remain structurally preserved.

Source: Mathematics

DOI: 10.3390/math14071123

Authors: Sanghyuk Lee, Eunmi Lee

Institutions: The American University of Vietnam, Kookmin University

Language: English

Topic: Fuzzy and Soft Set Theory

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: National Research Foundation, Ministry of Education, National Research Foundation of Korea