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

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.