<p>Inclusion and preference play a crucial role in decision-making processes and are closely related to hesitation, which involves analyzing the intermediary position between supportive and opposing information. In this research, the relationships between hesitation and inclusion/preference in intuitionistic fuzzy sets (IFSs) are visualized using each membership and non-membership value. These membership and non-membership values are considered independent coordinates and applied to an existing example of a car sale problem. The results reveal a distinct comparison between comparable data which transform to the IFSs and provide meaningful information on decision theory. Inclusion and preference relations with hesitation are also verified using a proposed <i>tanh</i> function and lattice structure and then examined using comparable data, and comparisons are performed. Together with the proposed membership and non-membership coordinations, their degrees are represented graphically, composed of two independent coordinates. Transformed data using IFSs are applied to Korean congressional and presidential election examples. By examining inclusion and preference relations, we observe that the preference relations are satisfied only when the strong third candidate unifies with the other major candidate, whereas inclusion relations are satisfied in both types of election.</p>