Dual bipolar measures of Atanassov's intuitionistic fuzzy sets

Measures of Atanassov's intuitionistic fuzzy sets (AIFSs), such as subsethood, cardinality, distance, similarity, correlation, and evaluation functions, are often used in application problems. This paper investigates such measures from various perspectives. First, based on the relative relations of an AIFS to other AIFSs, four functions, namely superiority, noninferiority, determinacy, and nonhesitancy, are constructed, which consist of dual bipolar scales, namely (superiority, noninferiority) and (determinacy, nonhesitancy). Then, the proposed measures of AIFSs are axiomatically defined using the dual bipolar scales. Geometrical demonstrations, in general, show consistency between the proposed measures and existing ones. However, unlike existing measures, the proposed measures can highlight the significant features of AIFSs. In addition, the attitude of decision makers is also implanted in measures to allocate the importance in the dual bipolar scales. Two numerical examples are used to demonstrate the applicability and distinctiveness of the proposed measures.