A New Representation of Intuitionistic Fuzzy Systems and Their Applications in Critical Decision Making

In decision-making problem, fuzzy system is considered as an effective tool with access to uncertain information by fuzzy representations. Evolutionary fuzzy systems have been developed with the appearance of intuitionistic fuzzy, hesitant fuzzy, neutrosophic representations, etc. Moreover, by capturing compound features and convey multifaceted information, complex numbers are utilized to generalize fuzzy and intuitionistic fuzzy sets. However, the order relations established in these existing systems have certain limitations, such as they are not total order relations or they are defined based on intermediate functions, hence it is difficult to use in building and ensuring important properties of logical operators and distance measures in the systems. In this article, a representation of the intuitionistic fuzzy systems based on complex numbers (IFS-C) in the polar form by a new way is proposed to overcome the above restrictions. Specifically, an intuitionistic fuzzy set is characterized by the two functions of modulus and argument. A new order relation, set-theoretic operations, and a new distance measure by the polar form of IFS-C are defined and investigated. The applicability of the proposal is illustrated by a new decision-making model called P-distance measure. It is tested on the benchmark medical datasets in comparison with the existing methods. The experiments confirm the advantages of the proposal.