An extended TOPSIS and entropy measure based on Sugeno integral in Pythagorean fuzzy set setting

As an extension of the concepts of fuzzy set and intuitionistic fuzzy set, the concept of Pythagorean fuzzy set better models some real life problems. Distance, entropy, and similarity measures between Pythagorean fuzzy sets play important roles in decision making. In this paper, we give a new entropy measure for Pythagorean fuzzy sets via the Sugeno integral that uses fuzzy measures to model the interaction between criteria. Moreover, we provide a theoretical approach to construct a similarity measure based on entropies. Combining this theoretical approach with the proposed entropy, we define a distance measure that considers the interaction between criteria. Finally, using the proposed distance measure, we provide an extended Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) for multi-criteria decision making and apply the proposed technique to a real life problem from the literature. Finally, a comparative analysis is conducted to compare the results of this paper with those of previous studies in the literature.