Extending Set Measures to Orthopair Fuzzy Sets

Abstract

Yager have proposed the extending set measures to Pythagorean fuzzy sets, which is able to efficiently solve the problems of uncertain information representation in Pythagorean fuzzy environment. However, the Pythagorean fuzzy sets represent a limited range of fields, while the q-rung orthopair fuzzy sets can represent many fuzzy sets, including the Pythagorean fuzzy sets, Fermatean fuzzy sets, and intuitionistic fuzzy sets. In order to extend the extending set measures to Pythagorean fuzzy sets to a broader range, the paper proposes the extending set measures to orthopair fuzzy sets, which can extend the extending set measures to Pythagorean fuzzy sets to q-rung orthopair fuzzy environment. The extending set measures to orthopair fuzzy sets combined with level sets, measure, principle extension and Choquet Integral, which can greatly extend the ability of representing unknown information and processing unknown information. If the q-rung orthopair fuzzy sets degenerate into to Pythagorean fuzzy sets, then the extending set measures to orthopair fuzzy sets will be generated as the extending set measures to Pythagorean fuzzy sets. Numerical examples are designed to prove the effectiveness of the proposed models and the experimental results demonstrate that the proposed method can extend the extending set measures to Pythagorean fuzzy sets to q-rung orthopair fuzzy environment successfully and solve issues of decision making under q-rung orthopair fuzzy environment effectively.