Generating method of Pythagorean fuzzy sets from the negation of probability

Abstract

Fuzzy sets have been widely concerned due it can better deal with more complex and uncertain problems. To expand the application of fuzzy sets, Yager proposed Pythagorean fuzzy sets (PFS) which has been used in many fields. However, in the most cases, the PFS can be generated by expert assessment, which can limit the application of PFS. Hence, how to reasonably generate Pythagorean fuzzy number from known information is a problem worthy of discussion. The paper proposed a method to generate the Pythagorean fuzzy number by considering the negation of probability, namely Pythagorean fuzzy sets based on negation (NPFS). The probability and the probability after negation can be understood as membership and non-membership in the Pythagorean fuzzy number. Besides, NPFS is also set the connection between probability and PFS. There are some numerical examples used to explain the proposed NPFS. In order to explore the effectiveness of NPFS, the paper can not only apply NPFS to artificial decision-making, but also to data-driven applications, which used to handle the multi-criterion decision making (MCDM) and classification problems. In MCDM, the paper applied the NPFS into TOPSIS and used the fault diagnosis to verify its effectiveness by comparing with the results of probability. In the application of classification, the paper proposed the classification method based on NPFS and used real world data to verify the effectiveness of the proposed method.