Exponential information measures-driven Pythagorean fuzzy MADM method and its application to new energy battery supplier evaluation problem

Abstract

Under the Pythagorean fuzzy environment, this paper presents a multi-attribute decision-making (MADM) model based on exponential entropy measure and exponential similarity measure to evaluate new energy battery supplier’s performance. In this method, the notion of Pythagorean fuzzy linguistic sets (PFLSs) is first introduced by combining the linguistic fuzzy sets (LFSs) and the Pythagorean fuzzy sets (PFSs). Then, the axiomatic definitions of Pythagorean fuzzy entropy and Pythagorean fuzzy similarity measure are developed to measure the degree of uncertainty and similarity between two Pythagorean fuzzy linguistic values (PFLVs). The PFLVs can be expressed by the linguistic membership degree (LMD) and linguistic non-membership degree (LNMD). In addition, we construct two new information measure formulas based on exponential function. Through a series of proofs, we verify that they satisfy the axiomatic conditions of entropy and similarity measure of Pythagorean fuzzy language respectively. On this basis, we research the relationship between the two information measures. Finally, we present a novel Pythagorean fuzzy linguistic MADM model. An example for evaluating performance of new energy battery supplier is given to explain the effectiveness of the newly-developed approach. The stability and validity of the newly-developed approach is performed by sensitivity analysis and comparative analysis.