1. School of Science, Wuhan University of Technology, Wuhan 430070, China; 2. School of Mathematics and Physics, North China Electric Power University,Beijing 102206, China
Abstract：In response to the problems of unknown objective weights of attributes and missing hesitancy in the existing entropy formulas of interval-valued Pythagorean fuzzy sets, the fuzziness is defined according to the characteristics of the set. A new axiomatic definition of the entropy for interval-valued Pythagorean fuzzy set is given based on the fuzziness and hesitancy. An improved entropy formula is proposed to calculate objective weights of attributes, and the bidirectional projection method is extended to interval-valued Pythagorean fuzzy environments. A multi-attribute decision-making method based on the improved entropy and bidirectional projection is constructed. Through theoretical proofs and numerical analysis, the related properties, the rationality and effectiveness of the proposed method are verified, providing new ideas for solving multi-attribute decision-making problems with unknown objective weights.
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