Fuzzy-Entropy-Based Game Theoretic Shadowed Sets: A Novel Game Perspective From Uncertainty

Abstract

As a three-way approximation of fuzzy sets, shadowed sets have attracted extensive attention in recent years. A fundamental issue in the process of constructing shadowed sets is the interpretation and determination of the threshold pair <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$({\alpha, \beta } )$</tex-math></inline-formula> , and the uncertainty consistency, that is, the consistency of fuzzy entropy. However, there may be a large fuzzy entropy loss between a fuzzy set and its corresponding game theoretic shadowed sets (GTSS), and the GTSS model is also accompanied by a large time cost when the precision of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$({\alpha, \beta } )$</tex-math></inline-formula> is improved. Therefore, the fuzzy-entropy-based GTSS (FeGTSS) is proposed in this article from the perspective of fuzzy entropy loss. First, based on the compromise principle of game theory, the fuzzy entropy loss of shadowed sets is analyzed in this article. Second, in the process of calculating <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$({\alpha, \beta } )$</tex-math></inline-formula> , the optimal game strategy is searched based on the dichotomy algorithm. Third, the FeGTSS model is extended and discussed based on the analysis of different data distribution types. Finally, the rationality and validity of the FeGTSS model are illustrated through instances and experimental analysis.