Mean-entropy-based shadowed sets: A novel three-way approximation of fuzzy sets

Abstract

Shadowed set provide a three-way approximation scheme for transforming a fuzzy set into three disjoint areas (elevated, reduced, and shadow areas). A fundamental issue in the construction of shadowed sets is the interpretation and determination of a pair of thresholds (α,β). Several extended shadowed set models have been proposed to calculate (α,β). However, the construction of a few of these models may have a large fuzzy entropy loss, and the determination of (α,β) involves artificial subjective parameters. Therefore, in this study, a novel shadowed set model is proposed, namely, mean-entropy-based shadowed sets (MESS). At first, based on the principle of uncertainty invariance, a novel framework of three-way approximations of fuzzy sets is proposed based on the mean of fuzzy entropy. Secondly, new decision rules are generated based on the fuzzy entropy loss, and (α,β) is obtained. Thirdly, the MESS model is optimized more reasonably using an iterative method, and thus the fuzzy entropy loss of the MESS model can be minimized. Finally, the validity and rationality of the proposed model are verified by instances and experimental analysis.