Mean-value-based decision-theoretic shadowed sets

The model of decision-theoretic shadowed sets provides a cost-sensitive approach to three-valued approximation of a fuzzy set on a finite universe. We introduce a semantic meaningful objective function for modeling shadowed sets using the decision theory. This paper is an extension and generalization of the decision-theoretic shadowed sets. We improve the cost-sensitive approach by generalizing the three-valued shadowed sets approximation using mean values. In particular, a mean value of the membership grades that are neither 1 nor 0 is used to represent the shadow. As a result, we have a more general and practical decision-theoretic shadowed set model, in which the optimal pair of thresholds is related to the membership structures of objects.