Shadowed sets of dynamic fuzzy sets

Abstract

In practical situations, fuzzy sets with time-varying membership degrees are frequently encountered. In this paper, we interpret dynamic fuzzy sets by means of shadowed sets. We provide an analytic solution to computing the pair of thresholds by searching for a balance of uncertainty in the framework of shadowed sets. Subsequently, we construct errors-based three-way approximations of shadowed sets and present an alternative decision-theoretic formulation for calculating the pair of thresholds. Finally, we employ several examples to illustrate how to calculate thresholds for making a decision by means of dynamic loss functions.