No abstract

Knowledge reduction is complicated with the dynamic change of the object set in applications. In this paper, we propose incremental approaches to computing the type-1 and type-2 characteristic matrices of coverings with respect to variation of objects. Also we present two incremental algorithms of calculating the second and sixth lower and upper approximations of sets when adding and deleting more objects in dynamic covering approximation spaces. Subsequently, we employ experiments to validate that the incremental approaches are more effective and efficient to construct approximations of sets in dynamic covering information systems. Finally, we preform knowledge reduction of dynamic covering decision information systems by using the incremental approaches.

In practical situations, fuzzy sets with timevarying 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 decisiontheoretic 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.

No abstract