Indiscernibility and Discernibility Relations Attribute Reduction with Variable Precision

Abstract

Attribute reduction is a popular topic in research on rough sets. In the classical model, much progress has been made in the study of the attribute reduction of indiscernibility and discernibility relations. To enhance the fault tolerance of the model, concepts of both indiscernibility and discernibility relations involving uncertain or imprecise information are proposed in this paper. The attribute reductions of the relative β -indiscernibility relation and relative β -discernibility relation and their algorithms are proposed. When the precision satisfies certain conditions, the reduction of two relation concepts can be converted into a positive region reduction. Therefore, the discernibility matrix is used to construct the reductions of the two relation concepts and the positive region. Furthermore, the corresponding algorithm of the relative β -indiscernibility (discernibility) relation reduction can be optimized when the precision is greater than 0.5, and this is used to develop an optimization algorithm that constructs the discernibility matrix more efficiently. Experiments show the feasibility of the two relation reduction algorithms. More importantly, the reduction algorithms of the two relations and the optimization algorithm are compared to demonstrate the feasibility of the optimization algorithm proposed in this paper.

New Variable Precision Reduction Algorithm for Decision Tables

“…Attribute reduction in classical rough sets has been studied thoroughly. The indiscernibility relations between any object have been constructed to study the relationship between the positive region and indiscernibility relation sets in depth [30], [31], [32]. Because some information in information tables will be missing, as the binary relation is equivalence, the reduction method research is limited.…”