A Conditional Discernibility Reduction for Relation Decision Systems

Attribute reduction is also called feature selection, which comes from machine learning. In recent years., the study of reduction has been extended from equivalence relation to non- equivalence binary relation, and the research has achieved fruitful results. Through the classification of condition (decision) attributes, the definitions of reduction are proposed and then reduction algorithms are proposed. Firstly, Without considering the properties of symmetry and similarity, the relation is extended to the general relation, and the discernibility relation and indiscernibility relation between any objects in the universe set are analyzed. As a result, considering the cardinality of set, which is made up of discernibility objects, the concept of conditional discernibility is put forward. Secondly, according to the concept of conditional discernibility, the concept of conditional discernibility reduction is proposed. Then, a reduction algorithm that is based on the matrix is proposed, where the corresponding discernibility matrix is strictly proved. Finally, we present a simple example to illustrate conditional discernibility reduction algorithm. At the same time, we demonstrate the feasibility of the reduction algorithm through example.