Effect rough degree and its application in attribute reduction

Roughness measure, a quantitative index of processing uncertain information by fuzzy set theory, is the basis of resource management, system optimization and many other decision problems. Constructing a roughness measure reflecting different decision preference has important theoretical and practical value. In this paper, we firstly analyze the characteristics and shortcomings of the existing measure methods. We secondly establish an effect-based roughness measure model, named as effect rough degree (ERD) by combining with a basic measure factor for roughness-lower (upper) accuracy of rough set. Finally, we propose an ERD-based attribute reduction method (abbreviated as ERD-RM), and then combine with specific cases to discuss the difference and relation between ERD-RM and the existing reduction methods. The theoretical analysis and practical applications shows that ERD has good structural features and interpretability and can simply integrate decision preference into the measure system. Therefore, it can not only enrich the existing theories, but also has wide application value in many fields.