Abstract
Roughness measure, a quantitative index for processing uncertain information using fuzzy set theory, is the basis of resource management, system optimization and many other decision-making problems. The construction of a roughness measure which reflects different decision preferences has important theoretical and practical value. In this paper, we first analyze the characteristics and shortcomings of the existing methods for measuring roughness. Following this, a new effect-based roughness measure model is established using a combination of a basic measure factor, the lower (or upper) accuracy of rough sets, entitled the effective rough degree (ERD). Next, the characteristics of ERD are analyzed in combination with different synthesis functions, and several further necessary and sufficient conditions are given. Finally, we propose an ERD-based attribute reduction method (abbreviated as ERD-RM), and then discuss the differences and relationships between ERD-RM and existing reduction methods. The theoretical analysis and practical applications show that ERD has good structural features and interpretability and can integrate decision preference into the measure system in a straightforward manner.
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