Decision-theoretic rough sets under dynamic granulation

Abstract

Decision-theoretic rough set theory is quickly becoming a research direction in rough set theory, which is a general and typical probabilistic rough set model with respect to its threshold semantics and decision features. However, unlike the Pawlak rough set, the positive region, the boundary region and the negative region of a decision-theoretic rough set are not monotonic as the number of attributes increases, which may lead to overlapping and inefficiency of attribute reduction with it. This may be caused by the introduction of a probabilistic threshold. To address this issue, based on the local rough set and the dynamic granulation principle proposed by Qian et al., this study will develop a new decision-theoretic rough set model satisfying the monotonicity of positive regions, in which the two parameters α and β need to dynamically update for each granulation. In addition to the semantic interpretation of its thresholds itself, the new model not only ensures the monotonicity of the positive region of a target concept (or decision), but also minimizes the local risk under each granulation. These advantages constitute important improvements of the decision-theoretic rough set model for its better and wider applications.