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Probabilistic tolerance rough set model

The probabilistic method have been applied to rough set theory in several forms, such as variable precision rough set model, decision-theoretic rough set model and probabilistic rough set model. All of them are extension of the original rough set model developed by Pawlak, and these models are all based on equivalence relation. In this paper, the idea of tolerance relation instead of equivalence relation is introduced into the probabilistic rough set model, and the probabilistic tolerance rough set (PTRSM) is proposed. The properties of lower approximation operator and upper approximation operator of PTRSM are investigated, and furthermore, the relations with other rough set models are also studied.