Matrix-Based Rough Set Approach for Dynamic Probabilistic Set-Valued Information Systems

Set-valued information systems (SvIS), in which the attribute values are set-valued, are important types of data representation with uncertain and missing information. However, all previous investigations in rough set community do not consider the attribute values with probability distribution in SvIS, which may be impractical in many real applications. This paper introduces probabilistic set-valued information systems (PSvIS) and presents an extended variable precision rough sets (VPRS) approach based on \(\lambda \)-tolerance relation for PSvIS. Furthermore, due to the dynamic variation of attributes in PSvIS, viz., the addition and deletion of attributes, we present a matrix characterization of the proposed VPRS model and discuss some related properties. Then incremental approaches for maintaining rough approximations based on matrix operations are presented, which can effectively accelerate the updating of rough approximations in dynamic PSvIS.

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