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Modeling and reasoning with paraconsistent rough sets. (English)
Fundam. Inform. 97, No. 4, 405-438 (2009).
Summary: We present a language for defining paraconsistent rough sets and reasoning about them. Our framework relates and brings together two major fields: rough sets and paraconsistent logic programming. To model inconsistent and incomplete information we use a four-valued logic. The language discussed in this paper is based on ideas of our previous work developing a four-valued framework for rough sets. In this approach membership function, set containment and set operations are four-valued, where logical values are {\bf t} (true), {\bf f} (false), {\bf i} (inconsistent) and {\bf u} (unknown). We investigate properties of paraconsistent rough sets as well as develop a paraconsistent rule language, providing basic computational machinery for our approach.