COMPARISON OF ROUGH-SET AND INTERVAL-SET MODELS FOR UNCERTAIN REASONING

Abstract

In the rough-set model, a set is represented by a pair of ordinary sets called the lower and upper approximations. In the interval-set model, a pair of sets is referred to as the lower and upper bounds which define a family of sets. A significant difference between these models lies in the definition and interpretation of their extended set-theoretic operators. The operators in the rough-set model are not truth-functional, while the operators in the interval-set model are truth-functional. Within the framework of possible-worlds analysis, we show that the rough-set model corresponds to the modal logic system S₅, while the interval-set model corresponds to Kleene's three-valued logic system K₃. It is argued that these two models extend set theory in the same manner as the logic systems S₅ and K₃ extend standard propositional logic. Their relationships to probabilistic reasoning are also examined.