Comparison Of Rough-Set And Interval-Set Models For Uncertain Reasoning

  • Authors:

  • Y.Y. Yao;Xining Li

  • Affiliations:

  • Department of Computer Science, Lakehead University, Thunder Bay, Ontario, Canada P7B 5E1;Department of Computer Science, Lakehead University, Thunder Bay, Ontario, Canada P7B 5E1

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 1996

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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 S 5, while the interval-set model corresponds to Kleene's three-valued logic system K 3. It is argued that these two models extend set theory in the same manner as the logic systems S 5 and K 3 extend standard propositional logic. Their relationships to probabilistic reasoning are also examined.