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Generalized rough set models. (English) Zbl 0946.68137
Polkowski, Lech (ed.) et al., Rough sets in knowledge discovery 1. Methodology and applications. Heidelberg: Physica-Verlag. Stud. Fuzziness Soft Comput. 18, 286-318 (1998).
From the introduction: This paper is a sequel of the review by Y. Y. Yao, S. K. M. Wong and T. Y. Lin [A review of rough set models. T. Y. Lin (ed.) et al., Rough sets and data mining: analysis of imprecise data. Selected papers presented at a workshop of the 1995 ACM computer science conference, CSC ’95. Boston, MA: Kluwer Academic Publishers. 47-75 (1997; Zbl 0861.68101)]. We present some new results on generalized rough set models from both the constructive and the algebraic point of view. The rest of the paper is organized as follows. From Section 2 to 5, we concentrate on an operator-oriented view of rough sets. In Section 2, we review a constructive method of rough set theory, which builds approximation operators from binary relations. In Section 3, we introduce and examine alternative representations of approximation operators, and transformations from one to another. In Section 4, we present an algebraic method of rough set theory. Axioms for approximation operators are studied. In Section 5, we study the connections between the theory of rough sets and other related theories of uncertainty. Two special classes of rough set models are studied. They are related to belief and plausibility functions, and necessity and possibility functions, respectively. Section 6 deals with a set-oriented view of rough sets based on probabilistic rough set models and rough membership functions. It enables us to draw connections between rough sets and fuzzy sets. The notion of interval rough membership functions is introduced. For simplicity, we restrict our discussion to finite and nonempty universes. Some of the results may not necessarily hold for infinite universes.
68T30Knowledge representation