Foundations of Rough Sets from Vagueness Perspective
نویسنده
چکیده
Handling vagueness was one of the motivations for proposing the rough set theory (Pawlak, 2004, see also Pawlak, 1982, 1991, 2003). In this chapter, we present algebraic foundations of the rough set theory from that perspective. Vagueness is understood according to the tertium.non.datur principle from traditional logic; the contemporary version of this principle is called the law of excluded middle (Frege, 1903; Hempel, 1939; Pawlak, 2004; Russell, 1923). Concepts in the rough set theory are represented by subsets of a universe of discourse. Each concept, X, can be represented by two subsets: that consisting of examples of X (i.e., objects, which can be certainly classified as belonging to X) called a positive region of X, and that consisting of objects that certainly do not belong to X, called a negative region of X. Positive region of a given concept is represented AbstrAct
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