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Rough set theory applied to (fuzzy) ideal theory. (English) Zbl 1030.68085

Summary: We use covers of the universal set to define approximation operators on the power set of the given set. In Section 1, we determine basic properties of the upper approximation operator and show how it can be used to give algebraic structural properties of certain subsets. We define a particular cover on the set of ideals of a commutative ring with identity in such a way that both the concepts of the (fuzzy) prime spectrum of a ring and rough set theory can simultaneously be brought to bear on the study of (fuzzy) ideals of a ring.

MSC:

68T30 Knowledge representation
13A99 General commutative ring theory
03E72 Theory of fuzzy sets, etc.
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