Cozero Divisor Graph of a Commutative Rough Semiring
01 Jan 2018-pp 67-75
TL;DR: In this article, the ideal generated by an element in the commutative rough semiring (T, Δ, ∇) is defined and the characterization of this ideal along with its properties are studied.
Abstract: In this paper, we define the ideal generated by an element in the commutative rough semiring (T, Δ, ∇). The characterization of this ideal along with its properties are also studied. The cozero divisor graph of a commutative rough semiring is defined using this ideal. These concepts are illustrated through examples.
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01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
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Book•
01 Jan 1995
TL;DR: Inverse semigroups as discussed by the authors are a subclass of regular semigroup classes and can be seen as semigroup amalgamations of semigroup groups, which is a special case of regular semiigroups.
Abstract: 1. Introductory ideas 2. Green's equivalences regular semigroups 3. 0-simple semigroups 4. Completely regular semigroups 5. Inverse semigroups 6. Other classes of regular semigroups 7. Free semigroups 8. Semigroup amalgams References List of symbols
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TL;DR: Some fundamental properties of generalized rough sets induced by binary relations on algebras are considered and it is shown that any reflexive binary relation determines a topology.
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TL;DR: The idea of a rough left [right, two-sided, bi-] ideal in a semigroup is introduced, which is an extended notion of a left [ right,Two-sided], bi-, and some properties of such ideals are given.
232 citations