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On Interval-valued Anti Fuzzy Prime bi-ideal of Semigroup
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In this paper, we introduce the notions of interval-valued anti fuzzy prime (resp. strongly prime and semiprime) bi-ideals of semigroup. By using these ideas, we characterize those semigroup for which each interval anti-fuzzy bi-ideal is semiprime and strongly prime.
Introduction: The theory of fuzzy sets proposed by Zadeh [6], in his classic paper of 1965, deal with the applications of fuzzy technology in information processing. Mordeson, Malik and Kuroki gave a systematic exposition fuzzy semigroups in [2], where one can find theoretical results on fuzzy semigroups. Shabir and Kanwal [5], introduced the concept of prime bi-ideal, strongly prime bi-ideals and semiprime bi-ideal of a semigroup and studied those semigroups.
In this paper we introduced the concept of interval valued anti fuzzy prime, strongly prime and semiprime bi-ideal of semigroups and give characterization of semigroups in terms of these notions we characterize those semigroups for which each interval-valued anti fuzzy bi-ideal is semiprime and strongly irreducible.
Tikrit University
Title: On Interval-valued Anti Fuzzy Prime bi-ideal of Semigroup
Description:
In this paper, we introduce the notions of interval-valued anti fuzzy prime (resp.
strongly prime and semiprime) bi-ideals of semigroup.
By using these ideas, we characterize those semigroup for which each interval anti-fuzzy bi-ideal is semiprime and strongly prime.
Introduction: The theory of fuzzy sets proposed by Zadeh [6], in his classic paper of 1965, deal with the applications of fuzzy technology in information processing.
Mordeson, Malik and Kuroki gave a systematic exposition fuzzy semigroups in [2], where one can find theoretical results on fuzzy semigroups.
Shabir and Kanwal [5], introduced the concept of prime bi-ideal, strongly prime bi-ideals and semiprime bi-ideal of a semigroup and studied those semigroups.
In this paper we introduced the concept of interval valued anti fuzzy prime, strongly prime and semiprime bi-ideal of semigroups and give characterization of semigroups in terms of these notions we characterize those semigroups for which each interval-valued anti fuzzy bi-ideal is semiprime and strongly irreducible.
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