On Interval-valued Anti Fuzzy Prime bi-ideal of Semigroup

Abstract

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.

Keywords

• On Interval-valued
• bi-ideal
• Semigroup