Intuitionistic fuzzy semiprime ideals in ordered semigroups |
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Authors: | Asghar Khan Muhammad Shabir |
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Institution: | (1) Department of Mathematic, COMSATS Institute of Information Technology, Abbottabad, Pakistan;(2) Department of Mathematics Education and RINS, Gyeongsang National University, Chinju, 660-701, Korea |
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Abstract: | We give characterizations of different classes of ordered semigroups by using intuitionistic fuzzy ideals. We prove that an
ordered semigroup is regular if and only if every intuitionistic fuzzy left (respectively, right) ideal of S is idempotent. We also prove that an ordered semigroup S is intraregular if and only if every intuitionistic fuzzy two-sided ideal of S is idempotent. We give further characterizations of regular and intra-regular ordered semigroups in terms of intuitionistic
fuzzy left (respectively, right) ideals. In conclusion of this paper we prove that an ordered semigroup S is left weakly regular if and only if every intuitionistic fuzzy left ideal of S is idempotent. |
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