On Intuitionistic Fuzzy Prime Bi-ideals of Semigroups
نویسندگان
چکیده
In this paper, we introduce the notions of intuitionistic fuzzy prime (resp. strongly prime and semiprime) bi-ideals of a semigroup. By using these ideas we characterize those semigroups for which each intuitionistic fuzzy bi-ideal is semiprime and strongly prime. Key words: Intuitionistic fuzzy set; intuitionistic fuzzy bi-ideal; intuitionistic fuzzy prime (resp. strongly prime and semiprime) bi-ideal; regular and intra-regular semigroups. 1. Introduction The theory of fuzzy sets proposed by Zadeh [30] in his classic paper of 1965, deal with the applications of fuzzy technology in information processing. The information processing is already important and it will certainly increase in importance in the future. Mordeson, Malik and Kuroki gave a systematic exposition of fuzzy semigroups in [23], where one can nd theoretical results on fuzzy semigroups and their use in fuzzy coding, fuzzy nite state machines and fuzzy languages. The 1
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Intuitionistic Q-Fuzzy Prime Bi-∧-Ideals of ∧-Semigroups
After the introduction of fuzzy sets by Zadeh [20] in 1965, several researchers have been working on the generalization of the fuzzification. In 1986, Atanassov [2] introduced the notion of intuitionistic fuzzy sets. For more details on the intuitionistic fuzzy sets, we refer to [2-4]. Fuzzy sets are intuitionistic fuzzy sets but the converse is not necessarily true [18]. Kim and Jun [7, 8] int...
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