2009
DOI: 10.5831/hmj.2009.31.1.125
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Quasi-Associative Ideals in Bci-Algebras Based on Bipolar-Valued Fuzzy Sets

Abstract: Abstract. After the introduction of fuzzy sets by Zadeh, there have been a number of generaizations of this fundamental concept. The notion of bipolar-valued fuzzy sets introduced by Lee is one among them. In this paper, we apply the concept of a bipolarvalued fuzzy set to quasi-associative ideals in BCI-algebras. The notion of a bipolar fuzzy quasi-associative ideal of a BCI-algebra is introduced, and some related properties are investigated. Characterizations of a bipolar fuzzy quasi-associative ideal are gi… Show more

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Cited by 12 publications
(14 citation statements)
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“…In 1994, Zhang [12] introduced the notion of a bipolar fuzzy set (refer to [13][14][15]). After then, Jun and Park [16], Jun et al [17], and Lee [18] applied bipolar fuzzy sets to BCK/BCI-algebras. Moreover, Akram and Dudek [19] studied bipolar fuzzy graph, and Majumder [20] introduced the bipolar fuzzy Γ-semigroup.…”
Section: Introductionmentioning
confidence: 99%
“…In 1994, Zhang [12] introduced the notion of a bipolar fuzzy set (refer to [13][14][15]). After then, Jun and Park [16], Jun et al [17], and Lee [18] applied bipolar fuzzy sets to BCK/BCI-algebras. Moreover, Akram and Dudek [19] studied bipolar fuzzy graph, and Majumder [20] introduced the bipolar fuzzy Γ-semigroup.…”
Section: Introductionmentioning
confidence: 99%
“…Meng introduced the concept of CI-algebra, which is as a generalization of BE-algebra, and studied the structures and closed filters of CI-algebras [35][36][37]. After that, the CI-algebras and their related algebraic structures (such as Q-algebras, pseudo Q-algebras, pseudo CI-algebras, and pseudo BCHalgebras) have been extensively studied [38][39][40][41][42][43][44][45][46]. This paper will combine the above two directions to study general neutrosophic triplet structures and the relationships between these structures and generalized BE-algebras.…”
Section: Introductionmentioning
confidence: 99%
“…The authors of [5] studied the concepts of Intuitionistic L-fuzzy p-ideals of BF-algebras and their related results. Inspired by the concepts recently, the concept of Filters of BCH-Algebras Based on Bipolar-Valued Fuzzy Sets [6] has been discussed. In this paper, these concepts are intended to α-ideal of BF-algebras and bipolar valued fuzzy α-ideal of a BF-algebra is proposed.…”
Section: Introductionmentioning
confidence: 99%