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World Applied Sciences Journal 18 (12): 1825-1838, 2012
ISSN 1818-4952
© IDOSI Publications, 2012
DOI: 10.5829/idosi.wasj.2012.18.12.1355
Intuitionistic Q-Fuzzy Prime Bi-∧-Ideals of ∧-Semigroups
Muhammad Akram
Department of Mathematics, University of Gujrat, Gujrat, Pakistan
Abstract: In this paper, we introduce the notion of intuitionistic Q-fuzzy prime (strongly prime, semiprime,
irreducible and strongly irreducible) bi-Γ-ideals in a Γ-semigroup. Also, we investigate some of the
properties related to these bi-Γ-ideals.
AMS classifications [2010]: 08A72 • 03F55 • 20M99 • 03E72
Key words: Γ-semigroup • intuitionistic Q-Fuzzy set • intuitionistic Q-Fuzzy bi-Γ-ideal • intuitionistic Q-
Fuzzy Prime bi-Γ-ideals
INTRODUCTION
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] introduced the notion of several intuitionistic fuzzy ideals of
semigroups. Kim and Lee [9] gave the concept of intuitionistic fuzzy bi-ideals of semigroups.
In 1986, Sen and Saha [16] defined the Γ-semigroup and established a relation between regular Γ-semigroup
and Γ-group [13, 14]. The notion of bi-Γ-ideals in Γ-semigroup was introduced by Chinram and Jirojkul in [5].
Shabir and Ali [17] introduced the notion of prime
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