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http://dx.doi.org/10.14317/jami.2012.30.3_4.603

ON INTUITIONISTIC FUZZY PRIME ${\Gamma}$-IDEALS OF ${\Gamma}$-LA-SEMIGROUPS  

Abdullah, Saleem (Department of Mathematics, Quaid-i-Azam University)
Aslam, Muhammad (Department of Mathematics, Quaid-i-Azam University)
Publication Information
Journal of applied mathematics & informatics / v.30, no.3_4, 2012 , pp. 603-612 More about this Journal
Abstract
In this paper, we introduce and study the intuitionistic fuzzy prime (semi-prime) ${\Gamma}$-ideals of ${\Gamma}$-LA-semigroups and some interesting properties are investigated. The main result of the paper is: if $A={\langle}{\mu}_A,{\gamma}_A{\rangle}$ is an IFS in ${\Gamma}$-LA-semigroup S, then $A={\langle}{\mu}_A,{\gamma}_A{\rangle}$ is an intuitionistic fuzzy prime (semi-prime) ${\Gamma}$-ideal of S if and only if for any $s,t{\in}[0,1]$, the sets $U({\mu}_A,s)=\{x{\in}S:{\mu}_A(x){\geq}s\}$ and $L({\gamma}_A,t)=\{x{\in}S:{\gamma}_A(x){\leq}t\}$ are prime (semi-prime) ${\Gamma}$-ideals of S.
Keywords
${\Gamma}$?LA-semigroup; Intuitionistic fuzy set; Prime; Semi-prime;
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