• Title/Summary/Keyword: ${\Gamma}$?LA-semigroup

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

  • Abdullah, Saleem;Aslam, Muhammad
    • Journal of applied mathematics & informatics
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    • v.30 no.3_4
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    • pp.603-612
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    • 2012
  • 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.