Geodesic
$(\lambda,\mu)$-fuzzy interior ideals of ordered $\Gamma$-semigroups
Algebra and discrete mathematics, Tome 16 (2013) no. 1, pp. 61-70.

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For all $\lambda,\mu\in [0,1]$ such that $\lambda\mu$, we first introduced the definitions of $(\lambda,\mu)$-fuzzy ideals and $(\lambda,\mu)$-fuzzy interior ideals of an ordered $\Gamma$-semigroup. Then we proved that in regular and in intra-regular ordered semigroups the $(\lambda,\mu)$-fuzzy ideals and the $(\lambda,\mu)$-fuzzy interior ideals coincide. Lastly, we introduced the concept of a $(\lambda,\mu)$-fuzzy simple ordered $\Gamma$-semigroup and characterized the simple ordered $\Gamma$-semigroups in terms of $(\lambda,\mu)$-fuzzy interior ideals.
Keywords: $\Gamma$-semigroup; $(\lambda,\mu)$-fuzzy interior ideal; $(\lambda,\mu)$-fuzzy simple; regular ordered $\Gamma$-semigroup; intra-regular ordered $\Gamma$-semigroup. 
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Yuming Feng; P. Corsini. $(\lambda,\mu)$-fuzzy interior ideals of ordered $\Gamma$-semigroups. Algebra and discrete mathematics, Tome 16 (2013) no. 1, pp. 61-70. http://geodesic.mathdoc.fr/item/ADM_2013_16_1_a6/

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