• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.3
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• pp.389-394
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• 2005

The purpose of this paper is to introduce the notions of L-fuzzy topological towers by using a completely distributive lattic L and show that the category L-FPrTR of L-fuzzy pretopoplogical tower spaces and the category L-FPsTR of L-fuzzy pseudotopological tower spaces are extensional topological constructs. And we show that L-FPsTR is the cartesian closed topological extension of L-FPrTR. Hence we show that L-FPsTR is a topological universe.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.115-127
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• 2009

In the present paper we introduce and study L-pre-$T_0$-, L-pre-$T_1$-, L-pre-$T_2$ (L-pre-Hausdorff)-, L-pre-$T_3$ (L-pre-regularity)-, L-pre-$T_4$ (L-pre-normality)-, L-pre-strong-$T_3$-, L-pre-strong-$T_4$-, L-pre-$R_0$-, L-pre-$R_1$-separation axioms in (2, L)-topologies where L is a complete residuated lattice.Sometimes we need more conditions on L such as the completely distributive law or that the "$\bigwedge$" is distributive over arbitrary joins or the double negation law as we illustrate through this paper. As applications of our work the corresponding results(see[1,2]) are generalized and new consequences are obtained.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.461-470
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• 2006

As a continuation of [4], characterizations of fuzzy implicative ideals are given. An extension property for fuzzy implicative ideals is established. We prove that the family of fuzzy implicative ideals is a completely distributive lattice. Using level subsets of a BCk-algebra X with respect to a fuzzy set $\={A}$ in X, we construct a fuzzy implicative ideal of X containing $\={A}$.