• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.247-256
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• 2014

In this paper, we investigate the relationships between fuzzy relations and Alexandrov L-topologies in complete residuated lattices. Moreover, we give their examples.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.79-89
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• 2020

We introduce the concepts of fuzzy join-complete lattices and Alexandrov L-pre-topologies in complete residuated lattices. We investigate the properties of fuzzy join-complete lattices on Alexandrov L-pre-topologies and fuzzy meet-complete lattices on Alexandrov L-pre-cotopologies. Moreover, we give their examples.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.59-64
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• 2009

In this paper, we study the relations between L-fuzzy topologies and L-filters on a strictly two-sided, commutative quantale lattice L. We define an L-fuzzy neighborhood filter and introduce the notion of L-filter convergence in L-fuzzy topological spaces.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.7
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• pp.649-652
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• 2001

In this paper, we introduce neighborhood systems in an L-fuzzy topology using complete MV-algebras. We investigate the relationship between L-fuzzy topologies and the neighborhood systems. We study the properties of neighborhood system.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.1
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• pp.57-65
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• 2014

In this paper, we investigate the properties of L-lower approximation operators as a generalization of fuzzy rough set in complete residuated lattices. We study relations lower (upper, join meet, meet join) approximation operators and Alexandrov L-topologies. Moreover, we give their examples as approximation operators induced by various L-fuzzy relations.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.27-41
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• 2011

This paper studies the relationship between L-fuzzy proximities and L-fuzzy topologies by topological fuzzy remote neigh-borhood systems. We will prove that the category of L-fuzzy topo- logical spaces can be embedded in the category of L-fuzzy quasi-proximity spaces as a core ective full subcategory.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.4
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• pp.296-302
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• 2010

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies) introduced by Ying [16, (I)]. It investigates topological notions defined by means of regular open sets when these are planted into the frame-work of Ying's fuzzifying topological spaces (in ${\L}$ukasiewwicz fuzzy logic). The concept of fuzzifying nearly compact spaces is introduced and some of its properties are obtained. We use the finite intersection property to give a characterization of fuzzifying nearly compact spaces. Furthermore, we study the image of fuzzifying nearly compact spaces under fuzzifying completely continuous functions, fuzzifying almost continuity and fuzzifying R-map.

• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.347-362
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• 2023

We introduce an algebraic structure induced by a fuzzy bipartial order on a complete residuated lattices with the double negative law. We undertake an investigation into the properties of fuzzy bi-partial orders, including their various characteristics and features. We demonstrate that the two families of l-stable and r-stable fuzzy sets can be regarded as complete lattices, and we establish that these two families are anti-isomorphic. Furthermore, we provide two examples related to them.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.3
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• pp.282-287
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• 2002

In this paper, we introduce the degrees of fuzzy net-convergences in L-fuzzy topologies using complete MV-algebras. We investigate the relationships among the degrees of fuzzy convergent, fuzzy cluster and fuzzy adherent points. We study the properties of net-convergences.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.1
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• pp.100-104
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• 2004

In this paper, we introduce the fuzzy limit degrees in L-fuzzy topologies using complete MV-algebras. We investigate the properties of net-convergences (the degrees of fuzzy convergent, fuzzy cluster, fuzzy adherent points and fuzzy limits).