• Korean Journal of Mathematics
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• 제22권3호
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• pp.553-565
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• 2014

In this paper, we investigate the properties of Alexandrov fuzzy topologies and join-meet approximation operators. We study fuzzy preorder, Alexandrov topologies join-meet approximation operators induced by Alexandrov fuzzy topologies.We give their examples.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권3호
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• pp.183-194
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• 2014

In this paper, we investigate the properties of Alexandrov fuzzy topologies and meet-join approximation operators. We study fuzzy preorder, Alexandrov topologies and meet-join approximation operators induced by Alexandrov fuzzy topologies. We give their examples.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권4호
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제15권1호
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• pp.72-78
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• 2015

Alexandrov topologies are the topologies induced by relations. This paper addresses the properties of Alexandrov topologies as the extensions of strong topologies and strong cotopologies in complete residuated lattices. With the concepts of Zhang's completeness, the notions are discussed as extensions of interior and closure operators in a sense as Pawlak's the rough set theory. It is shown that interior operators are meet preserving maps and closure operators are join preserving maps in the perspective of Zhang's definition.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제14권1호
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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.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.547-557
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• 2020

In this paper, we introduce the notions of (dual) residuated frames for a fuzzy logic as an extension of residuated frames for classical relational semantics. We investigate the relations between residuated connections and residuated frames on Alexandrov topologies based on [0, ∞]. Moreover, we study their properties and give their examples.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.81-89
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• 2021

In this paper, we introduce the notions of a distance function, Alexandrov topology and ⊖-upper (⊕-lower) approximation operator based on complete co-residuated lattices. Under various relations, we define (⊕, ⊖)-fuzzy rough set on complete co-residuated lattices. Moreover, we study their properties and give their examples.

• Journal of Applied and Pure Mathematics
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• 제5권5_6호
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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.