• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.105-116
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• 2021

Information systems and decision rules with imprecision and uncertainty in data analysis are studied in complete residuated lattices. In this paper, we introduce the notions of distance spaces, Alexandrov pretopology (precotopology) and join-meet (meet-join) operators in complete co-residuated lattices. We investigate their relations and properties. Moreover, we give their examples.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.499-510
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• 2024

We introduce the concepts of right join-dense, right meet-dense, left join-dense and left meet-dense induced by bi-partially ordered sets on complete generalized residuated lattices. We investigate properties of these concepts and give an example related to them.

• Korean Journal of Mathematics
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• v.22 no.3
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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.

• 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.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.19-29
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• 2022

Information systems and decision rules with imprecision and uncertainty in data analysis are studied in complete residuated lattices. In this paper, we introduce the notions of Alexandrov pretopology (precotopology) and join-meet (meet-join) operators in complete co-residuated lattices. Moreover, their properties and examples are investigated.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.265-277
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• 2014

We investigate the properties of join and meet preserving maps in complete residuated lattices. In particular, we give their examples.

• The Pure and Applied Mathematics
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• v.21 no.3
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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.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.267-280
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• 2021

In this paper, we introduce the notions of fuzzy join (resp. meet) complete lattices and distance spaces in complete co-residuated lattices. Moreover, we investigate the relations between Alexandrov pretopologies (resp. precotopologies) and fuzzy join (resp. meet) complete lattices, respectively. We give their examples.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.3
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• pp.222-230
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• 2014

In this paper, we investigate the properties of join and meet preserving maps in complete residuated lattice using Zhang's the fuzzy complete lattice which is defined by join and meet on fuzzy posets. We define L-upper (resp. L-lower) approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between L-upper (resp. L-lower) approximation operators and L-fuzzy preorders. We study various L-fuzzy preorders on $L^X$. They are considered as an important mathematical tool for algebraic structure of fuzzy contexts.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.15 no.1
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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.