• 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.

• 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.

• 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.

• 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.

• 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.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.119-130
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• 2016

In this paper, we introduce the notions of soft L-fuzzy preproximities in complete residuated lattices. We prove the existence of initial soft L-fuzzy preproximities. From this fact, we define subspaces and product spaces for soft L-fuzzy preproximity spaces. Moreover, 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.10 no.3
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• pp.247-252
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• 2010

In this paper, we investigate the relations among formal concepts, attribute oriented concept and object oriented concepts on a complete residuated lattice.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.2
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• pp.107-112
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• 2010

In this paper, we investigate the properties of antitone Galois connection and formal concepts. Moreover, we show that order reverse generating maps induce formal, attribute oriented and object oriented concepts on a complete residuated lattice.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.3
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• pp.232-237
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• 2012

We introduce the notion of (L, e)-filters with fuzzy partially order e on complete residuated lattice L. We investigate (L, e)-filters induced by the family of (L, e)-filters and functions. In fact, we study the initial and final structures for the family of (L, e)-filters and functions. From this result, we define the product and co-product for the family of (L, e)-filters and functions.