• 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.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.155-168
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• 2015

Strong uni-soft filters and divisible uni-soft filters in residuated lattices are introduced, and several properties are investigated. Characterizations of a strong and divisible uni-soft filter are discussed. Conditions for a uni-soft filter to be divisible are established. Relations between a divisible uni-soft filter and a strong uni-soft filter are considered.

• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.85-97
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• 2017

The notions of regular uni-soft filters, uni-soft MV -filters and Boolean uni-soft filters are introduced, and related properties are investigated. Characterizations of regular uni-soft filters, uni-soft MV -filters and Boolean uni-soft filters are discussed.Relations between regular uni-soft filters and uni-soft MV -filters are considered. It is shown that the notion of a uni-soft MV -filter coincides with the notion of a regular uni-soft filter in BL-algebras.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.769-783
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• 2021

Demirci ((1999) Vague groups. J. Math. Anal. Appl. 230, 142-156) introduced the concept of vague groups as one of uncertain reasoning structures where indistinguishable operators separate points. In this paper, we consider vague groups in which an indistinguishable operator does not need to separate points because it seems more appropriate to handle ambiguous situations. For our purposes we generalize or redefine some notions such as: vague closed subset, vague subgroup, vague kernel and vague injectiveness. Consequently we generalize most of the known results and obtain some new additional fundamental properties of vague groups, some of which are similar to ones of ordinary groups.