Elsevier

Fuzzy Sets and Systems

Volume 114, Issue 3, 16 September 2000, Pages 431-436
Fuzzy Sets and Systems

Concept lattices defined from implication operators

https://doi.org/10.1016/S0165-0114(98)00182-1Get rights and content

Abstract

We introduce the work with two extensions of the concept definition of Wille to the fuzzy theory, showing the relationship between them. We continue with the study of fuzzy material implications and their associated operators of Kohout and Bandler that lump together the definitions given until this moment.

To conclude, we show an example where we compare the results obtained from the L-fuzzy concepts using the fuzzy implications of Lukasiewicz, Kleene–Dienes and Gödel–Brower.

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There are more references available in the full text version of this article.

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    A direct approach to construct fuzzy concept lattice is considerably more efficient [1,2]. To directly deal with a formal context with uncertain and fuzzy data information, researchers have proposed a variety of methods [3,19,25]. The approach of Pollandt and Belohlavek has become the usual method [4].

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    For this reason, binary fuzzy relations are used to analyze Galois connections between objects and attributes. Burusco and Fuentes-Gonzáles [4] first examined FCA in a fuzzy setting, and they defined L-fuzzy concepts using implication operators. In recent years, many researchers have extended FCA theory by using the ideas from fuzzy logic reasoning or fuzzy set theory, and several generalizations of formal fuzzy concept have been made (please see [1,9,12,13,15,34,40,48]).

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