Interval-valued fuzzy galois connections: Algebraic requirements and concept lattice construction

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Journal Article
Fundamenta Informaticae, 2010, 99 (2), pp. 169 - 186
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Fuzzy formal concept analysis is concernedwith formal contexts expressing scalar-valued fuzzy relationships between objects and their properties. Existing fuzzy approaches assume that the relationship between a given object and a given property is a matter of degree in a scale L (generally [0,1]). However, the extent to which "object o has property a" may be sometimes hard to assess precisely. Then it is convenient to use a sub-interval from the scale L rather than a precise value. Such formal contexts naturally lead to interval-valued fuzzy formal concepts. The aim of the paper is twofold. We provide a sound minimal set of algebraic requirements for interval-valued implications in order to fulfill the fuzzy closure properties of the resulting Galois connection. Secondly, a new approach based on a generalization of Gödel implication is proposed for building the complete lattice of all interval-valued fuzzy formal concepts. © 2010-IOS Press and the authors. All rights reserved.
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