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Published in:
2009 | OriginalPaper | Chapter
Interval-Valued Fuzzy Formal Concept Analysis
Authors : Yassine Djouadi, Henri Prade
Published in: Foundations of Intelligent Systems
Publisher: Springer Berlin Heidelberg
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Fuzzy formal concept analysis is concerned with 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 formal concepts. The aim of the paper is twofold. We provide a sound minimal set of 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 formal concepts.