×

zbMATH — the first resource for mathematics

Fuzzy notions. Formal concept analysis of fuzzy data. (Fuzzy-Begriffe. Formale Begriffsanalyse unscharfer Daten.) (German) Zbl 0870.06008
Berlin: Springer. 146 p. DM 34.00; öS 248.20; sFr. 30.50 (1997).
The author extends the lattice-theoretic approach to formal concept analysis, as essentially developed by R. Wille [cf. B. Ganter and R. Wille: Formale Begriffsanalyse (1996; Zbl 0861.06001)], to cover the case of fuzzy concepts. In the standard case, formal contexts are determined by a binary relation between objects and attributes, or – in the valued case – by a ternary relation between objects, attributes, and values. Accordingly, in the fuzzy case fuzzy contexts are determined either by a fuzzy relation between objects and attributes, or – in the valued case – by a (crisp!) ternary relation between objects, attributes, and values, which now are supposed to be fuzzy sets.
The author develops formal concept analysis for fuzzy context (in simple as well as valued version), discusses attribute implications together with some relationships to approximate reasoning, and closes with a chapter on complementary fuzzy contexts. All the generalisations are quite natural, but not obvious, and well presented.

MSC:
06B99 Lattices
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
03E72 Theory of fuzzy sets, etc.
06-02 Research exposition (monographs, survey articles) pertaining to ordered structures
94-02 Research exposition (monographs, survey articles) pertaining to information and communication theory
03B52 Fuzzy logic; logic of vagueness
PDF BibTeX XML Cite