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Similarity and compatibility in fuzzy set theory. Assessment and applications. (English) Zbl 0992.03066

Studies in Fuzziness and Soft Computing. 93. Heidelberg: Physica-Verlag. xii, 209 p. (2002).
The book is devoted to the very important concepts of science: “similarity” and “compatibility”. In Part 1 their nature and the historic assessment of their roles in taxonomy, psychology and statistics are discussed with respect to their mathematical and philosophical sense. The authors determine the role of compatibility in fuzzy inference (and especially: interpolative and analogical inference) and approximate reasoning in fuzzy expert systems, fuzzy logic control, information retrieval, fuzzy relational databases, and similarity assessment experiments. In Part 2, called “Taxonomy of compatibility measures”, the concept of “measure” is discussed with respect to several points of view: set-theoretic, proximity, logic, and fuzzy-valued. The last Part 3 is devoted to the empirical analysis of compatibility measures. The book is addressed to specialists from various areas.

MSC:

03E72 Theory of fuzzy sets, etc.
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
62-02 Research exposition (monographs, survey articles) pertaining to statistics
68-02 Research exposition (monographs, survey articles) pertaining to computer science
91-02 Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory

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