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Mathematical aspects of the theory of measures of fuzziness. (English) Zbl 0859.04007

The author recalls the axiomatic definition of a measure of fuzziness (so that crisp sets have fuzziness measure zero that increases to 1 as sets get “fuzzier”), discusses properties of this measure with respect to operations on fuzzy sets and establishes relationships with Sugemo’s and Choquet’s integrals. Particular attention is paid to homogeneous measures of fuzziness.

MSC:

03E72 Theory of fuzzy sets, etc.
28E99 Miscellaneous topics in measure theory
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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