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Constructing membership functions using statistical data. (English) Zbl 0617.94017

The authors present a guideline to construct the membership functions for fuzzy sets whose elements have a defining feature with a known probability density function in the universe of discourse. The method finds the smallest fuzzy set which assigns high average membership values to those objects with the defining features distributed according to the given density function.
Reviewer: L.Pardo

MSC:

94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
Full Text: DOI

References:

[1] Czogała, E.; Gottwald, S.; Pedrycz, W., Contribution to application of energy measure of fuzzy sets, Fuzzy Sets and Systems, 8, 205-214 (1982) · Zbl 0488.94052
[2] Civanlar, M. R., Digital signal restoration using projection and fuzzy set techniques, (Ph.D. Dissertation (August 1984), N.C. State University, Electrical and Computer Engineering Department: N.C. State University, Electrical and Computer Engineering Department Raleigh, NC)
[3] Devijver, P. A.; Kittler, J., Pattern Recognition (1982), Prentice-Hall: Prentice-Hall London · Zbl 0476.68057
[4] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: Academic Press New York · Zbl 0444.94049
[5] Hersh, H. M.; Caramazza, A., A fuzzy-set approach to modifiers and vagueness in natural languages, J. Exp. Psychol. Gen., 105, 254-276 (1976)
[6] Luenberger, D. G., Optimization by Vector Space Methods (1969), John Wiley and Sons: John Wiley and Sons New York · Zbl 0176.12701
[7] Norwich, A. M.; Turksen, I. B., A model for the measurement of membership and consequences of its empirical implementation, Fuzzy Sets and Systems, 12, 1-25 (1984) · Zbl 0538.94026
[8] Nowakowska, M., Fuzzy concepts in social sciences, Behav. Sci., 22, 107-115 (1977)
[9] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3-28 (1978) · Zbl 0377.04002
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