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On possibilistic mean value and variance of fuzzy numbers. (English) Zbl 1016.94047
The authors introduce a lower possibilistic mean and an upper possibilistic mean of a fuzzy number. Both constitute the interval-valued possibilistic mean, which is a proper subset of the interval-valued mean introduced by D. Dubois and H. Prade [ibid. 24, 279–300 (1987; Zbl 0634.94026)]. Formally, also a possibilistic variance of a fuzzy number is introduced. Both possibilistic mean and possibilistic variance share some properties known from the probabilistic counterparts.

MSC:
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
03E72 Theory of fuzzy sets, etc.
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References:
[1] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic Press New York · Zbl 0444.94049
[2] Dubois, D.; Prade, H., The Mean value of a fuzzy number, Fuzzy sets and systems, 24, 279-300, (1987) · Zbl 0634.94026
[3] Goetschel, R.; Voxman, W., Elementary fuzzy calculus, Fuzzy sets and systems, 18, 31-43, (1986) · Zbl 0626.26014
[4] Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
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