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.


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


Zbl 0634.94026
Full Text: DOI


[1] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: 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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