an:01929348
Zbl 1022.94032
Full??r, Robert; Majlender, P??ter
On weighted possibilistic mean and variance of fuzzy numbers
EN
Fuzzy Sets Syst. 136, No. 3, 363-374 (2003).
00095814
2003
j
94D05 03E72 94A17
fuzzy number; possibilistic mean value; possibilistic variance
Summary: \textit{D. Dubois} and \textit{H. Prade} [ibid. 24, 279--300 (1987; Zbl 0634.94026)] defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. \textit{C. Carlsson} and \textit{R. Full??r} [ibid. 122, 315--326 (2001; Zbl 1016.94047)] defined an interval-valued mean value of fuzzy numbers, viewing them as possibility distributions. In this paper, we introduce the notion of weighted interval-valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval-valued probabilistic mean. We also introduce the notions of the crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. Furthermore, we show that the weighted variance of a linear combination of fuzzy numbers can be computed in a similar manner as in probability theory.
Zbl 1016.94047; Zbl 0634.94026