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On Weighted Possibilistic Mean and Variance of Fuzzy Numbers

Robert Fullér, Péter Majlender, On Weighted Possibilistic Mean and Variance of Fuzzy Numbers. TUCS Technical Reports 466, Turku Centre for Computer Science, 2002.

Abstract:

Dubois and Prade
defined an interval-valued expectation of fuzzy numbers,
viewing them as consonant random sets.
Carlsson and Fullér defined an interval-valued
mean value of fuzzy numbers, viewing them
as possibility distributions. In this paper
we shall introduce the notation of weighted interval-valued
possibilistic
mean value of fuzzy numbers and investigate
its relationship to the interval-valued
probabilistic mean.
We shall also introduce the notations of
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 linear combination
of fuzzy numbers
can be computed in a similar manner as in probability theory.

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BibTeX entry:

@TECHREPORT{tFuMa02a,
  title = {On Weighted Possibilistic Mean and Variance of Fuzzy Numbers},
  author = {Fullér, Robert and Majlender, Péter},
  number = {466},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2002},
  keywords = {Fuzzy number; Possibilistic mean value; Possibilistic variance},
}

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