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The \(\vec \lambda\)-mean squared dispersion associated with fuzzy random variable. (English) Zbl 0973.60005

The framework of the paper is based on the notions of fuzzy random variable and fuzzy expected value of a fuzzy random variable, introduced by M. I. Puri and D. A. Ralescu [J. Math. Anal. Appl. 114, 409-422 (1986; Zbl 0592.60004)]. This paper defines a parameterized real-valued measure of the mean dispersion of a fuzzy random variable with respect to an arbitrary fuzzy number. The proposed measure extends the second moment of a classical random variable, and it is based on a parameterized distance between fuzzy numbers. Properties of the measure presented are examined, including the extension of the variance of a classical random variable, and its particular case as a mean squared dispersion. Some examples illustrating the proposed measure within the computation and use of the fuzzy random variables are enclosed. Other examples of its application are just mentioned: (a) the evaluation of the precision of the sample expected value of a fuzzy random variable in estimating the population value, when a random sampling from a finite population is considered, and (b) estimation of fuzzy parameters for fuzzy random variables in a Bayesian context.

MSC:

60A99 Foundations of probability theory
28E10 Fuzzy measure theory

Citations:

Zbl 0592.60004
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References:

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