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On the Variance of Fuzzy Random Variables (1997)
| Venue: | Fuzzy Sets and Systems |
| Citations: | 13 - 0 self |
BibTeX
@ARTICLE{Körner97onthe,
author = {Ralf Körner},
title = {On the Variance of Fuzzy Random Variables},
journal = {Fuzzy Sets and Systems},
year = {1997},
volume = {92},
pages = {83--93}
}
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Abstract
This paper deals with an expectation and a real-valued variance of fuzzy random variables. The expectation and the variance of a fuzzy random variable is characterized by Fr'echet's principle in a metric space. We study properties of the variance of a fuzzy random variables and compare it with the common variance of real-valued random variables. Using the expectation and the variance of fuzzy random variables, we consider a linear regression problem and limit theorems. Keywords: Probability theory and statistics, Random fuzzy variables, Expectation and variance, Linear regression, Limit theorems 1 Introduction In many real situations the variability is given by two kinds of uncertainty: randomness (stochastic variability) and imprecision (vagueness). The concept of fuzzy random variables, introduced by Puri and Ralescu (1986) as a generalization of compact random sets, combines both randomness and imprecision. The stochastic variability is described by use of probability theory and t...
