In this paper, we simulate different types of random fuzzy variables to get some conclusions concerning fuzzy-valued random variables. This simulation has been carried out to illustrate certain limit results formalizing the convergence of the arithmetic mean of sample fuzzy data to the population mean (or expected value of the random fuzzy variable), like the well-known strong law of large numb...

one-way analysis of covariance is a popular and common statisticalmethod, wherein the equality of the means of several random variables whichhave a linear relationship with a random mathematical variable, is tested. inthis study, a method is presented to improve the one-way analysis of covari-ance when there is an uncertainty in accepting the statistical hypotheses. themethod deals with a fuzzy...

Article Outline Glossary I. Definition of the Subject and Its Importance II. Introduction III. Mathematical modeling of imprecise data IV. Fuzzy random variables V. Statistical analysis of random fuzzy perceptions VI.1 Fuzzy estimators and fuzzy confidence intervals VI.2 Fuzzy statistical tests VII. Statistical analysis of random fuzzy variables VIII. Future directions Bibliography Glossary Fuz...

The aim of this paper is to extend the classical problem of confidence interval estimation for the mean of a random variable to the case of a fuzzy random variable. The key idea consists in considering a confidence region defined as a ball w.r.t. a given metric, which is centered in the sample mean and whose radius is determined via bootstrapping. The developed approach is illustrated both by m...

The equilibrium measure is a natural extension of both probability and credibility measures. The convergence modes of random fuzzy variables with respect to equilibrium measure is an important issue for research. In this paper, we first introduce several convergence concepts for sequences of random fuzzy variables, including convergence in equilibrium measure and convergence in equilibrium dist...

a weighted linear regression model with impercise response and p-real explanatory variables is analyzed. the lr fuzzy random variable is introduced and a metric is suggested for coping with this kind of variables. a least square solution for estimating the parameters of the model is derived. the result are illustrated by the means of some case studies.

In some point estimation problems, we may confront imprecise (fuzzy) concepts. One important case is a situation where all observations are fuzzy rather than crisp. In this paper, using fuzzy set theory, we define a fuzzy-valued random variable, a fuzzy unbiased estimator, a fuzzy exponential family, and then we state and prove a Cramér-Rao lower bound for such fuzzy estimators. Finally, we giv...