Fuzzy Random Variables and Statistical Inference

Statistical Inference about the Variance of Fuzzy Random Variables

The variance of a fuzzy random variable plays an important role as a measure of central tendency. Some of the main contributions in this topic are consolidated and discussed in this paper. In case of the hypothesis testing problem, bootstrap techniques (Efron and Tibshirani, 1993) have empirically been shown to be efficient and powerful. Algorithms to apply these techniques in practice and some...

OPTIMAL STATISTICAL TESTS BASED ON FUZZY RANDOM VARIABLES

A novel approach is proposed for the problem of testing statistical hypotheses about the fuzzy mean of a fuzzy random variable.The concept of the (uniformly) most powerful test is extended to the (uniformly) most powerful fuzzy-valued test in which the test function is a fuzzy set representing the degrees of rejection and acceptance of the hypothesis of interest.For this purpose, the concepts o...

Dominated Convergence for Fuzzy Random Variables

SOME PROBABILISTIC INEQUALITIES FOR FUZZY RANDOM VARIABLES

In this paper, the concepts of positive dependence and linearlypositive quadrant dependence are introduced for fuzzy random variables. Also,an inequality is obtained for partial sums of linearly positive quadrant depen-dent fuzzy random variables. Moreover, a weak law of large numbers is estab-lished for linearly positive quadrant dependent fuzzy random variables. Weextend some well known inequ...

ESTIMATORS BASED ON FUZZY RANDOM VARIABLES AND THEIR MATHEMATICAL PROPERTIES

In statistical inference, the point estimation problem is very crucial and has a wide range of applications. When, we deal with some concepts such as random variables, the parameters of interest and estimates may be reported/observed as imprecise. Therefore, the theory of fuzzy sets plays an important role in formulating such situations. In this paper, we rst recall the crisp uniformly minimum ...