12:45 pm Lunch 02:30–03:30 pm A. COLUBI: Statistical inference about the means of fuzzy random variables: applications to the analysis of fuzzy-and real-valued data Estimation of a simple linear regression model for fuzzy random variables 04:00 pm Coffee break 04:30–05:00 pm A. WÜNSCHE: Asymptotic tests for the Aumann-expectation of fuzzy random variables 05:00–05:30 pm K. LENDELOVÁ, B. RIEČAN:...

In this communication we will consider hypothesis-tests for the (fuzzy-valued) mean value of a fuzzy random variable in a population. For this purpose, we will make use of a generalized metric for fuzzy numbers, and we will develop two different approaches for the case of fuzzy random variables taking on a finite number of possible values, both leading to close statistical inferences.

The concept of fuzzy random variable has been shown to be as a valuable model for handling fuzzy data in statistical problems. The theory of fuzzy-valued random elements provides a suitable formalization for the management of fuzzy data in the probabilistic setting. A concise overview of fuzzy random variables, focussed on the crucial aspects for data analysis, is presented. © 2006 Elsevier B.V...

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...

A bootstrap approach to the multi-sample test of means for imprecisely valued sample data is introduced. For this purpose imprecise data are modelled in terms of fuzzy values. Populations are identified with fuzzy-valued random elements, often referred to in the literature as fuzzy random variables. An example illustrates the use of the suggested method. Finally, the adequacy of the bootstrap a...

The present paper is devoted to the transition from crisp domains of probability to fuzzy domains of probability. First, we start with a simple transportation problem and present its solution. The solution has a probabilistic interpretation and it illustrates the transition from classical random variables to fuzzy random variables in the sense of Gudder and Bugajski. Second, we analyse the proc...

In this paper, we propose a novel approach for Fuzzy random-valued Optimization. The main idea behind our approach consists of taking advantage of interplays between fuzzy random variables and random sets in a way to get an equivalent stochastic program. This helps avoiding pitfalls due to severe oversimplification of the reality. We consider a numerical example that shows the efficiency of the...

In this paper, a decomposition theorem for a (square integrable) fuzzy random variable FRV is proposed. The paper is mainly divided in two parts. In the first part, for any FRV X, we define the Hukuhara set as the family of (deterministic) fuzzy sets C for which the Hukuhara difference X ⊖H C exists almost surely; in particular, we prove that such a family is a closed (with respect to different...