Propagating possibilistic and probabilistic variables through a mapping yields a fuzzy random variable. We propose a method to attach probability intervals to events pertaining to the output variable. We show that this method is consistent with classical approaches to fuzzy random variables and that the obtained probability interval is the mean value of the fuzzy probability defined by viewing ...

Fuzzy random variables possess several interpretations. Historically, they were proposed either as a tool for handling linguistic label information in statistics or to represent uncertainty about classical random variables. Accordingly, there are two different approaches to the definition of the variance of a fuzzy random variable. In the first one, the variance of the fuzzy random variable is ...

Fuzzy representations of a real-valued random variable have been introduced with the aim of capturing relevant information on the distribution of the variable, through the corresponding fuzzy-valued mean value. In particular, characterizing fuzzy representations of a random variable allow us to capture the whole information on its distribution. One of the implications from this fact is that tes...

We show that analogously to classical probability theory the conditional expectation E ( ? ~ X ) of a fuzzy random variable Y w.r.t. a fuzzy random variable X is w.r.t. a suitable metric the best approximation o f ? by measurable functions ofX. Furthermore, several linear regression functions, i.e. best approximation of ? by linear functions o f z and examples for random LR-fuzzy numbers and Ga...

In this paper the convergence criterion of fuzzy random variable is investigated. An attempt is made to study the equivalence relation of uniform integrability of fuzzy random variables. Mean convergence theorem, Lebesgue dominated convergence theorem and Mean Ergodic theorem for the case of fuzzy random variable are introduced.

A fuzzy random variable (FRV) has been conceptualized as a vague perception of a crisp but unobservable random variable (RV) and also as a random fuzzy set. Since actuaries seem receptive to these notions of FRV, and there are sources of uncertainty that RVs can not accommodate, but FRVs can, one would expect FRVs to be a component of the actuarial arsenal, but generally this is not the case. A...

According to the current literature, there are two different approaches to the definition of the variance of a fuzzy random variable. In the first one, the variance is defined as a fuzzy interval, offering a gradual description of our incomplete knowledge about the variance of an underlying, imprecisely observed, classical random variable. In the second case, the variance of the fuzzy random va...

Fuzziness is discussed in the context of multivalued lo&, and a corresponding view of fuzzy sets is given. Fuzzy random variables are introduced as random variables whose values are not real but fuzzy numbers, and subsequently redefined as a particular kind of fuzzy set. Expectations of fuzzy random variables, characteristic f~cti~ of fuzzy events, probabilities connected to fuzzy random variab...

The concept of Fuzzy-random-variable was introduced as an analogous notion to randomvariable in order to extend statistical analysis to situations when the outcomes of some random experiment are fuzzy sets. But in contrary to the classical statistical methods no unique definition has been established yet. In this paper a set-theoretical concept of fuzzy-random-variable will be presented. This n...