The notion of a proposition as a set of possible worlds or states occupies central stage in probability theory, semantics and epistemology, where it serves as the fundamental unit both of information and meaning. But this fact should not blind us to the existence of prospects with a di¤erent structure. In the paper I examine the use of random variables in particular, proposition-valued random v...

The aim of this paper is to present in a concise and integrated way the bootstrap approach to statistical testing of hypotheses about means of fuzzy-valued random variables. We will deal with the one-, two-sample and ANOVA testing problems in a way that will allow us to see also some differences in approaching them, and also to conclude the suitability of bootstrap techniques in handling these ...

Abstract: We introduce some fuzzy set-valued functional equations, i.e. the generalized Cauchy type (in n variables), the Quadratic type, the Quadratic-Jensen type, the Cubic type and the Cubic-Jensen type fuzzy set-valued functional equations and discuss the Hyers-Ulam-Rassias stability of the above said functional equations. These results can be regarded as an important extension of stability...

In this paper we introduce the notion of levelwise convergence of sequence of fuzzy random variables. We derive equivalent conditions for left quasi uniform convergence of fuzzy random variables. Conditions are obtained for eventually equi-right continuity for the sequence of fuzzy random variables. A necessary and sufficient condition is obtained under which for a sequence of fuzzy random vari...

In this paper we propose an extension to the Fuzzy Cognitive Maps (FCMs) that aims at aggregating a number of reasoning tasks into a one parallel run. The described approach consists in replacing real-valued activation levels of concepts (and further influence weights) by random variables. Such extension, followed by the implemented software tool, allows for determining ranges reached by concep...

We obtain asymptotic expansions for local probabilities of partial sums uniformly bounded independent but not necessarily identically distributed integer-valued random variables. The involve products polynomials and trigonometric polynomials. These results also have counterparts triangular arrays. Our do require any additional assumptions. As an application our we find necessary sufficient cond...