Random sets and fuzzy random variables

Abstract

In this section we will consider situations in which two different types of uncertainty — vagueness and randomness, appear simultaneously. A random experiment is described as usual by a probability space (ΩuP), where Ω is the set of all possible outcomes of the experiment, u is a σ-algebra of subsets of Ω (the set of all possible events), and the set function P, defined on u, is a probability measure. In the simplest case we have a finite set Ω = {ω₁,...,ω_n} of possible outcomes, where the element ω _i ∈ Ω has the probability p _i .