In this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy
random variable. The new definition of expectation generalizes the integral of a set-valued …

Stochastic geometry is a relatively new branch of mathematics. Although its predecessors
such as geometric probability date back to the 18th century, the formal concept of a random …

This monograph is an attempt to unify existing works in the field of random sets, random
variables, and linguistic random variables with respect to statistical analysis. It is intended to …

A strong law of large numbers and a central limit theorem are proved for independent and
identically distributed fuzzy random variables, whose values are fuzzy sets with compact …

In this paper we deal with the general theory of fuzzy stochastic processes. We give the
suitable definitions of fuzzy random function, fuzzy stochastic process and their fall-shadow …

Fatou's lemmas and Lebesgue's convergence theorems are established for multivalued
conditional expectations of random variables having values in the closed subsets of a …

Strong laws of large numbers have been stated in the literature for measurable functions
taking on values on different spaces. In this paper, a strong law of large numbers which …

We discuss some relationships between probability theory and statistics on one hand, and
the theory of fuzzy sets on the other hand. We develop various statistical techniques for the …

We study fuzzy set-valued measures in a Banach space and their relationships to fuzzy
random variables. Our main result is a convergence theorem for fuzzy martingales. Our tool …

The three-or four-dimensional world in which we live is full of objects to be measured and
summarized. Very often a parsimonious finite collection of measurements is enough for …