Weak laws of large numbers for weighted sums of Banach space valued fuzzy random variables

Abstract

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.

Strong Law of Large Numbers for Fuzzy Random Variables in Fuzzy Metric Space

“…Li and Ogura [6] presented the SLLN for independent (not necessarily identically distributed) fuzzy-set-valued random variables in a separable Banach space or a Euclidean space. Kim [7] established some results on weak laws of large numbers for weighted sums of fuzzy random variables. Kramosil and Michalek [8] defined the concept of a fuzzy metric space that generalized the probabilistic metric space concept given by Menger [9].…”