The paper presents quite general weak and strong laws of large numbers for weighted sums of triangular arrays of random fuzzy sets. The proofs of the results rely on an appropriate identification of random fuzzy sets with random elements in Banach spaces which satisfy a useful convexity property.
In this paper we obtain some strong laws of large numbers (SLLNs) for arrays of rowwise independent (not necessary identically distributed) random compact sets and fuzzy random sets whose underlying spaces are separable Banach spaces. © 2008 Elsevier B.V. All rights reserved.
TIEN.CHUNG HU Department of Mathematics National Tsing-Hua University Hsin-chu, Taiwan R.O.C. (Received November 18, 1986) ABSTRACT. Let {Xnk be an array of rowwise independent random elements in a separable Banach space of type p + 6 with EXnk 0 for all k, n. The complete conver
if and only if E|X| < ∞. In the case of independence, Hu and Taylor 1 proved the following strong law of large numbers. Theorem 1.1. Let {Xni : 1 ≤ i ≤ n, n ≥ 1} be a triangular array of rowwise independent random variables. Let {an, n ≥ 1} be a sequence of positive real numbers