The author presents weak laws of large numbers for sums of convex-compactly uniformly integrable fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets in \(R^p\) with compact support. The paper is motivated by the work of \textit{R. L. Taylor} [``Stochastic convergence of weighted sums of random elements in linear spaces'' (1978; Zbl 0443.60004), pp. 153--184], which obtained weak laws of large numbers for \(D[0,1]\)-valued random variables. It turns out, that the techniques used there are also useful in fuzzy cases.