We generalize the results of Rao and Rashed ((1981), 285-292) and the results of Nahmias ((1978), 97-110) for the membership function of a finite sum of mutually unrelated fuzzy variables. The main result is to give a necessary and sufficient condition to the following problem: if X-1,X-2,...,X-n are mutually unrelated fuzzy variables with common membership function mu and alpha(1),alpha(2),...alpha(n) are real numbers satisfying alpha(i) greater than or equal to 0 for every i and Sigma(i=1)(n) alpha(i), when does Z = Sigma(i=1)(n), alpha(i)X(i) have the same membership function mu? (C) 1998 Elsevier Science B.V. References: 4
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