Fractional programming approach to fuzzy weighted average

This paper proposes a fractional programming approach to construct the memb ership function for fuzzy weighted average. Based on the alpha -cut represe ntation of fuzzy sets and the extension principle, a pair of fractional pro grams is formulated to find the alpha -cut of fuzzy weighted average. Owing to the special structure of the fractional programs, in most cases, the op timal solution can be found analytically. Consequently, the exact form of t he membership function can be derived by taking the inverse function of the alpha -cut. For other cases, a discrete but exact solution to fuzzy weight ed average is provided via an efficient solution method. Examples are given for illustration. (C) 2001 Elsevier Science BY. All rights reserved.