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