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Fractional programming approach to fuzzy weighted average. (English) Zbl 1103.90411

Summary: 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.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C32 Fractional programming
90C31 Sensitivity, stability, parametric optimization
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