TY - JOUR
T1 - Fractional programming approach to fuzzy weighted average
AU - Kao, Chiang
AU - Liu, Shiang Tai
PY - 2001/6/1
Y1 - 2001/6/1
N2 - This paper proposes a fractional programming approach to construct the membership function for fuzzy weighted average. Based on the α-cut representation of fuzzy sets and the extension principle, a pair of fractional programs is formulated to find the α-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 α-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.
AB - This paper proposes a fractional programming approach to construct the membership function for fuzzy weighted average. Based on the α-cut representation of fuzzy sets and the extension principle, a pair of fractional programs is formulated to find the α-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 α-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.
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U2 - 10.1016/s0165-0114(99)00137-2
DO - 10.1016/s0165-0114(99)00137-2
M3 - Article
AN - SCOPUS:0035371895
VL - 120
SP - 435
EP - 444
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
SN - 0165-0114
IS - 3
ER -