Fuzzy weighted averages and implementation of the extension principle
Fuzzy Sets and Systems
Hyperbolic 0-1 programming and query optimization in information retrieval
Mathematical Programming: Series A and B
Fuzzy weighted average: an improved algorithm
Fuzzy Sets and Systems
An efficient algorithm for fuzzy weighted average
Fuzzy Sets and Systems
Fractional programming approach to fuzzy weighted average
Fuzzy Sets and Systems
The fuzzy weighted average within a generalized means function
Computers & Mathematics with Applications
Centroid defuzzification and the maximizing set and minimizing set ranking based on alpha level sets
Computers and Industrial Engineering
A decision support system for engineering design based on an enhanced fuzzy MCDM approach
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Enhanced Karnik-Mendel algorithms
IEEE Transactions on Fuzzy Systems
A Fuzzy Query Mechanism for Human Resource Websites
AICI '09 Proceedings of the International Conference on Artificial Intelligence and Computational Intelligence
FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 7
ICIC'10 Proceedings of the 6th international conference on Advanced intelligent computing theories and applications: intelligent computing
Study on enhanced Karnik-Mendel algorithms: Initialization explanations and computation improvements
Information Sciences: an International Journal
Analytical solution methods for the fuzzy weighted average
Information Sciences: an International Journal
Applying fuzzy weighted average approach to evaluate office layouts with Feng-Shui consideration
Mathematical and Computer Modelling: An International Journal
Simplified type-2 fuzzy sliding controller for wing rock system
Fuzzy Sets and Systems
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The fuzzy weighted average operations are common operations in risk and decision analysis. Based on Zadeh's extension principle, Dong and Wang (Fuzzy Sets and Systems 21 (1987) 183) proposed a FWA method: a method based on the α-cut representation of fuzzy sets and interval analysis. The FWA method provides a discrete approximation of the α-cuts of fuzzy weighted average. The FWA method has an exponential complexity. Subsequently, Liou and Wang (Fuzzy Sets and Systems 49 (1992) 307) proved that indeed the FWA method can be simplified to be a nonconstrainted linear fractional programming problem with lower and upper bounds for each of the variables. They proposed an improved algorithm, called IFWA, which is of O(N2) complexity, where N is the number of decision variables in IFWA. Guh et al. (Comput. Math. Appl. 32 (8) (1996) 115) proposed a "max-min paired elimination method" (PFWA). They claimed their PFWA was of order N in complexity. Yet, the PFWA is a heuristic method lacking any proof of convergence. In 1997, Lee and Park proposed an algorithm (EFWA) which is of O(NlogN) complexity. Most recently, Kao and Liu (Fuzzy Sets and Systems 120 (2001) 435) solved the FWA by transforming the fractional program into a linear program.In this note, we shall relate the IFWA framework with the nonconstrainted 0-1 integer linear fractional programming problem. In the mathematical programming literature, several O(N)-time algorithms have been existing, for instance, Robillard (Naval Res. Logist. Quart. 18 (1971) 47) and Hansen et al. (Math. Programming 52 (1991) 255). The algorithm of Hansen et al. will be presented for easy reference.