Abstract
The fuzzy weighted average operations are common operations in risk and decision analysis. Dong and Wang [6] proposed a fuzzy weighted average method (FWA) for the performance evaluation under group decision making, which ends up with an exponential complexity. Liou and Wang [11] proved that indeed the FWA could be simplified to be a non-constrained linear fractional programming problem (called IFWA) with lower and upper bounds for each variable. For thiss implified problem, a steepest descend/ascend method was proposed and required an O(n2)-time, where n is the number of decision variables in the IFWA. Later on, based on Liou and Wang's simplified framework, Guh et al. [8] proposed a max-min paired elimination method (PFWA), which essentially was a heuristic one for lacking of the proof of convergence. Recently, Lee and Park [10] proposed an algorithm requiring an O(n logn)-time. In this paper, we shall propose a new method for solving IFWA. Our algorithm requires an O(n)-time. Proof of convergence and an example are provided, and the efficiency of our method is not worse than Robillard's in practice.
Original language | English |
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Pages (from-to) | 7-12 |
Number of pages | 6 |
Journal | Journal of the Chinese Institute of Industrial Engineers |
Volume | 19 |
Issue number | 3 |
DOIs | |
State | Published - 2002 |
Externally published | Yes |
Keywords
- Directional derivative
- Fuzzy weighted average
- Linear fractional programming