Linear-time algorithm for the fuzzy weighted average method

Yeong Cheng Liou*, Sy Ming Guu

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

6 Scopus citations

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 languageEnglish
Pages (from-to)7-12
Number of pages6
JournalJournal of the Chinese Institute of Industrial Engineers
Volume19
Issue number3
DOIs
StatePublished - 2002
Externally publishedYes

Keywords

  • Directional derivative
  • Fuzzy weighted average
  • Linear fractional programming

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