Analytical solution methods for the fuzzy weighted average |
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Authors: | Xinwang Liu Jerry M Mendel Dongrui Wu |
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Affiliation: | 1. School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran |
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Abstract: | For the fuzzy weighted average (FWA), despite various discrete solution algorithms and their improvements, attempts at analytical solutions are very rare. This paper provides an analytical solution method for the FWA based on the conclusions of the Karnik–Mendel (KM) algorithm. Compared with the two current popular kinds of α-cut based computational methods for the FWA (mathematical programming transformations and direct iterate computations), our method is precise, and, has a concise structure, efficient computation process, and sound theoretical proofs. We propose two algorithms for computing the analytical solution of the FWA. Two numerical examples illustrate our proposed approach. |
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