On the extent analysis method for fuzzy AHP and its applications.

*(English)*Zbl 1144.90011Summary: In a paper by D.Y. Chang [Eur. J. Oper. Res. 95, No. 3, 649–655 (1996; Zbl 0926.91008)], an extent analysis method on fuzzy AHP was proposed to obtain a crisp priority vector from a triangular fuzzy comparison matrix. It is found that the extent analysis method cannot estimate the true weights from a fuzzy comparison matrix and has led to quite a number of misapplications in the literature. In this paper, we show by examples that the priority vectors determined by the extent analysis method do not represent the relative importance of decision criteria or alternatives and that the misapplication of the extent analysis method to fuzzy AHP problems may lead to a wrong decision to be made and some useful decision information such as decision criteria and fuzzy comparison matrices not to be considered. We show these problems to avoid any possible misapplications in the future.

##### MSC:

90B50 | Management decision making, including multiple objectives |

##### Keywords:

analytic hierarchy process; multiple criteria decision analysis; fuzzy comparison matrix; extent analysis
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\textit{Y.-M. Wang} et al., Eur. J. Oper. Res. 186, No. 2, 735--747 (2008; Zbl 1144.90011)

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