A Method for Determining the Relative Importance in AHP Using Logarithmic Fuzzy Numbers

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  • AHPにおける対数型ファジィ数を用いた相対的重要度決定法
  • AHP ニ オケル タイスウガタ ファジィスウ オ モチイタ ソウタイテキ ジュウヨウド ケッテイホウ

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Abstract

The Analytic Hierarchy Process (AHP) is used for decision-making with difficult quantification. In AHP, we decide the relative importance of each criteria and alternative, and modifiers, such as "Weak" or "Strong" are used for pairwise comparison. In this paper, we propose a method for determining relative importance by using fuzzy numbers which represent the feelings of the decision maker. In the conventional AHP, a numerical value for the modifier, which increases linearly from one to nine, is used. However, in this paper, it is assumed that the numerical value of the modifier increases exponentially. Therefore, the fuzzy numbers are expressed using a logarithmic scale. The procedure in this paper is as follow. Firstly, the numerical value applied to each modifier and the sufficiently satisfactory range of each value are informed to the decision maker. Secondly, the membership functions of the fuzzy numbers are created by these values on a logarithmic scale. Finally, the membership functions are formulated into a fuzzy linear planning problem and the relative importance of each element is calculated. Moreover, we propose a method for application to group decisionmaking. The proposed method is compared with conventional methods by numerical experiment, and the efficiency of the proposed method is shown.

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