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A method for repairing the inconsistency of fuzzy preference relations

机译：一种修正模糊偏好关系不一致的方法

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This paper investigates the inconsistency problems of preference information about alternatives expressed as a fuzzy preference relation by a decision maker. An analysis method is presented to identify the inconsistency and weak transitivity of a fuzzy preference relation and to repair its inconsistency to reach weak transitivity. First, several definitions are given on additive consistency, inconsistency and weak transitivity of a fuzzy preference relation. Next, two methods derived from graph theory are presented to judge whether a fuzzy preference relation has weak transitivity or not. Then, an algorithm is developed to repair an inconsistent fuzzy preference relation and to make it become one with weak transitivity, via a synthesis matrix which reflects the relationship between the fuzzy preference relation with additive consistency and the initial one given by a decision maker. A convergence theorem is also given for the algorithm. Lastly, two numerical examples are shown to illustrate the proposed method.
机译：本文研究了决策者以模糊偏好关系表示的关于替代品的偏好信息的不一致性问题。提出了一种分析方法，用于识别模糊偏好关系的不一致性和弱传递性，并修​​复其不一致性以达到弱传递性。首先，给出了关于模糊偏好关系的加性一致性，不一致性和弱传递性的几种定义。接下来，提出了两种基于图论的方法来判断模糊偏好关系是否具有弱传递性。然后，通过一个综合矩阵，开发出一种算法来修复不一致的模糊偏好关系并使它成为具有较弱传递性的算法，该矩阵反映具有加性一致性的模糊偏好关系与决策者给出的初始偏好之间的关系。该算法还给出了一个收敛定理。最后，通过两个数值例子说明了该方法。

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