模糊偏好关系一致性改进算法及其决策应用-计算机工程与应用.PDF

62 2016 ，52（24 ） Computer Engineering and Applications 计算机工程与应用 模糊偏好关系一致性改进算法及其决策应用 丁宪成 DING Xiancheng 常州大学 信息化建设与管理中心，江苏 常州 213164 Informatization Construction and Management Center, Changzhou University, Changzhou, Jiangsu 213164, China DING Xiancheng. Algorithm for improving consistency of fuzzy preference relations and its application to decision making. Computer Engineering and Applications, 2016, 52 （24 ）：62-69. Abstract ：Fuzzy Preference Relation （FPR ）is a kind of effective tool in the process of decision making problems. As for FPRs, the determination conditions of additive consistent FPR are investigated, and the additive consistent characteristic FPR is constructed. This paper also presents the concepts of consistency index, acceptable additive consistency of FPR. Based on the characteristic FPR, a convergent consistency-improving algorithm is proposed to adjust unacceptably additive consistent FPR into an acceptably additive one, and it helps the decision maker to obtain the reasonable and reliable decision making results. Finally, a decision making model is put forward on the basis of the additive consistent FPR. The numerical example is provided to demonstrate the proposed decision making model ’s feasibility and effectiveness. Key words ：fuzzy preference relation; additive consistency; characteristic preference relation; consistency index; iterative algorithm 摘 要：模糊偏好关系是处理决策问题的一种有效工具。针对模糊偏好关系，研究了加性一致性模糊偏好关系的若 干判定条件，构造了满足加性一致性的特征模糊偏好关系，并提出一致性指数、满意加性一致性等概念。在此基础 上，构建了不满足加性一致性模糊偏好关系的改进算法，论证了算法的收敛性，该算法使得改进后的模糊偏好关系 具有满意一致性条件，进而使得决策者获得合理可靠的决策结果。最后建立了基于模糊偏好关系加性一致性的决 策模型。实例分析说明提出的模糊偏好关系决策模型是可行和有效的。 关键词：模糊偏好关系；加性一致性；特征偏好关系；一致性指数；迭代算法 文献标志码：A 中图分类号：TP35 doi ：10.3778/j.issn. 1002-8331.1604-0071 [4] 1 引言 提出了模糊集理论 。模糊集理论使得数学理论与应用 决策是人类在生产生活中的一项重要活动，人类的