基于参照点的区间数TOPSIS方法研究
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摘要
在多属性决策问题中,由于客观事物和环境的复杂性以及人类知识背景和认知能力的局限性,导致人们很难获得属性的精确评价值。为了解决现实中存在着的大量的不确定多属性决策问题,人们越来越重视对不确定多属性决策问题的研究。
本文在总结与分析国内外关于区间数多属性决策理论与方法研究现状的基础上,对考虑参照点的区间数多属性决策问题进行了深入的研究。主要研究工作和创新点如下：
(1)研究了区间数多属性决策中的若干基础理论问题。对已有区间型数据标准化的两种方法进行了改进,改进的方法不仅保留了原有方法的优点,还能够保证在区间型数据退化为精确值时,与传统的精确数标准化方法相一致,从而能够更好地处理精确数和区间数混合信息下的多属性决策问题；给出了一种基于不确定思想的区间数距离度量方法,该度量方法考虑了区间数的不确定性,能够保留更加饱满的决策信息。
(2)研究了考虑参照点的多属性决策方法。阐述了多属性决策中参照点的生成机制与分类；将反映决策者主观偏好的参照点引入传统TOPSIS方法,使得相对贴近系数不仅能反映备选方案的相对优劣,还能反映其绝对的优劣水平；利用最优化理论和方法寻找多属性决策的评价基点和方案优越性的最速上升方向,避免了原始方法中评价基点和方案优越性最速上升方向可能偏离备选方案集较远的弊端。
(3)研究了考虑参照点的区间数多属性决策方法。给出解决区间数多属性决策问题的方法——区间数TOPSIS方法,并对区间跨度进行了灵敏度分析；将参照点引入区间数TOPSIS方法,.针对两种不同形式的参照点——点值向量形式的参照点和区间值向量形式的参照点,分别给出基于主观参照点和客观参照点的区间数TOPSIS方法。
(4)将基于参照点的区间数TOPSIS方法应用于某企业的研发成果评估问题。所得结果较好的反映了决策者的偏好,验证了所提方法的有效性与合理性。
Because of the complexity of objective things and environments as well as the limitations of the human knowledge and cognitive ability, it is difficult to obtain the accurate evaluation of attributes. In order to solve the uncertain multi-attribute decision making problems, people are attaching more and more importance to the research on uncertain multi-attribute decision-making problems.
Based on the summary and analysis on the research status of interval multi-attribute decision making in domestic and foreign, this paper carry out an in-depth study on interval multi-attribute decision making problems which consider the reference points. The main contributions of this dissertation are listed as follows:
(1) Some basic theoretical problems of multi-attribute decision making with interval numbers are researched. Two methods on standardization of interval numbers are improved. When the interval data degenerate into accurate values, the improved methods are consistent with the traditional standard methods, so they can better deal with the multi-attribute decision making problems under hybrid information of accurate numbers and interval numbers. A distance measurement method of interval numbers based on uncertainty is given which considers the uncertainty of interval numbers and retain more information for decision making.
(2) The multi-attribute decision making method considering reference points is researched. The generation mechanism and classification of reference points are discussed in multi-attribute decision making. The reference point which reflects the decision-maker's preference is introduced into the traditional TOPSIS method, so the relative closeness coefficient can not only reflect the relative performance of alternatives, but also reflect its absolute performance level. Using the optimization theory and method to look for the base point and the steepest ascent direction of superiority in multi-attribute decision making, it avoids the drawback of traditional method that the base point and the steepest ascent direction of superiority may deviate far from the alternatives.
(3) The multi-attribute decision making method with interval numbers considering reference points is researched. The TOPSIS method with interval numbers is given, and the sensitivity analysis of interval span is undertaken. Introducing reference point to TOPSIS method with interval numbers, according to reference point in different forms——point vector and interval vector, providing the TOPSIS method with interval numbers based on subjective reference point and objective reference point respectively.
(4) The TOPSIS method with interval numbers based on reference point is applied in the evaluation of R&D projects in an enterprise. The evaluation results reflect the preference of decision makers, which verify the effectiveness and rationality of the proposed method.
本文在总结与分析国内外关于区间数多属性决策理论与方法研究现状的基础上,对考虑参照点的区间数多属性决策问题进行了深入的研究。主要研究工作和创新点如下：
(1)研究了区间数多属性决策中的若干基础理论问题。对已有区间型数据标准化的两种方法进行了改进,改进的方法不仅保留了原有方法的优点,还能够保证在区间型数据退化为精确值时,与传统的精确数标准化方法相一致,从而能够更好地处理精确数和区间数混合信息下的多属性决策问题；给出了一种基于不确定思想的区间数距离度量方法,该度量方法考虑了区间数的不确定性,能够保留更加饱满的决策信息。
(2)研究了考虑参照点的多属性决策方法。阐述了多属性决策中参照点的生成机制与分类；将反映决策者主观偏好的参照点引入传统TOPSIS方法,使得相对贴近系数不仅能反映备选方案的相对优劣,还能反映其绝对的优劣水平；利用最优化理论和方法寻找多属性决策的评价基点和方案优越性的最速上升方向,避免了原始方法中评价基点和方案优越性最速上升方向可能偏离备选方案集较远的弊端。
(3)研究了考虑参照点的区间数多属性决策方法。给出解决区间数多属性决策问题的方法——区间数TOPSIS方法,并对区间跨度进行了灵敏度分析；将参照点引入区间数TOPSIS方法,.针对两种不同形式的参照点——点值向量形式的参照点和区间值向量形式的参照点,分别给出基于主观参照点和客观参照点的区间数TOPSIS方法。
(4)将基于参照点的区间数TOPSIS方法应用于某企业的研发成果评估问题。所得结果较好的反映了决策者的偏好,验证了所提方法的有效性与合理性。
Because of the complexity of objective things and environments as well as the limitations of the human knowledge and cognitive ability, it is difficult to obtain the accurate evaluation of attributes. In order to solve the uncertain multi-attribute decision making problems, people are attaching more and more importance to the research on uncertain multi-attribute decision-making problems.
Based on the summary and analysis on the research status of interval multi-attribute decision making in domestic and foreign, this paper carry out an in-depth study on interval multi-attribute decision making problems which consider the reference points. The main contributions of this dissertation are listed as follows:
(1) Some basic theoretical problems of multi-attribute decision making with interval numbers are researched. Two methods on standardization of interval numbers are improved. When the interval data degenerate into accurate values, the improved methods are consistent with the traditional standard methods, so they can better deal with the multi-attribute decision making problems under hybrid information of accurate numbers and interval numbers. A distance measurement method of interval numbers based on uncertainty is given which considers the uncertainty of interval numbers and retain more information for decision making.
(2) The multi-attribute decision making method considering reference points is researched. The generation mechanism and classification of reference points are discussed in multi-attribute decision making. The reference point which reflects the decision-maker's preference is introduced into the traditional TOPSIS method, so the relative closeness coefficient can not only reflect the relative performance of alternatives, but also reflect its absolute performance level. Using the optimization theory and method to look for the base point and the steepest ascent direction of superiority in multi-attribute decision making, it avoids the drawback of traditional method that the base point and the steepest ascent direction of superiority may deviate far from the alternatives.
(3) The multi-attribute decision making method with interval numbers considering reference points is researched. The TOPSIS method with interval numbers is given, and the sensitivity analysis of interval span is undertaken. Introducing reference point to TOPSIS method with interval numbers, according to reference point in different forms——point vector and interval vector, providing the TOPSIS method with interval numbers based on subjective reference point and objective reference point respectively.
(4) The TOPSIS method with interval numbers based on reference point is applied in the evaluation of R&D projects in an enterprise. The evaluation results reflect the preference of decision makers, which verify the effectiveness and rationality of the proposed method.
引文
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