摘要
现有的多属性决策方法大多建立在期望效用理论基础上,而不确定条件下期望效用理论描述性功能的缺陷使得以其为基础的效用测度不能对人类的价值偏好进行正确的反映,继而,基于偏差的效用测度用作决策分析,将导致不正确的决策。且现实生活中,由于决策问题本身的复杂性,决策者知识的有限性,被评价事物自身的模糊性,以及获取精确信息所需要的高成本等条件的限制,决策信息往往很难或不可能用精确数来表示。这就要求人们不断地重新审视已有理论、方法和技术,并结合变化做出科学的、合理的批判和改进。
针对不确定条件下的多属性决策问题,本研究从前景理论的视角对基于直觉梯形模糊信息的复杂大群体多属性决策方法进行研究,将前景理论纳入到多属性决策的分析框架。一方面,前景理论中的效用测度是建立在参考点基础上的价值判断,与期望效用理论相比,更符合实际和更准确地描述和解释不确定性情况下决策者的决策选择行为。考虑到决策分析主要是一种建立在描述性和规范性研究范式基础上的指导性学科,因而,为了使得复杂大群体直觉梯形模糊多属性决策模型在现实中更具有指导价值,本文将前景理论的思想融入到多属性决策模型中,以决策者给出的属性前景价值信息为基础构建决策模型,用前景理论改进期望效用理论下的多属性决策理论与方法。另一方面,对于决策信息的模糊性和不确定性,决策者愿意以语言信息或者模糊信息给出自己的决策信息,用直觉梯形模糊数描述模糊决策信息是解决模糊多属性群决策问题的一种思路。论文主要工作和成果如下：
首先,构建了直觉模糊环境下基于多参考点的前景价值确定方法。基于前景理论和直觉梯形模糊数,构建直觉梯形模糊环境下前景价值确定方式,将前景理论拓展到直觉梯形模糊环境。进一步,考虑到多个参考点的情形,鉴于证据理论在处理不确定性信息方面的优势,本文运用证据理论作为处理多参考点下前景价值的融合问题的框架,提出了基于mRP和DS-TrIF-IOWA的直觉梯形模糊前景价值确定方法。
其次,提出了基于关联信息与前景理论的直觉梯形模糊多属性决策方案优选方法。考虑到不确定条件下前景理论相对期望效用理论更符合人类实际的决策模式,运用上述直觉模糊环境下基于多参考点的前景价值确定方法来计算直觉梯形模糊多属性决策中方案单属性价值。进一步,考虑到现实决策问题中属性间往往存在或多或少的关联信息,引入Choquet积分来解决不确定决策中属性相互关联的决策问题。为此,提出了几个基于Choquet积分的直觉梯形模糊集结算子,TrIC算子、ITrIC、TrICD算子和ITrICD算子,并对各算子的性质作了探讨。在这些概念基础上提出了基于TrIF-Choquet算子的综合前景值确定方法以及基于TrIF-Choquet距离和前景理论的直觉梯形模糊TOPSIS方法。
再次,提出了基于ITrIFC和TrIF-OWAD算子的大群体聚类算法。群体聚类方法引进前景理论的思想,以直觉梯形模糊前景价值矩阵为基础聚类信息,为了综合考虑属性之间的交互信息和方案排序位置在聚类分析中的重要性,我们在相似矩阵的构建中运用ITrIFC和TrIF-OWAD算子对相关决策信息进行集结,构建了决策者之间的相似度,基于此,建立直觉梯形模糊信息下大群体聚类算法。
在此基础上,提出了基于大群体聚类算法的复杂大群体直觉梯形模糊多属性决策一致性分析和一致性修正自动算法。考虑到在大群体内部可能存在子群体簇或“联盟”的可能性,根据上文提出的大群体聚类算法对复杂大群体进行聚类,根据群体聚类结果来设计聚集一致度指标和大群体的一致度指标,建立基于大群体聚类算法的群体判断一致性分析方法。对于评价信息的修改,考虑到尽可能的尊重决策者原始评价信息,建立基于大群体聚类的群体一致性修正方法。考虑到时间和成本的限制以及从众行为的影响,提出一种大群体一致性分析的自动算法。根据算法编制计算机程序,算例分析表明该方法具有较强的可操作性和实用性。
然后,提出了复杂大群体下直觉梯形模糊前景价值矩阵群集结方法。在上述复杂大群体直觉梯形模糊多属性决策一致性分析和一致性修正基础上,考虑到聚集内的个体前景价值矩阵具有相似的特征,首先,根据直觉梯形模糊距离、个体决策信息和聚集虚拟核心人物的偏好信息来确定决策者聚集内权重信息,构建聚集直觉梯形模糊前景价值共识矩阵,在此基础上根据类间权重信息将聚集直觉梯形模糊前景价值共识矩阵集结为大群体直觉梯形模糊前景价值共识矩阵。该群集结方法可以更好的减少信息的损失,尽可能的保留决策者的原始信息。
最后,提出了一个基于前景理论的复杂大群体直觉梯形模糊多属性决策模型(mRP-TrIFPV-MAGDM)。决策流程上,该模型整合了属性前景价值确定、群体一致性分析和修正、群体共识形成和方案优选,为决策支持系统的开发提供了支持。研究范式上,该模型结合规范性研究范式和描述性研究范式,综合考虑了基于多个参考点的效用测度方式、属性间的关联信息、决策者复杂的观念特征,从而构建的复杂大群体直觉梯形模糊多属性决策模型更具有指导价值。将上文提出的mRP-TrIFPV-MAGDM模型应用到产品两型化多属性决策问题中,该模型的实用性和可操作性得到了证明。
The existing multi-attribute decision making methods are mostly established on the basis of expected utility theory, but the defects of its descriptive function under uncertain conditions makes utility measure based on which can not correctly reflect the values and preferences of the human; then, the biased utility measure of a decision analysis will lead to incorrect decisions. And in real life, due to the complexity of the decision problem itself, the limited knowledge of the decision-makers, that fuzzy of the evaluation of things, as well as the high cost and other constraints needed to obtain accurate information, decision-making information is often difficult or impossible to represent with exact numbers. This requires people to re-examine the existing theories, methods and techniques, and to make a scientific and reasonable criticism and improvement by combining with the changes.
For multi-attribute decision making problems under uncertainty, we study on multiple attribute complex-large group decision making method based on intuitionistic trapezoidal fuzzy information from the perspective of prospect Theory, and introduce the prospect theory into the analysis framework for multi-attribute decision-making. On one hand, prospect theory's utility function is value judgments based on reference points, compared with the expected utility theory, more practical and more accurately to describe and explain the decision-choice behavior of decision makers under uncertainty. Taking into account the decision analysis is a priscrible discipline based on descriptive research and normative research paradigm, in order to make the intuitionistic trapezoidal fuzzy multiple attribute complex-large group decision making model more guiding value in reality, this paper introduces the idea of prospect theory into the multi-attribute decision model and build decision-making model based on the prospect value information of attributes. On the other hand, as for the vagueness and uncertainty of decision-making information, decision-makers are willing to give their decision-making information with the form of linguistic information or fuzzy information. Intuitionistic trapezoidal fuzzy numbers provide an idea to solve the problem of fuzzy multiple attribute group decision-making. Research work and the results are as follows:
First, this paper establishs a prospect value determination method based on prospect theory and intuitionistic trapezoidal fuzzy numbers and extende prospect theory to the intuitionistic trapezoidal fuzzy environment. Further, the case of multiple reference points is taken into account. In view of the advantages of evidence theory in handling uncertainty information, this paper uses evidence theory to integrate prospect value under multi-reference points, and proposes a prospect value determination method based on mRP and DS-TrIF-IOWA operator.
Second, this paper proposes a optimal selection method for multi-attribute decision making based on associated information and prospect theory. Taking into account prospect theory instead of the expected utility theory being more in line with the actual human decision-making mode, this paper use the proposed prospect value determination method based on prospect theory and intuitionistic trapezoidal fuzzy numbers to compute single attribute value in the multi-attribute decision-making. On the other hand, taking into account the interactive characteristics among the attributes in the reality of decision-making, this paper introduces the Choquet integral to solve the uncertain decision problem with attributes interrelated. This paper proposes several Intuitionistic trapezoidal fuzzy aggregation operators based on Choquet integral such as the TrIC, ITrIC, TrICD, and ITrICD operator, and the nature of the operators are discussed. On the basis of these concepts, this paper proposes comprehensive prospect value method based on TrIF-Choquet operator and intuitionistic trapezoidal fuzzy TOPSIS method based on TrIF-Choquet distance operator.
Again, this paper proposes the group clustering algorithm based on ITrIFC TrIF-OWAD operator. By introducing the idea of prospect theory, this clustering algorithm take intuitionistic trapezoidal fuzzy prospect value matrix as basis information. Considering the properties of the interaction between information and programs sort position in the cluster analyzes, in the construction of similarity matrix, ITrIFC and TrIF-OWAD operator are used to assemble the relevant information for decision-making,and based on the similarity matrix, large group clustering algorithm are establised.
On this basis, we propose intuitionistic fuzzy multiple attribute complex-large group decision making consistency analysis and consistency correction automatic algorithm. Taking into account the existence of the possibility of sub-groups of clusters or "Union" in large groups within groups, this paper first use the proposed large group clustering algorithm to cluster the large groups, and design cluster consistency index and group consistency index based on group clustering results, and then establish group consistency analysis method based on large group clustering algorithm. As for modification of the evaluation information, taking into account the respect of the original decision-makers evaluate information, this paper establishs consistency correction approach based clustering of large groups. Taking into account the time and cost constraints as well as the impact of herd behavior, complex-Large group decision making consistency correction automatic algorithm is proposed. According to this algorithm computer program are established; example analysis shows that the algorithm has strong maneuverability and practicability.
Then, we propose the complex large group intuitionistic trapezoidal fuzzy prospect value matrix assembly method. Based on the proposed intuitionistic fuzzy multiple attribute complex-large group decision making consistency analysis and consistency correction automatic algorithm, taking into account the similar characteristics among individual prospect value matrix in each sub-group, this paper determine the weights of decision-makers based on intuitionistic trapezoidal fuzzy distance, individual decision-making information and the preferences of cluster virtual central figure; secondly; build cluster consensus intuitionistic trapezoidal fuzzy prospect value matrix; and based on cluster consensus intuitionistic trapezoidal fuzzy prospect value matrix, build lager group consensus intuitionistic trapezoidal fuzzy prospect value matrix by using weight information between clusters. This group assembly method can be better to reduce the loss of information, as much as possible to retain the original information of the decision-makers.
Finally, we propose a intuitionistic trapezoidal fuzzy multiple attribute complex-large group decision making model based on prospect theory (MRP-TRIFPV-MAGDM). As for the decision-making process, the proposed model integrates the single attribute's prospect value determination method, group consistency analysis and consistency correction, lager group consensus intuitionistic trapezoidal fuzzy prospect value matrix and program selection, and provides support for the development of decision support systems. On the research paradigm, the model combined with the normative paradigm and descriptive research paradigm. We consider the utility measure based on multiple reference points, the associated information between attributes, complex characteristics of decision makers, and based on utility measure,construct a intuitionistic trapezoidal fuzzy multiple attribute complex-large group decision making model. Then the proposed intuitionistic trapezoidal fuzzy multiple attribute complex-large group decision making model is more valueable in practice. The practicality and operability of the model has been proven by applying the proposed mRP-TrIFPV-MAGDM model into evaluation of two types of products.
引文
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