基于前景理论的模糊多准则决策方法及应用研究

发布时间：2018-03-28 22:16

本文选题：多准则决策　切入点：前景理论　出处：《南京理工大学》2017年硕士论文

【摘要】：在经济生活中,常常需要进行多准则决策。由于决策矩阵、方案指标有时不确定,甚至决策者的心理因素也会对决策过程产生影响,基于期望效用理论的传统多准则决策思路已经难以适应新形势下的需求。模糊多准则决策是应用模糊理论和多准则决策方法进行方案排序、评价和决策的过程,而前景理论则是行为决策科学理论的代表性方法,将二者有机结合,可以有效解决经济生活中的新兴难题,尤其是各类特殊的模糊多准则决策问题,符合科学决策"程序性、创造性、择优性、指导性"的基本特征。论文首先分析了模糊多准则决策问题的特点,阐述了期望效用理论与前景理论的区别与联系,认为应用前景理论进行模糊多准则决策时,重点环节在于对模糊决策矩阵的预处理。由此,论文系统性梳理了各类模糊数的定义和应用范围,总结和提出模糊数预处理的策略,包括模糊数的去模糊化方法和无量纲处理方法。基于模糊数的预处理方法和前景理论的基本思想,论文重点研究了三类特殊的模糊多准则决策问题:即大样本混合型多准则决策问题、直觉梯形模糊数型多准则决策问题、以及风险型模糊多准则决策问题,针对这三类问题,分别设计对应的模糊多准则决策方法,并将所提出的决策方法应用于实际案例,体现理论研究的现实价值。对于研究主题,论文的主要成果是:(1)针对多方案、多准则情形下,决策矩阵又包含多种类型的模糊数时,参考点难以确定的问题,论文剖析了现有参考点设计思路的优缺点,提出了非参数检验方式确定参考点的方法,基于距离和可能度的思想设计价值函数。(2)针对直觉梯形模糊数型(ITFN)多准则决策问题,论文分析了现有直觉梯形模糊数记分函数的不足,设计一种改进型记分函数,考虑到决策者的行为因素,基于VIKOR方法的基本思想,给出了相应的决策模型。(3)针对风险型模糊多准则决策问题,论文以地区反恐情报体系建设评价问题作为决策背景,设计评价指标体系,根据决策权重难以确定的问题特点,引入TOPSIS法的思想进行评价和前景价值排序。
[Abstract]:In economic life, there is often a need for multi-criteria decision-making. Because of the decision-making matrix, the program indicators are sometimes uncertain, and even the psychological factors of the decision makers will have an impact on the decision-making process. The traditional multi-criteria decision-making method based on the expected utility theory has been unable to meet the needs of the new situation. Fuzzy multi-criteria decision making is the process of scheme ranking, evaluation and decision making based on fuzzy theory and multi-criteria decision method. The foreground theory is the representative method of the behavioral decision science theory. The combination of the two methods can effectively solve the emerging problems in economic life, especially various special fuzzy multi-criteria decision making problems, which accord with the scientific decision-making program. This paper first analyzes the characteristics of fuzzy multi-criteria decision making problem, and expounds the difference and relation between the expected utility theory and the foreground theory. It is considered that the preprocessing of fuzzy decision matrix is the key step in applying foreground theory to fuzzy multi-criteria decision making. Therefore, the definition and application range of various fuzzy numbers are systematically combed out, and the strategies of fuzzy number preprocessing are summarized and put forward. It includes fuzzy number de-fuzzification method and dimensionless processing method, preprocessing method based on fuzzy number and basic idea of foreground theory. This paper focuses on three kinds of special fuzzy multi-criteria decision making problems: large sample mixed multi-criteria decision making problem, intuitionistic trapezoidal fuzzy number multi-criteria decision making problem, and risk fuzzy multi-criteria decision making problem. The corresponding fuzzy multi-criteria decision making method is designed, and the proposed decision method is applied to practical cases to reflect the practical value of theoretical research. For the research topic, the main achievement of this paper is: 1) for multi-scheme and multi-criteria case, When the decision matrix contains many kinds of fuzzy numbers, the reference points are difficult to determine. This paper analyzes the advantages and disadvantages of the existing design ideas of reference points, and puts forward the method of determining reference points by non-parametric test. Aiming at the problem of intuitionistic trapezoid fuzzy number type (ITFN) multi-criteria decision making, this paper analyzes the shortcomings of the existing intuitionistic trapezoid fuzzy number scoring function and designs an improved scoring function. Considering the behavior factors of decision makers, based on the basic idea of VIKOR method, the corresponding decision model is given. Aiming at the risk type fuzzy multi-criteria decision-making problem, the paper takes the evaluation of regional anti-terrorism intelligence system as the decision-making background. The evaluation index system is designed. According to the characteristics of the problem that the weight of decision-making power is difficult to determine, the idea of TOPSIS method is introduced to evaluate and rank the foreground value.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C934

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