基于TODIM的模糊多属性决策研究

发布时间：2019-06-20 01:33

【摘要】：多属性决策是决策领域的一个热门话题。但现存的多属性决策方法大多建立在假设人是绝对理性的期望效用理论上。在现实生活中,由于决策问题本身的复杂性和决策者认知的有限性,决策者往往是有限理性的。TODIM是一个基于前景理论的基础上的行为决策方法,可以较好地刻画决策者的有限理性行为。然而经典的TODIM方法只适用于精确数环境下的单个决策者的多属性决策问题,对于模糊环境下的群决策问题却无能为力。因此,本文为了使行为决策方法更适用于现实,本文充分考虑决策信息的不确定性,将TODIM方法拓展到模糊的环境中。同时,由于社会复杂性增加,单个决策者很难将所有的相关因素考虑进去,所以将行为决策拓展到群决策具有很强的现实意义。基于这两个思想,论文主要完成了以下工作:首先,将TODIM方法拓展到多粒度语言,二维模糊语言及三角直觉模糊环境中,从而更好地反映了环境的不确定性及决策者的偏好信息。同时,在三角直觉模糊环境下,将TODIM方法扩展到群决策领域,从而使得决策问题考虑得更加的全面。其次,针对语言信息的处理,本文提出了一个将多粒度语言转化成区间直觉模糊数的方法,相比与将其转换为模糊数和直觉模糊数,能更好地处理语言信息的模糊性及不确定性。新定义了一个二维直觉模糊语言变量,使决策者不仅能对评估对象做出评价,还能对自身所做评价的可靠性再评价。然后,从概率的角度为三角直觉模糊数提出了交叉影响的运算法则,包括加法运算、乘法运算和幂运算。在这些新的运算基础上,提出了两个基于交叉影响的三角直觉模糊环境下的平均算子,分别为三角直觉模糊加权平均算子和三角直觉模糊算术平均算子。通过数学归纳法在理论上给出了严密的证明。最后,在考虑属性权重未知的情况时,本文提出了采用信息熵的方法来处理语言环境下的属性权重,采用相似度的方法处理三角模糊环境下的属性权重。对于群决策问题,本文基于一致性的思想来确定专家的权重,分别提出了基于灰色关联度的共识模型与基于相似度的线性规划模型,以协调各种不同的意见和看法,最终形成群体总的评价。
[Abstract]:Multi-attribute decision making is a hot topic in the field of decision making. However, most of the existing multi-attribute decision-making methods are based on the expected utility theory which assumes that human beings are absolutely rational. In real life, because of the complexity of decision-making problem itself and the limitation of decision-maker's cognition, decision-maker is often bounded rational. TODIM is a behavioral decision-making method based on prospect theory, which can depict the bounded rational behavior of decision-maker well. However, the classical TODIM method is only suitable for the multi-attribute decision making problem of a single decision maker in the exact number environment, but it is powerless for the group decision problem in fuzzy environment. Therefore, in order to make the behavioral decision-making method more suitable for reality, this paper fully considers the uncertainty of decision-making information, and extends the TODIM method to the fuzzy environment. At the same time, because of the increase of social complexity, it is difficult for a single decision maker to take all the relevant factors into account, so it is of great practical significance to extend behavioral decision to group decision making. Based on these two ideas, the main work of this paper is as follows: firstly, the TODIM method is extended to multi-granularity language, two-dimensional fuzzy language and triangular intuitionistic fuzzy environment, so as to better reflect the uncertainty of the environment and the preference information of decision makers. At the same time, in the triangular intuitionistic fuzzy environment, the TODIM method is extended to the field of group decision making, which makes the decision problem more comprehensive. Secondly, aiming at the processing of language information, this paper proposes a method to transform multi-granularity language into interval intuitionistic fuzzy number, which can deal with the fuzziness and uncertainty of language information better than converting it into fuzzy number and intuitionistic fuzzy number. A new two-dimensional intuitionistic fuzzy language variable is defined, which enables decision makers not only to evaluate the evaluation object, but also to re-evaluate the reliability of their own evaluation. Then, from the point of view of probability, the algorithm of cross influence is proposed for triangular intuitionistic fuzzy numbers, including addition operation, multiplication operation and power operation. On the basis of these new operations, two average operators in triangular intuitionistic fuzzy environment based on cross influence are proposed, which are triangular intuitionistic fuzzy weighted average operator and triangular intuitionistic fuzzy arithmetic average operator, respectively. Through the mathematical induction method, the strict proof is given in theory. Finally, when considering the unknown attribute weight, this paper proposes an information entropy method to deal with the attribute weight in the language environment, and the similarity method to deal with the attribute weight in the triangular fuzzy environment. For the group decision problem, this paper determines the weight of experts based on the idea of consistency, and puts forward the consensus model based on grey correlation degree and the linear programming model based on similarity respectively, in order to coordinate all kinds of different opinions and opinions, and finally form the overall evaluation of the group.
【学位授予单位】：深圳大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224

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