基于集对推理的格序决策及应用

发布时间：2018-05-02 13:18

本文选题：集对分析 + 集对推理　；参考：《华北理工大学》2015年硕士论文

【摘要】：科学决策一直是数学和管理学科的重要课题。将格理论的相关研究应用到决策模型中,是对理性行为决策理论的一种发展与完善。集对分析是一种新的处理不确定信息的工具,它的同异反联系度能够更加客观合理的描述不确定性问题。因此,对集对联系数进行格结构的刻画,并应用到决策系统中,对格序决策的发展与完善有着重要的理论意义。首先在二值逻辑和模糊逻辑的基础上提出了集对逻辑的概念,并给出了集对逻辑的演算规则,讨论了单论域和双论域上的模糊集对推理的基本概念和基本形式;其次提出了集对效用函数的概念,探讨了它的三维优先关系,给出了格结构的构建原理与方法,建立了基于集对效用函数的格序决策模型;最后针对模糊条件下的推理关系,给出了集对联系数形式的真域表达式以及推理运算规则,并结合决策原理,建立了真值联系函数集,给出了格结构的构建原理与方法,建立基于集对推理的格序决策模型。集对推理是一种更加符合客观实际的推理形式,这种集对推理模式能够更加客观的反应人们对不确定性问题的刻画与描述;在决策系统中,集对联系数的格序化研究,为解决多属性决策问题提供了一个新方法,同时也是对格序决策理论的发展与完善。
[Abstract]:Scientific decision-making has always been an important subject in mathematics and management. The application of lattice theory to decision-making model is a development and perfection of rational behavior decision theory. Set pair analysis (SPA) is a new tool for dealing with uncertain information, and its similarity, difference and inverse relation can describe uncertainty more objectively and reasonably. Therefore, it is of great theoretical significance for the development and perfection of lattice order decision making to characterize the lattice structure of the set couplet coefficient and apply it to the decision-making system. Firstly, on the basis of binary logic and fuzzy logic, the concept of set pair logic is put forward, the calculus rules of set pair logic are given, and the basic concepts and forms of fuzzy set pair reasoning on single and double fields are discussed. Secondly, the concept of set pair utility function is put forward, its three dimensional priority relation is discussed, the construction principle and method of lattice structure are given, and the lattice order decision model based on set pair utility function is established. In this paper, the true domain expression of the set couplet coefficient and the rules of reasoning operation are given. Combining with the decision principle, the set of truth relation functions is established, the construction principle and method of lattice structure are given, and the lattice order decision model based on set pair reasoning is established. Set pair reasoning is a kind of reasoning form which is more in line with objective reality. This kind of set pair reasoning model can more objectively reflect the characterization and description of uncertain problems, and in the decision system, the lattice order of set couplet coefficients is studied. It provides a new method for solving the problem of multi-attribute decision making, and it is also the development and perfection of the theory of lattice order decision making.
【学位授予单位】：华北理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O153.1;O225

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