【作者】 郝光；

【导师】 黄天民；

【作者基本信息】 西南交通大学 ， 应用数学， 2004， 硕士

【摘要】 Von-Neumann和Morgenstern提出的理性行为公理体系，标志着现代决策理论的开端，也为规范型决策理论奠定了基石。半个世纪以来，该公理体系的研究和应用一直是热点，许多学者在这方面取得了丰硕的成果。从二十世纪五十年代开始，以Allais和Edwards为首的一批学者参与实际决策的研究，考察理性决策模型在实际决策行为中的真实性，却不断发现这些模型在实际应用中出现各种偏差，其结果并不能让人满意。以往的研究主要集中在对其独立性公理和传递性公理的弱化，但最近一些学者如郭耀煌教授指出偏好关系通常是一个格结构，并建立了一套新的格序决策公理体系。本文运用现代数学理论——格论，将对方案的全序刻画拓展为格序刻画，并相应地弱化连续性公理，介绍了格序行为公理体系及其良好的发展前景。20世纪70年代以后，多目标决策得到了较大的发展，由于各个目标之间的冲突，因此要从中选出决策者的满意解，需要融入决策者的偏好、判断等模糊信息。模糊理论已成为研究含模糊信息的多目标决策问题的有效工具。 本文综合决策理论、格理论、模糊集理论等相关知识，(1) 提出模糊多目标格序决策的概念，通过正、负理想解等概念的引入，构造出模糊多目标格序决策模型，得到了相应的两种基本决策方法，并通过实例进一步予以说明；(2) 提出模糊多目标群格序决策的概念，通过引入正、负理想解等概念，构造出模糊多目标群格序决策模型，得到了相应的两种可行性决策方法，并举例进说明。总的思路：对方案集和目标集均为有限集的决策而言，如果任意两个方案均有上、下确界，那么顶元素(或底元素)即为最优方案。如果上述条件不具备，我们把虚拟方案——模糊正理想解和模糊负理想解，依次作为顶元素和底元素，构造一个格。通过比较每个方案与正理想解以及负理想解的接近程度，来判断最优解或满意解。 对策论自1912年问世以来，吸引了很多学者的兴趣，在自然科学、社会科学等领域中均有着十分广泛的应用。由于矩阵对策是对策论的基础，所以研究矩阵对策的性质有着十分重要的意义。本文首先建立了对称对策的模型，并利用了对称对策的性质给出了对称对策矩阵的解法，通过构造一个分块矩阵，实现了一般矩阵对策问题向对称对策的转化，从而为解决一般矩阵对策问题提供了一种较为简捷的方法。更多还原

【Abstract】 The famous axioms for rational behavior established by Von-Neumann and Morgenstern , as a sign of birth of modern decision-making, is a cornerstone of normative decision-making theory. In the past half century, the researching on the axioms and the applying them to practice have been a hot spot all the while, and numerous significant achievements have been gained. In the 1950s, Allais and Edwards with some other scholars began to do the research to check the facticity of the rational decision-making models applied to the real decision-making behavior, only to find all kinds of unsatisfying deviations. These researches mainly focused on weakening the independence axiom and transitivity axiom. But recently, some scholars such as Prof. Guo Yaohuang have pointed out that preference relation is often a lattice and developed a new set of axioms for lattice-order decision-makingbehavior. By using the modern mathematical theory--lattice theory inthis dissertation, the ordering axiom is generalized to the lattice order axiom , and the connected axiom is wakened . This dissertation introduces the lattice - order decision-making behavior axioms and their vast range of prospects. Since the 1970s, multiobjective decision-making has been developed greatly. Because of the conflicts among the objectives, the fuzzy information such as decision-maker’ preference and judgment must be considered in order to choose a satisfactory scheme. Fuzzy theory has been an efficient tool to solve all kinds of multiobjective decision-making problems in a fuzzy situation.The dissertation integrates decision-making theory, lattice theory, fuzzy set theory and other related knowledge, (1) puts forward the concepts of fuzzy multiobjective lattice-order decision-making, and constructs the models of fuzzy multiobjective lattice - order decision-making models, and attains two kinds of basic methods to solve them by illustrating by example. (2) presents the concepts of fuzzy multiobjective group lattice-order decision-making, and constructs the models of fuzzy multiobjective group lattice-order decision-making models, and obtains two kinds of feasible methods tosolve them by illustrating by example. The main idea: As for decision-making whose choice sets and objective sets are finite, if two arbitrary choices have supremum and infimum, then the top element (oar the bottom element) is the optimum choice. If the condition does not exist, in order to form a lattice, the fuzzy positive and negative ideal solutions which are suppositional are respectively regarded as the top element and the bottom element. The optimum solutions or satisfying solutions are found by the comparison of the distance between every choice and the positive or negative ideal solution.Since 1912, game theory has attracted many scholars’ intrest and had an extensive application in quite a few fields such as natural science and social science. Matrix game is the base of game theory , so it is of greater significance to study the properties of symmetric game. In this dissertation, the model of symmetric game is built first .A solution of symmetric game is gained by its properties .By constructing a block matrix,we can convert a general matrix game into a symmetric game, then we gain a rapid method to solve matrix game.更多还原