【作者】 张青；

【导师】 黄天民；

【作者基本信息】 西南交通大学 ， 应用数学， 2005， 硕士

【摘要】 由于人类对策环境的不确定性、目标的多样性、决策主体的多元化和决策行为的高度复杂化等原因,使对策研究者们不断进行新的对策理论与方法的探索,同时也推动了模糊集理论在对策论上的应用。于是,模糊对策作为对策论的一个分支在上世纪70年代问世了。随之也出现了一些研究成果,解决了一些问题,如:策略集的模糊性、支付矩阵的不精确性、模糊对策解的概念、模糊结盟及模糊多目标等。但用模糊集理论系统刻画和研究N人对策的文章还很少见,本文试图对模糊N人非合作对策及其解作一些探讨。 首先,本文借鉴二人零和矩阵对策中鞍点的思想,提出了N人非合作对策的安全点概念并作为对策的解,讨论了它的一些性质,给出了它的求法,说明了它是最优策略组合。在此基础上结合模糊集理论刻画了模糊N人非合作对策的三种情况,并对其解作了一些说明。 其次,在安全点的基础上,本文定义了多目标N人非合作对策的几种安全点并作为对策的解,而且作了一些论证。同时,本文以目标权重向量和模糊数排序函数来体现局中人的偏好信息,并就局中人对他人的偏好信息的不同知晓情况下的模糊N人非合作对策及其安全点的求法进行了刻画和讨论,并对各种情况下的模糊支付值和实际形成的对策局势进行了比较论证。更多还原

【Abstract】 For the reasons of uncertainty of human game environments, variety of objects, multiplicity of decision makers and high complexity of decision actions, researchers have studied new game theories and methods ceaselessly. Meanwhile, this has promoted fuzzy sets theory applied to game theory. Consequently, fuzzy game theory emerged as a branch of game theory in 1970’s. Soon afterwards, a few research achievements appeared and mainly solved some problems of the following aspects: fuzziness of strategy sets, imprecision of payoff matrixes, the concept of solutions of fuzzy games, fuzzy coalition, fuzzy multiobjects and so on. However, there are few articles which comprehensively depict and study N-person game with fuzzy sets theory. This paper tries to do some research on fuzzy N-person non-cooperative games and its solving methods.Firstly, using the ideal of saddle point of two-person zero-sum matrix games for reference, the paper proposes the definition of the security point of N-person non-cooperative games, regards it as the solution of the games, gives its properties and solving method and proves that it is an optimal strategy profile. Based on those, the paper depicts three cases of fuzzy N-person non-cooperative games and makes some explanations to their solving methods.Secondly, on the basis of security point, the definitions of some security points of multiobjective N-person non-cooperative games which are regarded as the solutions are presented and some demonstrations are given here. At the same time, the preference information of players are embodied by objective weight vectors and ranking functions of fuzzy numbers. Then fuzzy N-person non-cooperative games in the situation that players know others’ preference information or not are depicted here, with the solving methods of their security points discussed and the fuzzy payoffs and practically formed strategy profiles compared and proved.更多还原