【作者】 孙高峰；

【导师】 王绪柱；

【作者基本信息】 太原理工大学 ， 应用数学， 2005， 硕士

【摘要】 Fodor公理化定义是目前文献中最为广泛的模糊偏好结构定义方法,该定义包含三个重要的特例,其中特例二与特例三已被一些研究者进行了详细的研究,而对特例一,现有文献中未见任何讨论。鉴于此,本文就特例一下模糊偏好结构的基本性质进行全面系统的讨论,并对三类模糊偏好结构的三个基本关系(大偏好、严格偏好、无区别关系)分别在三种常见t模意义下的传递性作了详细的对比讨论。文章的具体研究内容与结果归纳如下: 在特例一的框架下,详细讨论了模糊偏好结构的各种性质。首先,我们给出用大偏好关系表出严格偏好、无区别关系及不可比关系的具体形式,并讨论该偏好结构的一般性质。其次,以两类常见t模为基础,我们讨论大偏好关系与严格偏好及无区别关系的传递性有关性质之间的联系。然后,在不可比关系为空的情况下,以一般t模为基础,讨论类似的性质,给出了一个大偏好关系为T传递的充要条件。最后,在不可比关系为空的条件下,讨论了大偏好关系与严格偏好及无区别关系的负传递性、半传递性、Ferrers性质之间的联系。 从我们的讨论及目前文献中有关模糊偏好结构的研究结果来看,三类结构性质存在一些差异,同时也有某些相同的地方。为了对这些结构的异同有较为全面的了解,我们对另两更多还原

【Abstract】 Currently, Fodor’s aximatic definition of fuzzy preference structure is the most general among the existing literature. This definition includes three particular cases among which Case II and III have been investigated in detail by some researchers while there is little discussion around Case I. In view of this, we carry out an overall research on some fundamental properties for Case I. Meanwhile, under a general t-norm, we do a comparative study of transitivity-related properties of the three basic relations (large preference, strict preference and indiffierence) in the three families of fuzzy preference structures. The concrete content and main results are summarized as follows:In the framework of Case I, we investigate various properties of fuzzy preference structures. Firstly, we represent strict preference, indifference and incomparability relation by means of large preference relation and discuss some general properties of the family of preference structures. Next,based on two types of t-norms, we estabish links between transitivity of large preference relation and that of strict preference and indifference relation. Then, under the assumption that the involved incomparability is empty, similar property is considered based on general t-norm and an necessary and sufficient condition is presented. Finally, the relationships between negative transitivity, semitransitiv-ity, Ferrers properties of large preference, strict preference and indifference relation are established without incomparability.From the results on fuzzy preference structures presented in this paper and other literature, we know that there are some difference and common points. To obtain a clear picture of the same and different points in the three preference structures, we carry out a complementary research on properties of the remaining two preference structures. Based on all these research, a detailed comparative study is performed from which we know that Lukasiewicz-like transitivity is a common property of the three types of preference structures without incomparability.In a summary, the research in this thesis is indispensable for the investigation of fuzzy preference structure under Fodor’s axiomatic definition. Together with the research on Case II and III, it forms an integrable system which lays a theoretic foundation for the practical mod-elling of decision-makers.更多还原