模糊关系的T-传递一致性及其指标的研究

发布时间：2018-03-25 16:11

本文选题：模糊关系　切入点：t-模　出处：《太原理工大学》2017年硕士论文

【摘要】：本文系统地讨论了模糊关系的T-传递一致性及其指标,其主要研究内容如下:首先,我们简单回顾了普通二元关系、模糊逻辑联结运算以及模糊二元关系的定义及性质.其次,我们系统地总结了普通二元关系传递一致性的研究成果,并对传递一致性的性质进行了一些研究,从而完善了普通二元关系传递一致性的研究.接着,我们利用t-模,将普通二元关系的传递一致性推广到了模糊情况下.同时,讨论了模糊关系的T-传递一致性、T-传递性、T-拟传递性以及T-非循环性之间的关系,并对模糊关系的T-传递一致性的性质做了详细研究.最后,我们定义了模糊关系的T-传递一致性指标.同时,讨论了模糊关系的T-传递一致性指标、T-传递性指标、T-拟传递性指标以及T-非循环性指标之间的关系,并且研究了模糊关系的T-传递一致性指标的一些性质.我们注意到,在我们的假设下,普通二元关系传递一致性的大部分结论都得到了相应的模糊以及指标推广,但仍然有一些结论不再成立,为此,我们给出例子进行了说明.总之,通过我们的研究,对模糊关系的T-传递一致性以及T-传递一致性指标有了更为深入的了解.这些研究对模糊决策理论的发展有一定的意义.
[Abstract]:In this paper, the T-transitive consistency and its index of fuzzy relations are discussed systematically. The main research contents are as follows: firstly, we briefly review the definitions and properties of ordinary binary relations, fuzzy logic join operations and fuzzy binary relations. In this paper, we systematically summarize the research results of transitive consistency of ordinary binary relations, and do some research on the properties of transitive consistency, so as to perfect the research of transitive consistency of ordinary binary relations. In this paper, the transitive consistency of ordinary binary relations is extended to fuzzy case. At the same time, the relations between T- transitive consistency and T- transitive quasi-transitivity and T- non-circularity of fuzzy relations are discussed. Finally, we define the T- transitive consistency index of fuzzy relations. In this paper, we discuss the relations between T- transitive consistency index and T- transitive index of fuzzy relation, and study some properties of T- transitive consistency index of fuzzy relation. Under our assumption, most of the conclusions of transitive consistency of ordinary binary relations have been generalized by corresponding fuzzy and index, but there are still some conclusions that no longer hold true. For this reason, we give an example to illustrate. Through our research, we have a deeper understanding of the T- transitive consistency and the T- transitive consistency of fuzzy relations, which are of significance to the development of fuzzy decision theory.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159

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