【作者】 李静；

【导师】 李法朝；

【作者基本信息】 河北科技大学 ， 应用数学， 2011， 硕士

【摘要】 模糊数具有数量和集合的双重特性,是实际问题中最为常用的模糊信息描述工具。由于在模糊数之间不存在确切的顺序关系,因而,模糊数的排序问题一直是学术和应用领域广泛关注的研究内容。虽然许多学者从不同的角度建立了具有不同特征的排序方法,但均没有系统地考虑排序的类型以及排序方法的构建准则。本文针对模糊数的排序做了以下几方面的工作:(1)提出了模糊信息排序的两种基本类型,即基于数量特征的排序和基于复合特征的排序,分析了两类不同排序问题的本质区别;(2)给出了基于数量特征的区间数排序应遵循的基本原则,并结合区间数的复合量化描述,从抽象化和结构化的角度研究了各指标综合的公理化体系,讨论了效应综合函数的构建问题,给出了加法型、乘法型、拟线性型效应综合函数的构建准则;(3)以模糊数的结构特征、基于数量特征的区间数排序方法以及水平效应函数为基础,以积分作为层次信息的综合工具,建立两种基于数量特征的模糊数排序模式(即基于数量特征的数量化排序方法和基于数量特征的模糊不等度模型);(4)通过分析区间数所具有的数量特征以及所反映信息的不确定性,建立了一种基于复合特征的区间数排序方法,并结合模糊数的结构特征提出了一种基于复合特征的模糊数排序方法;(5)通过具体的模糊决策和模糊规划问题,进一步分析了所建排序模式的特点和有效性。更多还原

【Abstract】 Fuzzy number, which has quantity and set these two characteristics, is most commonly used as a description tool of fuzzy information. Because fuzzy number does not have exact order relation, its ranking method is paid close attention in academic and application fields. From different angles, many scholars built ranking methods with different properties, but they did not systematically consider the sorting type and the construction principle of ranking method. In this paper, in view of the ranking method of fuzzy number, we have the following work:(1) We put forward two basic types of ranking method for fuzzy information, that is, ranking problem based on quantity property, and that based on compound property. Furthermore, analysis the essential difference between these two ranking problems;(2) We give the basic principle, which ranking method based on quantity property of interval numbers must abide by; after that, combining with the compound quantification description, from an abstract and structured angle, we get an axiomatic system for the synthesizing problem of each index, discuss the structural problem of synthesizing effect function, give the specific building criteria of additive, multiplicative and qusi-linear model;(3) Based on the strcture characteristics of fuzzy number, ranking method of interval numbers based on quantity property, and level effect function, making use of integral as a level information comprehension tool, build two ranking model of fuzzy number based on quantity property (i.e. ranking method of fuzzy number based on quantity property and fuzzy inequity degree model based on quantity property);(4) By analyzing the quantity property and uncertain information interval numbers reflected, we build an ranking method of interval numbers based on compound property, with the strcture characteristics of fuzzy number, we put forward a ranking method of fuzzy number based on compound property;(5) Through concrete fuzzy decision making and fuzzy programming problems, we further analysis the characteristics and effectiveness about the two ranking models.更多还原