【作者】 徐雪莲；

【导师】 刘晓东；

【作者基本信息】 大连海事大学 ， 应用数学， 2008， 硕士

【摘要】 自1965年美国控制论专家扎德(L.A.Zadeh)提出模糊集理论以来,模糊集与系统便作为一门新的工程数学方法被人们广泛地研究并应用到工程实际的各个领域。AFS(Axiomatic Fuzzy Set)理论即公理模糊集理论是一种新的模糊数学分析方法,由刘晓东教授于1995年提出。它是Zadeh提出的模糊集思想的数学公理化,是人类认识、思维的部分机理的数学抽象和表示,它比现有的模糊逻辑更接近于人类的思维逻辑,更便于计算机处理。针对一直以来广泛争论的模糊集理论的最基本问题:模糊概念的隶属函数的科学、统一的确立方法和人类思维的逻辑运算的正确表示,AFS理论进行了深入系统的研究和探讨,使隶属函数和模糊逻辑系统的建立更具客观性、严密性和统一性。许多应用实例说明AFS模糊逻辑系统比现有的模糊逻辑更接近于人类思维。目前,AFS理论被进一步研究并已经被应用到模糊聚类分析、模糊决策树,信用分析、模式识别和故障诊断等领域。本文对基于AFS模糊逻辑理论的聚类分析算法(X.D.Liu,W.Wang and T.YChai,IEEE Transaction on Systems,Man,Cybernetics,2005)进行进一步的研究,在原算法的基础上对样本的模糊描述的取法和聚类有效性函数进行了改进,弥补了原算法的缺欠之处,使其更加适用于对模糊数据进行聚类分析,并将改进后的聚类算法应用到实际的模糊数据(台湾30家航空公司的评估结果)中。本文的聚类算法模仿人脑对事物进行聚类的过程,仅仅依靠数据样本在属性上的序关系进行聚类分析。因此,AFS聚类算法可以处理那些无法用具体数值表示出来的模糊数据,甚至可以是诸如本文所研究的语言值模糊数据。本文的研究结果表明,应用所提出的新的AFS聚类算法得到的聚类结果与实际专家得到的经验描述几乎一致。实验结果也进一步说明了改进的算法具有很高的实用价值。更多还原

【Abstract】 The theory of fuzzy sets and systems has been studied widely and applied in many engineering fields as a new mathematics method since it was proposed by professor L.A.Zadeh, an American cyberneticist, in 1965. AFS theory is a new method to study fuzzy set which was proposed by professor Liu Xiaodong in 1995. It makes some of the mechanisms of decompose and composition of human conceptions to be understood with mathematical terms. It is more suitalbe to describe the logic of human and more comfortable to the disposal of computer. For ages, there exist the arguments for the basic issues exist in fuzzy set theroy about how to establish the membership function of the fuzzy concept with a rigor and uniform method and the accurate representions of the fuzzy logic operations. In order to deal with the above issues, AFS theory analyze and study these issues further. Many experimental studies show that AFS theroy is more close to the thought of humanity. Recently, AFS theory has been developed further and applied to fuzzy clustering analysis, fuzzy decision trees, credit rating analysis , pattern recognition and hitch diagnoses, etc.In this paper, in order to be more practical to the fuzzy data set, the AFS Fuzzy logic clustering algorithm (X. D. Liu, W. Wang and T. Y. Chai, IEEE Transaction on Systems, Man, Cybernetics, 2005) have been studied further by the improvement of the algorithm in the method to describe the objects and the fuzzy clustering validity index. Then it applies the new AFS fuzzy clustering method to the fuzzy data set (The evaluate results of 30 companies). The clustering algorithm proposed in this paper imitates the clustering procedure of human, and just depends on the ordered relation on the attributes. Thus AFS theory can be used to deal with the fuzzy data sets which can not be described by the numbers, even the fuzzy data described by the linguistic values of human as it shown in this paper. The study shows that the results can be almost consistent with the experts’ intuition descriptions by using the proposed new AFS clustering method. More further, the results present the proposed fuzzy clustering meth- od is practical and useful.更多还原