A Study on Fuzzy Symbolic Classifiers.

符号数据分析是在法国diday教授的指导下迅速发展起来的一个新的研究领域。在该领域中，数据描述的泛化是一个主流，其中每个样本数据不仅可以用数字特征来描述，而且可以用符号特征来描述。本文提出的“模糊符号模式分类器”可以处理非唯一性特征和符号特征同时描述的符号模式。本研究得到以下结果：1.研究结果表明：这里处理的方法是基于笛卡尔系统模型（CSM），这是我们自己的数学模型来处理符号数据。在这项研究中，我们推广了CSM本身，以便处理用于描述样本模式的更广泛类型的特征。当样本仅由数字特征描述时，存在基于给定样本模式集上定义的距离函数的模糊分类器。我们通过引入在csm上定义的广义闵可夫斯基度量来推广这种方法。作为一种不同的方法，我们开发了面向区域的模糊符号分类器，其中每个模式类由“事件”（数字特征情况下的矩形区域）描述，并在事件和样本模式之间定义隶属函数。我们发现，在这种方法中，为了在模式类之间的可分离性和类描述的通用性之间取得平衡，“特征选择”本质上是重要的。该结果作为在神户举行的第五届国际船级社联合会会议（IFCS-96）符号数据分析的特邀论文报告。

The symbolic data analysis is a new research field which has been rapidly grown up guided by Professor E.Diday in France. In this field, the generalization of the data descriptions is one main stream, where each sample data may be described not only by numeric features but also by symbolic features.The "fuzzy symbolic pattern classifiers" in this study can treat symbolic patterns which are simultaneously described by unmeric features and symbolic features. The following result are obtained in this study :1.The approach treated here is based on the Cartesian system model (CSM) which is our own mathematical model to treat symbolic data. In this study we generalized the CSM itself in order to treat wider types of features used to describe sample patterns.2.When samples are described only by numeric features, there exist fuzzy classifiers based on distance functions defined on the given set of sample patterns. We generalized this approach by introducing the generalized Minkowski metrics defined on the CSM.3.As a different method, we developed region oriented fuzzy symbolic classifier in which each pattern class is described by "events" (rectangular regions in numeric feature cases) and the membership functions are defined between events and sample patterns. We found that, in this approach, "feature selection" is essentially important in order to take balance between the separability among patterm classes and the generality of class descriptions. The result was reported as an invited paper for the symbolic data analysis in Fifth Conference of the International Federation of Classification Societies (IFCS-96) held in Kobe.