Study of information retrieval system using multiset model and clustering

通过引入一些新的运算和证明一些基本性质，建立了多集和模糊多集理论。在此基础上，将无穷引入多集，研究了与前述实值多集理论的关系，并定义了广义多集，包括普通模糊多集和实值多集。此外，还研究了广义多集的粗糙逼近。目前的聚类方法不假设多集空间，因此已经定义了聚类的多集空间和相似性/距离，从而可以使用清晰和模糊c-means方法，并研究了文档聚类的应用；考虑了使用多集框架和聚类的信息检索模型，并开发了信息聚类算法。特别是，使用支持向量机和c均值算法中的核技巧生成了具有非线性边界的聚类。由于模糊数据库使用了模糊多集，本文研究了模糊多集理论对模糊数据库的理论意义，并开发了一个利用聚类并在球面上显示聚类的信息检索系统原型。球体上的距离反映了原始空间中这对之间的距离。此外，该系统还能显示集群的层次结构

Theory of multisets and fuzzy multisets has been established by introducing several new operations and proving fundamental properties. Moreover infiniteness is introduced into multisets and relationships with a foregoing theory of real-valued multisets have been investigated : Moreover generalized multisets are defined which includes ordinary fuzzy multisets and real-valued multisets. In addition, rough approximations of generalized multisets are studied. Current methods of clustering do not assume multiset spaces, and therefore multiset spaces and similarities/distances for clustering have been defined whereby methods of crisp and fuzzy c-means can be used and application to document clustering has been studiedInformation retrieval models using the multiset framework and clustering has been considered and algorithms of information clustering have been developed. In particular, clusters with nonlinear boundaries have been generated by the use of kernel tricks in support vector machines and c-means algorithms. Moreover fast algorithms of nonlinear clustering have been developedAs fuzzy database uses fuzzy multisets, theoretical implications of the present theory of fuzzy multisets to fuzzy databases have been studiedAn information retrieval system prototype has been developed which employs clusters and displays clusters on a sphere. The distance on the sphere reflects the distance between those pair in the original space. Moreover this system can show hierarchies of clusters