Study of information retrieval system using multiset model and clustering

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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