Narrow Results

Case retrieval is one of the key steps of case-based reasoning. The quality of case retrieval determines the effectiveness of the system. The common similarity calculation methods based on attributes include distance and inner product. Different similarity calculations have different influences on the effect of case retrieval. How to combine different similarity calculation results to get a more widely used and better retrieval algorithm is a hot issue in the current case-based reasoning research. In this paper, the granularity of quotient space is introduced into the similarity calculation based on attribute, and a case retrieval algorithm based on granularity synthesis theory is proposed. This method first uses similarity calculation of different attributes to get different results of case retrieval, and considers that these classification results constitute different quotient spaces, and then organizes these quotient spaces according to granularity synthesis theory to get the classification results of case retrieval. The experimental results verify the validity and correctness of this method and the application potential of granularity calculation of quotient space in case-based reasoning.

In this paper, we find that for each given spatial graph, the number of its maximal trees is finite, and the quotient space corresponding to some maximal tree is also a spatial graph and it is homeomorphic to a disjoint union of wedge sum of circles. That means this quotient space is orientable and colorable. Thus, we define two equivalence invariants of spatial graphs, the coloring number bracket and the Alexander invariant set, which are coming from the coloring invariant and Alexander matrix.

This paper proposes a fuzzy granules clustering algorithm which based on quotient space. It makes use of metric space and F-statics approach. In this algorithm, information granule is represented by quotient space distance and different clustering results can be got by different granules. At the same time, it makes full use of accuracy of clustering by F-statics to find the optimal clustering mode from the different granules clustering results. The algorithm is especially efficient for the case that it is difficult to evaluate the performance of clustering in advance. As the experiment did by Matlab showed, it found the optimal clustering mode and proved its validity.