A new fuzzy clustering algorithm for optimally finding granular prototypes

Prototype Reasoning using granular objects is an important technology for knowledge discovery. Fuzzy clustering can be used to generate prototypes with different granularities. In order to find optimal granular prototypes through fuzzy clustering, for given data, two conditions are necessary: a good cluster validity function, which can be applied to evaluate the goodness of cluster schemes for varying number of clusters (different granularity); a good cluster algorithm that can produce an optimal solution for a fixed number of clusters. To satisfy the first condition, a new validity measure called granularity-dissimilarity (GD) measure is proposed, which is stable in evaluating granularities and works well even when the number of clusters is very large. For the second condition, we propose a new algorithm called multi-step maxmin and merging algorithm (3M algorithm). Experiments show that, when used in conjunction with the new cluster validity measure, 3M algorithm produces better results on the experimental data sets than several alternatives.