A new cluster validity index based on Fuzzy cardinality

Clustering techniques need to define the number of clusters before they can be applied to the partitioning problem. Determining suitable number of clusters in partitioning problem is the purpose of clustering validity indices, which are nowadays significantly considerable for data miners and this resulted in various numbers of related indices. Separation and compactness information of fuzzy clusters are both considered in developing the advance indices of clusters validity, while this makes the above mentioned indices inefficient because of mathematical sophistication and the need for more computational effort. Therefore, this paper proposes FCI as a new index, which employs fuzzy cardinality concept in defining the number of clusters in fuzzy clustering. FCI also considers both compactness and separation of fuzzy clusters while significantly decreases computational efforts. In this paper, after reviewing the cluster validity indices and fuzzy clustering algorithms, FCI index will be explained and ultimately to evaluate its effectiveness will be implemented.