عنوان مقاله [English]
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.
 Boroufar, A., Rezaian, A., Shokohyar, S.(2017), Identifying the customer behavior model in life insurance Sector using data mining, Management Research in Iran, 20 (4), 65-94.
 Zadeh, L. A. (1965). Fuzzy sets, Information and control, 8(3), pp.338-353.
 Dunn, J. C. (1974). Well-separated clusters and optimal fuzzy partitions.Journal of cybernetics, 4(1), 95-104.
 Bezdek JC. (1973), Fuzzy mathematics in pattern classification, PhD dissertation, Cornell University, Ithaca, NY.
 Bezdek, J. C., Coray, C., Gunderson, R., & Watson, J. (1981). Detection and characterization of cluster substructure i. linear structure: Fuzzy c-lines. SIAM Journal on Applied Mathematics, 40(2), 339-357.
 De Oliveira, J. V., & Pedrycz, W. (Eds.). (2007). Advances in fuzzy clustering and its applications. New York: Wiley.
 Sohrabi, B., Raeesi, V. I., Zare, M. F. (2016). Designing a Recommender System for Optimizing and Managing Bank Facilities through the Utilization of Clustering and Classification Algorithms, Modern Researches in Decision Making, 1(2), 53-76.
 Halkidi, M., Batistakis, Y., & Vazirgiannis, M. (2001). On clustering validation techniques. Journal of intelligent information systems, 17(2-3), 107-145.
 Fukuyama, Y., & Sugeno, M. (1989, June). A new method of choosing the number of clusters for the fuzzy c-means method. In Proc. 5th Fuzzy Syst. Symp (Vol. 247, pp. 247-250).
 Xie, X. L., & Beni, G. (1991). A validity measure for fuzzy clustering. IEEE Transactions on pattern analysis and machine intelligence, 13(8), 841-847.
 Kwon, S. H. (2004). Threshold selection based on cluster analysis. Pattern Recognition Letters, 25(9), 1045-1050.
 Wang, W., & Zhang, Y. (2007). On fuzzy cluster validity indices. Fuzzy sets and systems, 158(19), 2095-2117.
 Žalik, K. R. and Žalik, B.(2010), Validity index for clusters of different sizes and densities, Pattern Recognition Letters, 43(10), 3374 -3390.
 Döring, C., Lesot, M. J., & Kruse, R. (2006). Data analysis with fuzzy clustering methods. Computational Statistics & Data Analysis, 51(1), 192-214.
 Dunn, J.C., (1973), A fuzzy relative of the isodata process and its use in detecting compact well separated clusters ,J. Cybern, No.28, pp.32–57.
 Duda, R. O., Hart, P. E., & Stork, D. G. (2001). Unsupervised learning and clustering. Pattern classification, 519-598.
 Lucieer, V., & Lucieer, A. (2009). Fuzzy clustering for seafloor classification.Marine Geology, 264(3), 230-241.
 Fisher, P., Wood, J.,(1998), "What is a Mountain ? Or the Englishman who went up a Boolean geographical concept but realised it was fuzzy", Geography, No.83, pp.247–256.
 Chiu, S.L. (1994), Fuzzy model identification based on cluster estimation, J. Intell. Fuzzy Systems, No. 2,pp.267- 278
 Yao, J., Dash, M., Tan, S. T., & Liu, H. (2000). Entropy-based fuzzy clustering and fuzzy modeling. Fuzzy Sets and Systems, 113(3), 381-388.
 Gath, I., & Geva, A. B. (1989). Unsupervised optimal fuzzy clustering. IEEE Transactions on pattern analysis and machine intelligence, 11(7), 773-780.
 Duda, T., & Canty, M. (2002). Unsupervised classification of satellite imagery: choosing a good algorithm. International Journal of Remote Sensing, 23(11), 2193-2212.
 Dave, R.N.(1996), "Validating fuzzy partition obtained through c-shells clustering", Pattern Recognition, No.17, pp.613–623.
 Wu, K. L., Yang, M. S. (2005). A cluster validity index for fuzzy clustering.Pattern Recognition Letters, 26(9), 1275-1291.
 Pakhira, M. K., Bandyopadhyay, S., & Maulik, U. (2005). A study of some fuzzy cluster validity indices, genetic clustering and application to pixel classification. Fuzzy Sets and Systems, 155(2), 191-214.
 Hoppner, F., Klawonn, F., Kruse, R., Runkler, T., 1999. Fuzzy Cluster Analysis.Wiley, Chichester, UK.
 Bezdek, J.C., Keller, J.M., Krishnapuram, R., Kuncheva, L.I., Pal, N.R.(1999), Will the Real Iris data please stand up? IEEE Trans. Fuzzy Systems 7, pp.368-369.
 Tsekouras, G. and Haralambos, S.(2004),A new approach for measuring the validity of the fuzzy c-means algorithm, Advances in Engineering Software, No.35,pp.567–575.