How to cite this paper
Ahmadizar, F & Farahani, M. (2014). Clustering fuzzy objects using ant colony optimization.International Journal of Industrial Engineering Computations , 5(1), 115-126.
Refrences
Abbasbandy, S., & Hajjari, T. (2009). A new approach for ranking of trapezoidal fuzzy numbers. Computers and Mathematics with Applications, 57, 413–419.
Ahmadizar, F., & Hosseini, L. (2012). Bi-criteria single machine scheduling with a time-dependent learning effect and release times. Applied Mathematical Modelling, 36, 6203–6214.
Ahmadizar, F., & Soltanpanah, H. (2011). Reliability optimization of a series system with multiple-choice and budget constraints using an efficient ant colony approach. Expert Systems with Applications, 38, 3640–3646.
Al-Sultan, K.S. (1995). A tabu search approach to the clustering problem. Pattern Recognition, 28, 1443–1451.
Al-Sultan, K.S., & Fedjki, C.A. (1997). A tabu search-based algorithm for the fuzzy clustering problem. Pattern Recognition, 30, 2023–2030.
Bagirov, A.M. (2008). Modified global k-means algorithm for minimum sum-of-squares clustering problems. Pattern Recognition, 41, 3192–3199.
Bezdek, J.C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Plenum Press.
Bloch, I. (1999). On fuzzy distances and their use in image processing under imprecision. Pattern Recognition, 32, 1873–1895.
Brucker, P. (1978). On the complexity of clustering problems. in: Beckmenn, M., Kunzi, H.P. (Eds.), Optimization and Operations Research (Vol. 157). Berlin: Springer-Verlag, pp. 45–54.
Chang, D.X., Zhang, X.D., & Zheng, C.W. (2009). A genetic algorithm with gene rearrangement for K-means clustering. Pattern Recognition, 42, 1210–1222.
Chang, P.T., & Lee, E.S. (1994). Ranking of fuzzy sets based on the concept of existence. Computers and Mathematics with Applications, 27, 1–21.
Chu, T., & Tsao, C. (2002). Ranking fuzzy numbers with an area between the centroid point and original point. Computers and Mathematics with Applications, 43, 111–117.
D’Urso, P., & Giordani, P. (2006). A weighted fuzzy c-means clustering model for fuzzy data. Computational Statistics & Data Analysis, 50, 1496–1523.
Dorigo, M. (1992). Optimization, learning and natural algorithm. (in Italian). Ph.D. thesis, DEI, Politecnico di Milano, Itally.
Dorigo, M., & Gambardella, L.M. (1997). Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation, 1, 53–66.
Dorigo, M., & Stutzle, T. (2004). Ant Colony Optimization. London: Cambridge.
Fisher, R.A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7, 179–188.
Gustafson, D.E., & Kessel, W.C. (1979). Fuzzy clustering with a fuzzy covariance matrix. in: Proceedings of IEEE Conference on Decision and Control, San Diego, CA, pp. 761–766.
Handl, J., & Knowles, J. (2007). An evolutionary approach to multiobjective clustering. IEEE Transactions on Evolutionary Computation, 11, 56–76.
Hansen, P., Ngai, E., Cheung, B.K., & Mladenovic, N. (2005). Analysis of global k-means, an incremental heuristic for minimum sum-of-squares clustering. Journal of Classification, 22, 287–310.
Hathaway, R.J., Bezdek, J.C., & Pedrycz, W. (1996). A parametric model for fusing heterogeneous fuzzy data. IEEE Transactions on Fuzzy Systems, 4, 270–281.
Hung, W.L., & Yang, M.S. (2005). Fuzzy clustering on LR-type fuzzy numbers with an application in Taiwanese tea evaluation. Fuzzy Sets and Systems, 150, 561–577.
Hung, W.L., Yang, M.S., & Lee, E.S. (2010). A robust clustering procedure for fuzzy data. Computers and Mathematics with Applications, 60, 151–165.
Jafari, H.R., Soltani, A.R., & Soltani, M.R. (2013). Measuring the performance of FCM versus PSO for fuzzy clustering problems. International Journal of Industrial Engineering Computations, 4, 387–392.
Jain, A.K., Murty, M.N., & Flynn, P.J. (1999). Data clustering: A review. ACM Computing Surveys, 31, 264–323.
Kanade, P.M., & Hall, L.O. (2004). Fuzzy ant clustering by centroid positioning. in: Proceedings of IEEE International Conference on Fuzzy Systems, Piscataway: IEEE Press, Vol. 1, pp. 371–376.
Kaufmann, A., & Gupta, M.M. (1991). Introduction to Fuzzy Arithmetic: Theory and Applications. London: International Thompson Computer Press.
Kim, D.S., & Kim, Y.K. (2004). Some properties of a new metric on the space of fuzzy numbers. Fuzzy Sets and Systems, 145, 395–410.
Kivijarvi, J., Franti, P., & Nevalainen, O. (2003). Self-adaptive genetic algorithm for clustering. Journal of Heuristics, 9, 113–129.
Likas, A., Vlassis, M., & Verbeek, J. (2003). The global k-means clustering algorithm. Pattern Recognition, 36, 451–461.
Liu, Y., Yi, Z., Wu, H., Ye, M., & Chen, K. (2008). A tabu search approach for the minimum sum-of-squares clustering problem. Information Sciences, 178, 2680–2704.
MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. in: Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley: University of California Press, Vol. 1, pp. 281–297.
Pappis, C.P., & Karacapilidis, N.I. (1993). A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems, 56, 171–174.
Phadke, M.S. (1989). Quality Engineering using Robust Design. Englewood Cliffs, NJ: Prentice-Hall.
Pirzadeh, Y., Shahrabi, J., & Taghavifard, M.T. (2012). Rapid Ant based clustering-genetic algorithm (RAC-GA) with local search for clustering problem. International Journal of Industrial Engineering Computations, 3, 435–444.
Runkler, T.A. (2005). Ant colony optimization of clustering models. International Journal of Intelligent Systems, 20, 1233–1251.
Shelokar, P.S., Jayaraman, V.K., & Kulkarni, B.D. (2004). An ant colony approach for clustering. Analytica Chimica Acta, 509, 187–195.
Sun, L.X., Xie, Y.L., Song, X.H., Wang, J.H., & Yu, R.Q. (1994). Cluster analysis by simulated annealing. Computers & Chemistry, 18, 103–108.
Szmidt, E., & Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 114, 505–518.
Xiao, J., Yan, Y., Zhang, J., & Tang, Y. (2010). A quantum-inspired genetic algorithm for k-means clustering. Expert Systems with Applications, 37, 4966–4973.
Yang, M.S., Hwang, P.Y., & Chen, D.H. (2004). Fuzzy clustering algorithms for mixed feature variables. Fuzzy Sets and Systems, 141, 301–317.
Yang, M.S., & Ko, C.H. (1996). On a class of fuzzy c-numbers clustering procedures for fuzzy data. Fuzzy Sets and Systems, 84, 49–60.
Yang, M.S., & Liu, H.H. (1999). Fuzzy clustering procedures for conical fuzzy vector data. Fuzzy Sets and Systems, 106, 189–200.
Yang, M.S., & Wu, K.L. (2004). A similarity-based robust clustering method. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26, 434–448.
Yong, D., Wenkang, S., Feng, D., & Qi, L. (2004). A new similarity measure of generalized fuzzy numbers and its application to pattern recognition. Pattern Recognition Letters, 25, 875–883.
Ahmadizar, F., & Hosseini, L. (2012). Bi-criteria single machine scheduling with a time-dependent learning effect and release times. Applied Mathematical Modelling, 36, 6203–6214.
Ahmadizar, F., & Soltanpanah, H. (2011). Reliability optimization of a series system with multiple-choice and budget constraints using an efficient ant colony approach. Expert Systems with Applications, 38, 3640–3646.
Al-Sultan, K.S. (1995). A tabu search approach to the clustering problem. Pattern Recognition, 28, 1443–1451.
Al-Sultan, K.S., & Fedjki, C.A. (1997). A tabu search-based algorithm for the fuzzy clustering problem. Pattern Recognition, 30, 2023–2030.
Bagirov, A.M. (2008). Modified global k-means algorithm for minimum sum-of-squares clustering problems. Pattern Recognition, 41, 3192–3199.
Bezdek, J.C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Plenum Press.
Bloch, I. (1999). On fuzzy distances and their use in image processing under imprecision. Pattern Recognition, 32, 1873–1895.
Brucker, P. (1978). On the complexity of clustering problems. in: Beckmenn, M., Kunzi, H.P. (Eds.), Optimization and Operations Research (Vol. 157). Berlin: Springer-Verlag, pp. 45–54.
Chang, D.X., Zhang, X.D., & Zheng, C.W. (2009). A genetic algorithm with gene rearrangement for K-means clustering. Pattern Recognition, 42, 1210–1222.
Chang, P.T., & Lee, E.S. (1994). Ranking of fuzzy sets based on the concept of existence. Computers and Mathematics with Applications, 27, 1–21.
Chu, T., & Tsao, C. (2002). Ranking fuzzy numbers with an area between the centroid point and original point. Computers and Mathematics with Applications, 43, 111–117.
D’Urso, P., & Giordani, P. (2006). A weighted fuzzy c-means clustering model for fuzzy data. Computational Statistics & Data Analysis, 50, 1496–1523.
Dorigo, M. (1992). Optimization, learning and natural algorithm. (in Italian). Ph.D. thesis, DEI, Politecnico di Milano, Itally.
Dorigo, M., & Gambardella, L.M. (1997). Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation, 1, 53–66.
Dorigo, M., & Stutzle, T. (2004). Ant Colony Optimization. London: Cambridge.
Fisher, R.A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7, 179–188.
Gustafson, D.E., & Kessel, W.C. (1979). Fuzzy clustering with a fuzzy covariance matrix. in: Proceedings of IEEE Conference on Decision and Control, San Diego, CA, pp. 761–766.
Handl, J., & Knowles, J. (2007). An evolutionary approach to multiobjective clustering. IEEE Transactions on Evolutionary Computation, 11, 56–76.
Hansen, P., Ngai, E., Cheung, B.K., & Mladenovic, N. (2005). Analysis of global k-means, an incremental heuristic for minimum sum-of-squares clustering. Journal of Classification, 22, 287–310.
Hathaway, R.J., Bezdek, J.C., & Pedrycz, W. (1996). A parametric model for fusing heterogeneous fuzzy data. IEEE Transactions on Fuzzy Systems, 4, 270–281.
Hung, W.L., & Yang, M.S. (2005). Fuzzy clustering on LR-type fuzzy numbers with an application in Taiwanese tea evaluation. Fuzzy Sets and Systems, 150, 561–577.
Hung, W.L., Yang, M.S., & Lee, E.S. (2010). A robust clustering procedure for fuzzy data. Computers and Mathematics with Applications, 60, 151–165.
Jafari, H.R., Soltani, A.R., & Soltani, M.R. (2013). Measuring the performance of FCM versus PSO for fuzzy clustering problems. International Journal of Industrial Engineering Computations, 4, 387–392.
Jain, A.K., Murty, M.N., & Flynn, P.J. (1999). Data clustering: A review. ACM Computing Surveys, 31, 264–323.
Kanade, P.M., & Hall, L.O. (2004). Fuzzy ant clustering by centroid positioning. in: Proceedings of IEEE International Conference on Fuzzy Systems, Piscataway: IEEE Press, Vol. 1, pp. 371–376.
Kaufmann, A., & Gupta, M.M. (1991). Introduction to Fuzzy Arithmetic: Theory and Applications. London: International Thompson Computer Press.
Kim, D.S., & Kim, Y.K. (2004). Some properties of a new metric on the space of fuzzy numbers. Fuzzy Sets and Systems, 145, 395–410.
Kivijarvi, J., Franti, P., & Nevalainen, O. (2003). Self-adaptive genetic algorithm for clustering. Journal of Heuristics, 9, 113–129.
Likas, A., Vlassis, M., & Verbeek, J. (2003). The global k-means clustering algorithm. Pattern Recognition, 36, 451–461.
Liu, Y., Yi, Z., Wu, H., Ye, M., & Chen, K. (2008). A tabu search approach for the minimum sum-of-squares clustering problem. Information Sciences, 178, 2680–2704.
MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. in: Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley: University of California Press, Vol. 1, pp. 281–297.
Pappis, C.P., & Karacapilidis, N.I. (1993). A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems, 56, 171–174.
Phadke, M.S. (1989). Quality Engineering using Robust Design. Englewood Cliffs, NJ: Prentice-Hall.
Pirzadeh, Y., Shahrabi, J., & Taghavifard, M.T. (2012). Rapid Ant based clustering-genetic algorithm (RAC-GA) with local search for clustering problem. International Journal of Industrial Engineering Computations, 3, 435–444.
Runkler, T.A. (2005). Ant colony optimization of clustering models. International Journal of Intelligent Systems, 20, 1233–1251.
Shelokar, P.S., Jayaraman, V.K., & Kulkarni, B.D. (2004). An ant colony approach for clustering. Analytica Chimica Acta, 509, 187–195.
Sun, L.X., Xie, Y.L., Song, X.H., Wang, J.H., & Yu, R.Q. (1994). Cluster analysis by simulated annealing. Computers & Chemistry, 18, 103–108.
Szmidt, E., & Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 114, 505–518.
Xiao, J., Yan, Y., Zhang, J., & Tang, Y. (2010). A quantum-inspired genetic algorithm for k-means clustering. Expert Systems with Applications, 37, 4966–4973.
Yang, M.S., Hwang, P.Y., & Chen, D.H. (2004). Fuzzy clustering algorithms for mixed feature variables. Fuzzy Sets and Systems, 141, 301–317.
Yang, M.S., & Ko, C.H. (1996). On a class of fuzzy c-numbers clustering procedures for fuzzy data. Fuzzy Sets and Systems, 84, 49–60.
Yang, M.S., & Liu, H.H. (1999). Fuzzy clustering procedures for conical fuzzy vector data. Fuzzy Sets and Systems, 106, 189–200.
Yang, M.S., & Wu, K.L. (2004). A similarity-based robust clustering method. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26, 434–448.
Yong, D., Wenkang, S., Feng, D., & Qi, L. (2004). A new similarity measure of generalized fuzzy numbers and its application to pattern recognition. Pattern Recognition Letters, 25, 875–883.