由於資訊快速成長，複雜的資料能夠更容易的被蒐集。因此，如何從數據中找到重要的資訊，已變成非常重要的議題。在資料探勘中，分群分析是一個非常重要的技術。然而，沒有任何一種分群演算法能夠對所有不同的數據集進行正確的分群。因此，本研究提出多目標萬用演算法結合可能性直覺模糊c均值演算法(possibilistic intuitionistic fuzzy c-means, PIFCM)的新分群演算法。為了提供更好的分群結果，本研究考慮多目標分群而不是單目標分群。可能性直覺模糊c均值演算法結合了直覺模糊集合( intuitionistic fuzzy sets, IFSs)與可能性模糊c均值演算法(possibilistic fuzzy c-means, PFCM)。在本研究中，使用三種萬用演算法來改善分群結果，分別是實數型基因演算法、粒子群演算法和梯度進化演算法。因此，本研究提出三種分群演算法，分別是多目標實數型基因演算法為基礎之可能性直覺模糊c均值演算法(MOGA-PIFCM)、多目標粒子群演算法為基礎之可能性直覺模糊c均值演算法(MOPSO-PIFCM)及多目標梯度進化演算法為基礎之可能性直覺模糊c均值演算法(MOGE-PIFCM)。所提出的演算法將使用Ukm、Wine、Wbc、Tae、Vehicle、Pima、Iris、Breast、Liver及Banknote資料集的分群結果和其他分群演算法進行比較，包括直覺模糊c均值演算法、可能性直覺模糊c均值演算法、單目標實數型基因演算法為基礎之可能性直覺模糊c均值演算法、單目標粒子群演算法為基礎之可能性直覺模糊c均值演算法及單目標梯度進化演算法為基礎之可能性直覺模糊c均值演算法。本研究所使用的評比指標為Adjusted Rand Index (ARI)及準確率，根據實驗結果，MOGE PIFCM演算法比起其他演算法能夠獲得更佳的結果。

Due to the rapid growth of information, complicated data and information can be collected more easily. Therefore, how to reveal important information from the data becomes a very important issue. Clustering analysis is an important technique in data mining. However, there is no clustering method which can correctly cluster all different datasets. Thus, this study proposes hybrid of multi-objective meta-heuristics and possibilistic intuitionistic fuzzy c-means (PIFCM) algorithm. In order to provide a better clustering result, this study considers multi-objective clustering instead of single-objective clustering. The PIFCM algorithm combines Atanassov’s intuitionistic fuzzy set (IFSs) with possibilistic fuzzy c-means, (PFCM). In this study, three meta heuristic algorithms are used to improve the clustering results, which are genetic algorithm (GA), particle swarm optimization (PSO) algorithm, and gradient evolution (GE) algorithm. Therefore, there are three clustering algorithms which are proposed including multi-objective GA-based PIFCM (MOGA-PIFCM), multi-objective PSO based PIFCM (MOPSO-PIFCM), and multi-objective GE based PIFCM (MOGE-PIFCM). Their results are compared with those of other clustering algorithms, such as intuitionistic fuzzy c-means (IFCM), possibilistic intuitionistic fuzzy c-means (PIFCM), single-objective GA-PIFCM, single-objective PSO-PIFCM, and single-objective GE-PIFCM using Ukm, Wine, Wbc, Tae, Vehicle, Pima, Iris, Breast, Liver, and Banknote datasets. Adjusted Rand Index and accuracy measures are employed as performance indices for comparison. The experimental result shows that the MOGE-PIFCM can obtain better solutions than the other clustering algorithms in terms of all performance validation indices.

Agard, B., & Penz, B. (2009). A simulated annealing method based on a clustering approach to determine bills of materials for a large product family. International Journal of Production Economics, 117(2), 389-401.
Armano, G., & Farmani, M. R. (2014). Clustering analysis with combination of artificial bee colony algorithm and k-means technique. International Journal of Computer Theory and Engineering, 6(2), 141.
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96.
Atanassov, K. T. (1989). More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 33(1), 37-45.
Attea, B. a. A. (2010). A fuzzy multi-objective particle swarm optimization for effective data clustering. Memetic Computing, 2(4), 305-312.
Bezdek, J. C. (1981). Objective Function Clustering Pattern recognition with fuzzy objective function algorithms (pp. 43-93).
Biswas, R. (1989). Intuitionistic fuzzy subgroups. Paper presented at the Math. Forum.
Bonab, M. B., Hashim, S. Z. M., Alsaedi, A. K. Z., & Hashim, U. R. a. (2015). Modified K-means Combined with Artificial Bee Colony Algorithm and Differential Evolution for Color Image Segmentation Computational Intelligence in Information Systems (pp. 221-231).
Botía, J. F., Cárdenas, A. M., & Sierra, C. M. (2017). Fuzzy cellular automata and intuitionistic fuzzy sets applied to an optical frequency comb spectral shape. Engineering Applications of Artificial Intelligence, 62, 181-194.
Burillo, P., & Bustince, H. (1996). Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems, 78(3), 305-316.
Chaira, T. (2011). A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images. Applied Soft Computing, 11(2), 1711-1717.
Chen, C.-Y., & Ye, F. (2012). Particle swarm optimization algorithm and its application to clustering analysis. Paper presented at the Electrical Power Distribution Networks (EPDC), 2012 Proceedings of 17th Conference on.
Chen, Q., & Mo, J. (2009). Optimizing the ant clustering model based on k-means algorithm. Paper presented at the Computer Science and Information Engineering, 2009 WRI World Congress on.
Coello, C. A. C., Pulido, G. T., & Lechuga, M. S. (2004). Handling multiple objectives with particle swarm optimization. IEEE transactions on evolutionary computation, 8(3), 256-279.
Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation, 6(2), 182-197.
Dunn, J. C. (1973). A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters.
Eberhart, R., & Kennedy, J. (1995). A new optimizer using particle swarm theory. Paper presented at the Micro Machine and Human Science, 1995. MHS'95., Proceedings of the Sixth International Symposium on.
Evangelou, I. E., Hadjimitsis, D. G., Lazakidou, A. A., & Clayton, C. (2001). Data mining and knowledge discovery in complex image data using artificial neural networks. Paper presented at the in Proc. Workshop Complex Reason. Geogr. Data, Paphos.
Faceli, K., De Carvalho, A. C., & De Souto, M. C. (2007). Multi-objective clustering ensemble. International Journal of Hybrid Intelligent Systems, 4(3), 145-156.
Fan, J., Han, M., & Wang, J. (2009). Single point iterative weighted fuzzy C-means clustering algorithm for remote sensing image segmentation. Pattern Recognition, 42(11), 2527-2540.
Fonseca, C. M., & Fleming, P. J. (1993). Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization. Paper presented at the Icga.
Forgy, E. W. (1965). Cluster analysis of multivariate data: efficiency versus interpretability of classifications. biometrics, 21, 768-769.
Fukuyama, Y. (2008). Fundamentals of particle swarm optimization techniques. Modern Heuristic Optimization Techniques: Theory and Applications to Power Systems, 71-87.
Gan, G., Wu, J., & Yang, Z. (2009). A genetic fuzzy k-Modes algorithm for clustering categorical data. Expert Systems with Applications, 36(2), 1615-1620.
Guha, S., Rastogi, R., & Shim, K. (2000). ROCK: A robust clustering algorithm for categorical attributes. Information systems, 25(5), 345-366.
Holland, J. H. (1975). Adaptation in natural and artificial systems. An introductory analysis with application to biology, control, and artificial intelligence. Ann Arbor, MI: University of Michigan Press, 439-444.
Horn, J., Nafpliotis, N., & Goldberg, D. E. (1994). A niched Pareto genetic algorithm for multiobjective optimization. Paper presented at the Evolutionary Computation, 1994. IEEE World Congress on Computational Intelligence., Proceedings of the First IEEE Conference on.
Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of classification, 2(1), 193-218.
Janson, S., & Merkle, D. (2005). A new multi-objective particle swarm optimization algorithm using clustering applied to automated docking. Paper presented at the International Workshop on Hybrid Metaheuristics.
Jiang, B., Wang, N., & Wang, L. (2014). Parameter identification for solid oxide fuel cells using cooperative barebone particle swarm optimization with hybrid learning. International Journal of Hydrogen Energy, 39(1), 532-542.
Kachitvichyanukul, V. (2009). A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery. Computers & Operations Research, 36(5), 1693-1702.
Kackar, R. N. (1985). Off-line quality control, parameter design, and the Taguchi method. journal of Quality Technology, 17(4), 176-188.
Karypis, G., Han, E.-H., & Kumar, V. (1999). Chameleon: Hierarchical clustering using dynamic modeling. Computer, 32(8), 68-75.
Kotsiantis, S., & Pintelas, P. (2004). Recent advances in clustering: A brief survey. WSEAS Transactions on Information Science and Applications, 1(1), 73-81.
Krishna, K., & Murty, M. N. (1999). Genetic K-means algorithm. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 29(3), 433-439.
Krishnapuram, R., & Keller, J. M. (1993). A possibilistic approach to clustering. IEEE Transactions on Fuzzy systems, 1(2), 98-110.
Kuo, R. J., Ho, L. M., & Hu, C. M. (2002). Integration of self-organizing feature map and K-means algorithm for market segmentation. Computers & Operations Research, 29(11), 1475-1493.
Kuo, R. J., & Zulvia, F. E. (2015). The gradient evolution algorithm: A new metaheuristic. Information Sciences, 316, 246-265.
Kuo, R. J., Zulvia, F. E., & Suryadi, K. (2012). Hybrid particle swarm optimization with genetic algorithm for solving capacitated vehicle routing problem with fuzzy demand – A case study on garbage collection system. Applied Mathematics and Computation, 219(5), 2574-2588.
Lee, C.-Y., & Antonsson, E. (2000). Dynamic partitional clustering using evolution strategies. Paper presented at the Industrial Electronics Society, 2000. IECON 2000. 26th Annual Confjerence of the IEEE.
Li, X. (2003). A non-dominated sorting particle swarm optimizer for multiobjective optimization. Paper presented at the Genetic and Evolutionary Computation Conference.
Li, Z., Li, Y., & Xu, L. (2011). Anomaly intrusion detection method based on k-means clustering algorithm with particle swarm optimization. Paper presented at the Information Technology, Computer Engineering and Management Sciences (ICM), 2011 International Conference on.
Lin, K.-P. (2014). A novel evolutionary kernel intuitionistic fuzzy c -means clustering algorithm. IEEE Transactions on Fuzzy systems, 22(5), 1074-1087.
MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. Paper presented at the Proceedings of the fifth Berkeley symposium on mathematical statistics and probability.
Maulik, U., & Bandyopadhyay, S. (2000). Genetic algorithm-based clustering technique. Pattern Recognition, 33(9), 1455-1465.
Maulik, U., Bandyopadhyay, S., & Mukhopadhyay, A. (2011). Multiobjective Genetic Algorithms for Clustering: Applications in Data Mining and Bioinformatics.
Michielssen, E., Ranjithan, S., & Mittra, R. (1992). Optimal multilayer filter design using real coded genetic algorithms. IEE Proceedings J (Optoelectronics), 139(6), 413-420.
Milligan, G. W., & Sokol, L. M. (1980). A two-stage clustering algorithm with robust recovery characteristics. Educational and psychological measurement, 40(3), 755-759.
Mostaghim, S., & Teich, J. (2003). Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO). Paper presented at the Swarm Intelligence Symposium, 2003. SIS'03. Proceedings of the 2003 IEEE.
Özyer, T., Liu, Y., Alhajj, R., & Barker, K. (2004). Multi-objective genetic algorithm based clustering approach and its application to gene expression data. Paper presented at the International Conference on Advances in Information Systems.
Pal, N. R., Pal, K., Keller, J. M., & Bezdek, J. C. (2005). A possibilistic fuzzy c-means clustering algorithm. IEEE Transactions on Fuzzy systems, 13(4), 517-530.
Pedrycz, W., & Rai, P. (2008). Collaborative clustering with the use of Fuzzy C-Means and its quantification. Fuzzy Sets and Systems, 159(18), 2399-2427.
Qasem, S. N., & Shamsuddin, S. M. (2011). Radial basis function network based on time variant multi-objective particle swarm optimization for medical diseases diagnosis. Applied Soft Computing, 11(1), 1427-1438.
Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical association, 66(336), 846-850.
Rousseeuw, P. J., & Kaufman, L. (1990). Finding groups in data: Wiley Online Library Hoboken.
Saatchi, S., & Hung, C. C. (2005). Hybridization of the ant colony optimization with the k-means algorithm for clustering. Paper presented at the Scandinavian Conference on Image Analysis.
Shi, Y. (2001). Particle swarm optimization: developments, applications and resources. Paper presented at the evolutionary computation, 2001. Proceedings of the 2001 Congress on.
Shi, Y., & Eberhart, R. (1998). A modified particle swarm optimizer. Paper presented at the Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on.
Shi, Y., & Eberhart, R. C. (1998). Parameter selection in particle swarm optimization. Paper presented at the International conference on evolutionary programming.
Sivasubramani, S., & Swarup, K. (2011). Multi-objective harmony search algorithm for optimal power flow problem. International Journal of Electrical Power & Energy Systems, 33(3), 745-752.
Srinivas, N., & Deb, K. (1994). Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary computation, 2(3), 221-248.
Sumathi, S., Hamsapriya, T., & Surekha, P. (2008). Evolutionary intelligence: an introduction to theory and applications with Matlab.
Taguchi, G. (1986). Introduction to quality engineering: designing quality into products and processes. Retrieved from
Tan, P.-N. (2006). Introduction to data mining: Pearson Education India.
Van der Merwe, D., & Engelbrecht, A. P. (2003). Data clustering using particle swarm optimization. Paper presented at the Evolutionary Computation, 2003. CEC'03. The 2003 Congress on.
Verma, H., & Agrawal, R. (2015). Possibilistic intuitionistic fuzzy c-means clustering algorithm for MRI brain image segmentation. International Journal on Artificial Intelligence Tools, 24(05), 1550016.
Vinh, N. X., Epps, J., & Bailey, J. (2010). Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. Journal of Machine Learning Research, 11(Oct), 2837-2854.
Wang, K.-P., Huang, L., Zhou, C.-G., & Pang, W. (2003). Particle swarm optimization for traveling salesman problem. Paper presented at the Machine Learning and Cybernetics, 2003 International Conference on.
Wang, N., Zhao, W.-j., Wu, N., & Wu, D. (2017). Multi-objective optimization: A method for selecting the optimal solution from Pareto non-inferior solutions. Expert Systems with Applications, 74, 96-104.
Xu, R., & Wunsch, D. (2005). Survey of clustering algorithms. IEEE Transactions on neural networks, 16(3), 645-678.
Xu, Z., & Wu, J. (2010). Intuitionistic fuzzy C-means clustering algorithms. Journal of Systems Engineering and Electronics, 21(4), 580-590.
Yuqing, P., Xiangdan, H., & Shang, L. (2003). The k-means clustering algorithm based on density and ant colony. Paper presented at the Neural Networks and Signal Processing, 2003. Proceedings of the 2003 International Conference on.
Zadeh, L. A. (1965). Information and control. Fuzzy sets, 8(3), 338-353.
Zhang, Z., Wang, M., Hu, Y., Yang, J., Ye, Y., & Li, Y. (2013). A dynamic interval-valued intuitionistic fuzzy sets applied to pattern recognition. Mathematical Problems in Engineering, 2013.
Zhao, L., Tsujimura, Y., & Gen, M. (1996). Genetic algorithm for fuzzy clustering. Paper presented at the Evolutionary Computation, 1996., Proceedings of IEEE International Conference on.
Zitzler, E., Deb, K., & Thiele, L. (2000). Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary computation, 8(2), 173-195.
Zulvia, F. E. (2015). Cluster analysis using a gradient evolution algorithm.