模糊聚合網路能將資訊以階層的方式進行整合，此方法模仿了人類的決策流程並考量決策過程中的補償特性，分析的結果不僅捕捉了問題的決策要素而能以一組規則的方式呈現，更能辨識出決策準則間的相對重要性，來協助偵測對於決策過程沒有貢獻的多餘屬性。然而，以傳統坡度法為基礎的訓練方法，容易得到局部最佳解，並要求聚合函數連續且可微。為提升模糊聚合網路的效能與應用性，本研究提出以基因演算法和粒子群演算法為基礎的訓練方法來決定模糊聚合網路中的權重與參數，並使用七組具有不同決策準則數量和兩個電子電器業投資環境評估與餐飲業位址選擇的案例來進行效益的比較。針對實驗結果所進行的統計分析說明了本研究所提出以啟發式演算法為基礎的訓練方法優於傳統以坡度法為基礎的訓練方法，不僅有更好的歸納能力並產生更精確且可靠的估計。本研究所提出的方法可用於不同類型的模糊運算子，而有更廣泛的適用範圍。

Fuzzy-connective-based aggregation networks are capable of aggregating information in a hierarchical manner. It simulates the human decision-making process and taking the compensation into consideration. The result can be interpreted as a set of rules that capture an abstract model of the problem. Identifying the relative importance of criteria can also help detect redundant features that do not contribute to the decision-making process. Conventional gradient-based learning approach tends to generate local solutions, and requires the aggregation function to be continuous and differentiable. In order to enhance the effectiveness and applicability, this study proposed GA-based and PSO-based learning approaches to determine the weights and parameters in fuzzy-connective-based aggregation networks. The effectiveness of our proposed methods are demonstrated using seven datasets with different number of criteria and two practical cases with regard to investment environment evaluation and location selection. Statistical analysis of the experimental results confirms that the proposed approaches outperform the conventional method, having better generalization ability and generating more accurate and reliable estimates. The proposed approach is well suited to a broad range of fuzzy aggregation connectives, which further expands its applicability.

[1] Chang, C.A. and Su, C.T., A comparison of statistical regression and neural network methods in modeling measurement errors for computer vision inspection systems, Computers Industrial Engineering, vol.28, no.3, pp.593–603, 1995.
[2] Chiang, J.H. and Chen, Y.C., Incorporating fuzzy operators in the decision network to improve classification reliability, Computers and Electrical Engineering, vol.28, pp.547–560, 2002.
[3] Grabisch, M., Marichal, J.L., Mesiar, R., and Pap, E., Aggregation functions, Cambridge University Press, New York, 1992.
[4] Krishnapuram, R. and Lee, J., Fuzzy-connective-based hierarchical aggregation networks for decision making, Fuzzy Sets and Systems, vol.46, pp.11–27, 1992.
[5] Krishnapuram, R. and Lee, J., Fuzzy-set-based hierarchical networks for information fusion in computer vision, Neural Networks, vol.5, pp.335–350, 1992.
[6] Torra, V., Information fusion in data mining, Sprnger-Verlag, New York, 2003.
[7] Sexton, R.S., Dorsey, R.E., and Johnson, J.D., Toward global optimization of neural networks: A comparison of the genetic algorithm and backpropagation, Decision Support Systems, vol.22, pp.171–185, 1998.
[8] Goldberg, D.E., Genetic algorithms in search, optimization and machine learning, Addison-Wesley, New York, 1989.
[9] Holland, J.H., Adaption in natural and artificial systems, The University of Michigan Press, Ann Arbor, 1975.
[10] Kennedy, J. and Eberhard, R.C., Particle swarm optimization, Proceedings of the 1995 IEEE International Conference on Neural Networks, vol.4, pp.1942–1948, 1995.
[11] Venkatesan, D., Kannan, K., and Saravanan, R., A genetic algorithm-based artificial neural network model for the optimization of machining processes, Neural Computing and Applications, vol.18, pp.135–140, 2009.
[12] Liang, Y.H., Combining seasonal time series ARIMA method and neural networks with genetic algorithms for predicting the production value of the mechanical industry in Taiwan, Neural Computing and Applications, vol.18, pp.833–841, 2009.
[13] Leung, K.F., Leung, F.H.F., Lam, H.K., and Ling, S.H., Application of a modified neural fuzzy network and an improved genetic algorithm to speech recognition, Neural Computing and Applications, vol.16, pp.419–431, 2007.
[14] Wu, C.H., Tzeng, G.H., Goo, Y.J., and Fang W.C., A real-valued genetic algorithm to optimize the parameters of support vector machine for predicting bankruptcy, Expert Systems with Applications, vol.32, pp.397–408, 2007.
[15] Pan, W.T., Forecasting classification of operating performance of enterprises by ZSCORE combining ANFIS and genetic algorithm, Neural Computing and Applications, vol.18, pp.1005–1011, 2009.
[16] Rumelhart, D.E., McClelland, J.M., and the PDP Research Group, Parallel Distributed Processing, The MIT Press, Cambridge, 1986.
[17] Dyckhoff, H. and Pedrycz, W., Generalized means as a model of compensation connectives, Fuzzy Sets and Systems, vol.14, pp.143–154, 1984.
[18] Zimmermann, H.J. and Zysno, P., Latent connectives in human decision making, Fuzzy Sets and Systems, vol.4, pp.37–51, 1980.
[19] Zimmermann, H.J. and Zysno, P., Decision and evaluations by hierarchical aggregation of information, Fuzzy Sets and Systems, vol.10, pp.243–260, 1983.
[20] Zimmermann, H.J., Fuzzy set theory and its applications, 2nd edition, Maw Chang Book Company, Taipei, 1991.
[21] Yang, Z.X. and Zhang, Z.J., Hierarchical network-based safety assessment decision support system for thermal power plants, International Journal of Innovative Computing, Information and Control, vol.6, no.7, pp.2955–2964, 2010.
[22] Lin, L. and Lee, H.M., A new algorithm of software quality evaluation for user satisfaction, International Journal of Innovative Computing, Information and Control, vol.4, no.10, pp.2639–2647, 2008.
[23] Guo, H.Y., Structural damage detection using information fusion techniques, Mechanical Systems and Signal Processing, vol.20, pp.1173–1188, 2006.
[24] Li, R.Q., Chen, J., and Wu, X., Fault diagnosis for rotating machinery using knowledge-based fuzzy neural network, Applied Mathematics and Mechanics, vol.27, no.1, pp.99–108, 2006.
[25] Sangle, P.S. and George, S.M., Alternate neural network models as supervised classifiers for satellite data, Journal of Environmental Informatics, vol.6, no.2, pp.80–92, 2005.
[26] Chiang, J.H., Choquet fuzzy integral-based hierarchical networks for decision analysis, IEEE Transactions on Fuzzy Systems, vol.7, no.1, pp.63–71, 1999.
[27] Chiang, J.H. and Kuo, Y.H., Learning decision functions in the fuzzy γ-models, International Journal on Artificial Intelligence Tools, vol.9, no.4, pp.459–471, 2000.
[28] Herrera, F., Lozano, M., and Verdegay, J.L., Tackling real-coded genetic algorithms: operators and tools for behavioral analysis, Artificial Intelligence Review, vol.12, pp.265–319, 1998.
[29] Dorsey, R.E. and Mayer, W.J., Genetic algorithms for estimation problems with multiple optima, nondifferentiability, and other irregular features, Journal of Business and Economic Statistics, vol.13, no.1, pp.53–66, 1995.
[30] Haupt, R.L. and Haupt, S.E., Practical genetic algorithms, 2nd edition, John Wiley & Sons, Inc., New Jersey, 2004.
[31] Song, X. and Liu, X., ETL tasks matching and scheduling based on genetic algorithm, ICIC Express Letters, vol.4, no.4, pp.1245–1250, 2010.
[32] Lin, F.T., Performance comparison of differential evolution and genetic algorithms for the fuzzy transportation problem, ICIC Express Letters, vol.4, no.6, pp.2469–2474, 2010.
[33] Chung, H.Y., Ou, S.C., and Chung, C.Y., Drug Design via Novel Directivity Genetic Algorithms and Lyapunov Principle, International Journal of Innovative Computing, Information and Control, vol.5, no.7, pp.2061–2070, 2009.
[34] Engelbrecht, A. P., Fundamentals of computational swarm intelligence, John Wiley & Sons Ltd, Wiltshire, 2005.
[35] Blum, C. and Merkle, D., Swarm intelligence: introduction and applications, Springer-Verlag, Berlin, 2008.
[36] Panduro, M.A., Brizuela, C.A., Balderas L.I. and Acosta, D.A., A comparison of genetic algorithms, particle swarm optimization and the differential evolution method for the design of scannable circular antenna arrays, Progress In Electromagnetics Research B, vol.13, pp.171–186, 2009.
[37] Juang, C.F., A hybrid of genetic algorithms and particle swarm optimization for recurrent network design, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol.34, no.2, pp.997–1006, 2004.
[38] Elragal, H.M., Improving neural networks prediction accuracy using particle swarm optimization combiner, International Journal of Neural Systems, vol.19, no.5, pp.387–393, 2009.
[39] Chang, J.F. and Shi, P., Using investment satisfaction capability index based particle swarm optimization to construct a stock portfolio, Information Sciences, vol.181, pp.2989–2999, 2011.
[40] Wu, Q. and Law, R., Complex system fault diagnosis based on a fuzzy robust wavelet support vector classifier and an adaptive Gaussian particle swarm optimization, Information Sciences, vol.180, pp.4514–4528, 2010.
[41] Su, M.C. and Chang, H.T., Application of neural networks incorporated with real-valued genetic algorithms in knowledge acquisition, Fuzzy Sets and Systems, vol.112, pp.85–97, 2000.
[42] Sivanandam, S.N. and Deepa, S.N., Introduction to genetic algorithms, Sprnger-Verlag, New York, 2008.
[43] Wright, A.H., Genetic algorithms for real parameter optimization, in G.J.E. Rawlin (Ed.), Foundations of genetic algorithms, Morgan Kaufmann Publishers, San Mateo, pp.205–218, 1991.
[44] Michalewicz, Z., Genetic algorithms + Data structures = Evolution programs, Sprnger-Verlag, New York, 1992.
[45] De Jong, K.A., An analysis of the behavior of a class genetic adaptive systems, Doctorial dissertation, University of Michigan, 1975.
[46] Gurney, L.J., Mundy, C., and Porteus, M.C., Determining age and growth of abalone using stable oxygen isotopes: a tool for fisheries management, Fisheries Research, vol.72, pp.353–360, 2005.
[47] Hallowell, R., The relationships of customer satisfaction, customer loyalty, and profitability: an empirical study, International Journal of Service Industry Management, vol.7, no.4, pp.27–42, 1996.
[48] Liu, B.C., Energy, income, and quality of life management in U.S.A.: an information systems approach to decision analysis, Tamkang University, Taipei, 1988.
[49] Herrera, E.W., Islam, G., and Hamilton, M., Subjective well-being in cities: a multidimensional concept of individual, social and cultural variables, Applied Research in Quality of Life, vol.4, pp.201–221, 2009.
[50] Cracolici, M.F., Giambona, F., and Cuffaro, M., The determinants of subjective economic well-being: an analysis on Italian-Silc data, Applied Research in Quality of Life, 2011. doi:10.1007/s11482-011-9140-z
[51] Yonk, R.M. and Reilly, S., Citizen involvement & quality of life: exit, voice and loyalty in a time of direct democracy, Applied Research in Quality of Life, 2011. doi:10.1007/s11482-011-9142-x
[52] Nzeadibe, T.C. and Ajaero, C.K., Assessment of socio-economic characteristics and quality of life expectations of rural communities in Enugu State, Nigeria, Applied Research in Quality of Life, vol.5, pp.353–371, 2010.
[53] Farooq, U., Guo, X., Chuang, L.H., Fang, H., Zhuang, G., and Xia, C., Measuring health-related quality of life in Kashin–Beck disease using EQ-5D, Quality of Life Research, vol.20, pp.425–429, 2011.
[54] Kantardzic, M., Data mining: concepts, models, methods, and algorithms, John Wiley & Sons, Inc., New Jersey, 2003.
[55] Witten, I.H. and Frank, E., Data mining: practical machine learning tools and techniques with Java implementation, Morgan Kaufmann Publishers, New York, 2000.
[56] Liu, Z., Liu, A., Wang, C., and Niu, Z., Evolving neural network using real coded genetic algorithm (GA) for multispectral image classification, Future Generation Computer Systems, vol.20, pp.1119–1129, 2004.
[57] Clerc, M., Particle swarm optimization, ISTE Ltd, London, 2006.
[58] Gudise, V.G. and Venayagamoorthy, G.K., Comparison of particle swarm optimization and backpropagation as training algorithms for neural networks, Proceedings of the 2003 IEEE Swarm Intelligence Symposium, pp.110–117, 2003.
[59] Shi, Y. and Eberhart, R. C., Parameter selection in particle swarm optimization, Proceedings of the 7th International Conference on Evolutionary Programming VII, pp.591–600, 1998.
[60] Keegan, W.J., Global Marketing Management, 7th edition, Person Education, Inc., New Jersey, 2002.
[61] Chen, L.H. and Heh, D.C., Evaluation for overseas investment environments: the case of evaluating the Mainland China by electrical and electronic appliance industry, Chiao Ta Management Review, vol.15, no.2, pp.107–127, 1995.
[62] Jain, S.C., International marketing, 6th edition, South-Western, Ohio, 2001.
[63] Parkin, M., Economics, 8th edition, Person Education, Inc., New York, 2008.
[64] O'Sullivan, A. and Sheffrin, S.M., Economics: Principles in action, 4th edition, Pearson Prentice Hall, New Jersey, 2007.
[65] Frank, R.H. and Bernanke, B.S., Principle of economics, 3rd edition, Mc Graw Hill, New York, 2007.
[66] Cateora, P.R. and Graham, J.L., International marketing, 11th edition, Mc Graw Hill, New York, 2002.
[67] Kaiser, S.H., Local Sourcing in China: The Case of Braun Electric (Shanghai) Co. Ltd, Asia Pacific Business Review, vol.3, no.3, pp.64–86, 1997.
[68] Meissner, M., Schmuker, M. and Schneider, G., Optimized particle swarm optimization (OPSO) and its application to artificial neural network training, BMC Bioinformatics, vol.7, no.1, pp.125–135, 2006.
[69] Hu, X., Shi, Y. and Eberhart, R., Recent advances in particle swarm, Congress on Evolutionary Computation, vol.1, pp.90–97, 2004.