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Author: 黃翠華
Tsui-Hua - Huang
Thesis Title: 群體智能演算法於投資策略、財務預警及通貨發行量預測之應用研究
Swarm Intelligence in Constructing Investment Strategies, Financial Crisis Warning and Currency Issuance Volume Forecasting Models
Advisor: 呂永和
Yungho Leu
Committee: 林維垣
Wei-Yuan Lin
陳雲岫
Yun-Shiow Chen
楊維寧
Wei-Ning Yang
洪政煌
Cheng-Huang Hung
Degree: 博士
Doctor
Department: 管理學院 - 管理研究所
Graduate Institute of Management
Thesis Publication Year: 2017
Graduation Academic Year: 105
Language: 英文
Pages: 56
Keywords (in Chinese): 共同基金資料包絡法夏普指標崔那指標廣義迴歸神經網路果蠅演算法蜂群演算法粒子群演算法群體智能演算法
Keywords (in other languages): Treynor Ratio, Fruit Fly Optimization Algorithm, General Regression Neural Networks, Artificial Bee Colony Algorithm
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  • 隨著經濟的發展,科技的進步,人們一直在尋求更有效的預測方式,期能提升管理效能,以達利潤極大化為目標。類神經網路自1957年被提出後,由於不須符合多變量分析的諸多假設,且能處理不同的資料型態,其計算能力、適用性、學習能力與容錯能力不錯,被廣泛的應用於各種領域,如金融財務、電機工程及醫學領域等。隨著時代的演進,網路科技的發達,大數據儼然成為時代的趨勢,加以電腦科技的進步,提高了電腦的運算速度,使得人工智慧益顯重要,經後續學者不斷研發及改進,各式演算法如螞蟻、粒子群、蜂群及果蠅演算法等紛紛被提出,對於處理各種最佳化問題成效斐然。本論文以下三篇研究,實證群體智能演算法對人們在財經領域的貢獻,期望能幫助國家或企業提升管理效能或協助投資人建構投資策略。
    第一篇文章應用果蠅演算法(Fruit Fly Optimization Algorithm,FOA)及神經網路建構基金投資策略,分二階段進行,第一階段應用資料包絡法(Data Envelopment Analysis)、夏普指標(Sharpe index)和崔那指標(Treynor index)選擇投資策略. 第二階段,應用果蠅演算法優化廣義迴歸神經網路參數、廣義迴歸神經網路(General Regression Neural Network,GRNN)及傳統迴歸(Regression),以前1期每日報酬率為投入變數,以當日報酬率為依變數,建構投資模型,以比較各種投資策略之預測績效,發現以夏普指標所選擇的投資組合績效優於其他投資組合,以果蠅演算法優化廣義迴歸神經網路參數建構的投資預測模型績效優於其他模型。
    第二篇文章為應用果蠅演算法及神經網路建構以ZSCORE為基礎的的財務危機預警模型。首先,應用果蠅演算法(FOA)找出最適的ZSCORE 模型投入變數之係數,我們稱之為FOA_ZSCORE模型,其次找出預測值與實際值的差額當作新的依變數,再以果蠅演算法優化廣義迴歸(FOA_GRNN)及廣義迴歸神經網路進行預測,最後將預測結果加回原來的FOA_ZSCORE模型,以提高FOA_ZSCORE模型預測績效,我們分別稱之為FOA_ZSCORE+FOA_GRNN及FOA_ZSCORE+GRNN模型,本研究共包含了ZSCORE、FOA_ZSCORE、FOA_ZSCORE+GRNN及FOA_ZSCORE+FOA_GRNN有4種模型,其中以FOA_ZSCORE+FOA_GRNN模型效果最好,優於其他模型,另以多元雲型迴歸挑選之投入變數,亦能明顯改善預測績效。
    第三篇係應用蜂群演算法(Artificial Bee Colony Algorithm,ABCA)、粒子群演算法(Particle Swarm Optimization,PSO)、廣義迴歸神經網路(GRNN)及傳統多元迴歸(Multiple Regression,MR)模型預測美國通貨發行量,本文首先應用蜂群演算法及粒子群演算法優化廣義迴歸參數,其次建構各種模型以比較預測績效,各種模型包括ABCA+GRNN、PSO+GRNN、GRNN及MR模型,以群體智能演算法優化廣義迴歸神經網路參數建構的預測模型效果最好。
    依上述三篇研究結果均顯示,以群體智能演算法優化廣義迴歸神經網路參數確實能提高預測績效,可供各行業各階層管理人員,根據預測結果做決策以獲取較高報酬及提高管理效能,如提供給國家通貨發行單位,改善現金管理效率,或提供企業經理人及投資人企業營運狀況預警的功能,或建構較佳的基金投資策略。


    To enhance management efficacy and maximize utilities, more effective forecasting methodologies are required in the context of continued economic and technological developments. Due to its computing power, versatility, learning capability and fault tolerance, the neural network has been widely used in finance, electronic engineering and medicine since their inception in 1957. Neural networks are advantageous in that they do not require presumptions typically seen in multivariate analyses and have the ability to handle different data types. Due to the advances in computing technologies and computer networks, the swarm intelligence has become an important technology for problem solving. Algorithms mimicking ants, birds, bees and fruit flies have been developed to seek the optimal solution to a problem. This thesis refers to three studies to illustrate the contribution of swarm intelligence algorithms to the fields of finance and economics.
    In the first study entitled "A Mutual Fund Investment Method Using Fruit Fly Optimization Algorithm and Neural Network", an investing strategy was constructed in two stages. In the first stage, the data envelopment analysis (DEA), Sharpe ratio and Treynor ratio were used to select mutual fund portfolios. In the second stage, the Fruit Fly Optimization Algorithm, General Regression Neural Networks and traditional regression models were used to predict the closing net asset value (NAV) of a mutual fund based on the closing NAV of the previous day. Several experiments were conducted to compare the prediction accuracies and the accumulated return rates of different investment strategies. The results indicated that the investment portfolio constructed by Sharpe ratios outperformed the other portfolios. Furthermore, the investment prediction model built with the fruit fly optimization was superior to the other models.
    The second study is on "Constructing ZSCORE-based Financial Crisis Warning Models Using Fruit Fly Optimization Algorithm and General Regression Neural Network". First, the Fruit Fly Optimization Algorithm (FOA) was used to adjust the values of the coefficients of parameters in the ZSCORE model (FOA_ZSCORE model). Then, the difference between the forecasted value and the actual value of the dependent variable was calculated. Afterwards, the Generalized Regression Neural Network model (GRNN model), with the spread parameter optimized by the FOA (FOA_GRNN model), was used to forecast the difference to improve the forecasting accuracy. Various models, including ZSCORE, FOA_ZSCORE, FOA_ZSCORE+GRNN, and FOA_ZSCORE+FOA_GRNN, were trained and tested. The results showed that FOA_ZSCORE+FOA_GRNN model offered the highest prediction accuracy comparing to the others models.
    The third study is on "Swarm Intelligence and Neural Network in Constructing Prediction Models for Currency Issuance Volume: the US Experience". In this study, the Artificial Bee Colony Algorithm (ABCA) and Particle Swarm Optimization (PSO) were used to optimize the GRNN in constructing a predicting model for the volume of issuance of the United States. The constructed models include ABCA+GRNN, PSO+GRNN, GRNN and Multiple Regression. The experiments showed that the GRNNs optimized by the ABCA and the PSO, respectively, outperformed the non-optimized GRNN and the Multiple Regression model.
    The above three studies suggest that swarm intelligence algorithms can improve the prediction accuracy of a forecasting model. Managers in different industries can use the information as a reference to improve management efficiency and generate operational warnings. Governments can refer to the predictions of the volume of the currency issuance to promote efficiency in cash operation in their central banks. Finally, investors can utilize the swarm intelligence algorithm to construct investment strategies.

    論文摘要 II Abstract IV Acknowledgements VI Table of Contents VII List of Figures XI List of Tables XII Chapter 1 Introduction 1 Chapter 2 Research Method 4 2.1 Research Steps 4 2.2 General Regression Neural Networks 5 2.3 Fruit Fly Optimization Algorithm 6 2.4 Artificial Bee Colony Algorithm 9 2.5 Particle Swarm Optimization 11 Chapter 3 A Mutual Fund Investment Method Using Fruit Fly Optimization Algorithm and Neural Network 14 3.1 Introduction 14 3.2 Literature Reviews 15 3.2.1 Traditional performance indices of mutual funds 15 3.2.2 Mutual fund selection using data envelopment analysis 16 3.2.3 Applications of artificial intelligence in optimization and investment 16 3.3 Research method 17 3.3.1 Research architecture 17 3.3.2 The prediction model 18 3.3.3 Optimizing the GRNN by FOA 19 3.3.4 Performance evaluation 20 3.3.4.1 The directional symmetry 20 3.3.4.2 The return rate on investment 20 3.4 Empirical results and analysis 21 3.4.1 Description of variables 21 3.4.2 The mutual funds selected by different methods 21 3.4.3 Investment performance analysis 22 3.4.3.1 Return rate analysis 22 3.4.3.2 The directional symmetry of different methods 23 3.5 Summary 24 Chapter 4 Constructing ZSCORE-based Financial Crisis Warning Models Using Fruit Fly Optimization Algorithm and General Regression Neural Network 25 4.1 Introduction 25 4.2 Literature reviews 27 4.2.1 Bankruptcy forecast model created with the traditional quantitative method 27 4.2.2 The application of artificial intelligence in predicting bankruptcy 28 4.2.2.1 Construction of a forecast model with artificial intelligence. 28 4.2.2.2 Construction of a forecast model with algorithm and various hybrid models 29 4.3 Methodology 30 4.3.1 The ZSCORE model and its improvement 31 4.3.1.1 The ZSCORE model 31 4.3.1.2 Improvement to the ZSCORE model 32 4.3.1.3 Parameter selection using multivariate adaptive regression splines (MARS) 33 4.3.2 Optimizing the GRNN by FOA 34 4.4 Empirical study 35 4.4.1 Performance metrics 35 4.4.2 Research variables and scope 35 4.4.3 The ZSCORE-based models 36 4.4.4 Performance comparison 38 4.4.4.1 Comparisons on prediction accuracy. 38 4.4.4.2 ROC curve analysis. 40 4.5 Summary 42 Chapter 5 Swarm Intelligence and Neural Network in Constructing Prediction Models for Currency Issuance Volume: the US Experience 44 5.1 Introduction 44 5.2 Literature Reviews 46 5.3 Research Method 48 5.4 Empirical Analysis 51 5.4.1 Research variables and scope 51 5.4.2 Performance metrics 53 5.4.3 Comparison of Prediction Accuracy 53 5.5 Summary 54 Chapter 6 Conclusion 55 References 57 Published Works 63

    [1] Alam, P., Booth, D., Lee, K., & Thordarson, T. (2000). The use of fuzzy clustering algorithm and self-organizing neural networks for identifying potentially failing banks: an experimental study. Expert Systems with Applications, 18(3), 185-199.
    [2] Altman, E. I. (1968). Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. The Journal of Finance, 23(4), 589-609.
    [3] Altman, E. I. (2002). Revisiting Credit Scoring Models in a Basel 2 Environment, In: Ong, M., Credit Rating: Methodologies. Rationale and Default Risk, London Risk Books.
    [4] Bahrani, R. and Khedri, N. (2013). Evaluation of Relative Efficiency and Performance of Companies Using Data Envelopment Analysis (DEA) Approach. Elixir International Journal, Elixir Fin. Mgmt. 56, 13299-13304.
    [5] Basturk, B., & Karaboga, D. (2006). An Artificial Bee Colony (ABC) algorithm for numeric function optimization. Proceedings of IEEE Swarm Intelligence Symposium, Indiana, U.S.A., May 12-14.
    [6] Baumol and Tobin, W. J. (1952). The Transaction Demand for Cash: An Inventory Theoretic Approach. Quarterly Journal of Economics, 66(4), 545-46.
    [7] Beaver, W. (1966). Financial ratios as predictors of failure. Journal of Accounting Research. 4, Issue Empirical Research in Accounting: Selected Studies, 71-111.
    [8] Blum, M. P. (1974). Failing company discriminant analysis. Journal of Accounting Research, 12(1), 1-25.
    [9] Bradley, A. P. (1997). The Use of the Area under the ROC Curve in the Evaluation of Machine Learning Algorithms. Pattern Recognition, 30(7), 1145-1159.
    [10] Casey, C., & Baetczak, N. (1985). Using Operating Cash Flow Data to predict financial Distress: Some Extensions. Journal Accounting Research, 23(1), 384-401.
    [11] Chakraborty, K., Mehrotra, K., Mohan, C., & Ranka, S. (1992). Forecasting the behavior of mu ltivariate time series using neural networks. Neural Networks, 5, 961-970.
    [12] Chang, J. F. (2011). Using investment satisfaction capability index based particle swarm optimization to construct a stock portfolio. Information Sciences, 181(14), 2989–2999.
    [13] Chang, R. S., Chang, J. S. and Lin, P. S. (2009). An ant algorithm for balanced job scheduling in grids. Future Generation Computer Systems, 25(1), 20–27.
    [14] Chen, C. C. (2014). A Study of Particle Swarm Optimization Algorithm Combined with the General Regression Neural Network to Predict TAIEX (Unpublished master’s thesis). Department of Economics, Soochow University, Taiwan, ROC.
    [15] Chen, J. S., Hou, J. L., Wu, S. M., and Chang-Chien. Y. W. (2009). Constructing investment strategy portfolios by combination genetic algorithms. Expert Systems with applications, 36( 2), Part 2, pp. 3824–3828.
    [16] Chen, M. Y. (2013). A hybrid ANFIS model for business failure prediction utilizing particle swarm optimization and subtractive clustering. Information Sciences, 220(20), 180-195.
    [17] Cheng, T. H. (2013). Using Evolutionary Computation to Predict the U.S. Dow Jones (Unpublished master’s thesis). Department of Economics, Soochow University, Taiwan, ROC.
    [18] Chenga, M. Y., Hoangb, N. D., Limantoa, L., & Wua, Y.W. (2014). A novel hybrid intelligent approach for contractor default status prediction. Knowledge-Based Systems, 71, 314-321.
    [19] Ciampi, F., & Gordini, N. (2013). Small Enterprise Default Prediction Modeling through Artificial Neural Networks: An Empirical Analysis of Italian Small Enterprises. Journal of Small Business Management, 51(1), 23-45. doi: 10.1111/j.1540-627X.2012.00376.x.
    [20] Colormi, A., Dorigo, M. and Maniezzo, V. (1991). Distributed Optimization by ant colonies. Proceedings of the 1st European Conference on Artificial Life, 134-142.
    [21] Connor, J. T., Martin, R. D., Member, IEEE, & Atlas, L. E., Member IEEE (1994). Recurrent Neural Networks and Robust Time Series Prediction. IEEE Transactions on Neural Networks, 5(2), 240-254.
    [22] Cortes, C. and Vapnik, V. (1995). Support-Vector Networks, Machine Learning. 20(3), pp. 273-297.
    [23] Deakin, E. B. (1976). A discriminant analysis of predictors of business failure. Journal of Accounting Research, 10(1), 167-180.
    [24] Dorigo M, Maniezzo V and Colormi A. (1991). The Ant System:An Autocatalytic Optimizing Proeess [R], Italy:Politecnico di Milano, 34- 56.
    [25] Edmister, R. O. (1972). An empirical test of financial ratio analysis for small business failure prediction. Journal of Financial and Quantitative Analysis, 7(2), 1477-1493.
    [26] Fethi, M. D. and Pasiouras, F. (2010). Assessing bank efficiency and performance with operational research and artificial intelligence techniques: A survey. European Journal of Operational Research, 204( 2 ), 189–198.
    [27] Friedman (1957). A monetary theory of Nominal Income. The Journal of Political Economy, 79(2), 323-337.
    [28] Friedman, J. H. (1991). Multivariate adaptive regression splines. Annals of Statistics,19, 1-141.
    [29] Friedman, J. H. and C. B. Roosen, (1995). An Introduction to Multivariate Adaptive Regression Splines, Statistical Methods in Medical Research, 4(3), 197-217.
    [30] Frydman, H., Altman, E.I. and Kao, D. (1985). Introducing recursive partitioning for financial classification: the case of financial distress. Journal of Finance 40(1), 269-291.
    [31] Gestel, T.V., Suykens, J.A.K., Baestaens, D.E. Lambrechts, A., Lanckriet, G., Vandaele, B., Moor, B.D. and Vandewalle, J. (2001). Financial Time Series Prediction Using Least Squares Support Vector Machines Within the Evidence Framework, IEEE Transactions on Neural Networks, 12(4), 809-820.
    [32] Gentry, J. A., Newbold, P., & Witford, D. T. (1987). Funds flow components, financial ratios and bankruptcy. Journal of Business Finance and Accounting, 14(4), 596-606.
    [33] Guo, Z., Wang, H., & Liu, Q. (2013). Financial time series forecasting using LPP and SVM optimized by PSO. Methodolgies and Application, Soft Computing, 17(5), 805-818. doi: 10.1007/s00500-012-0953-y.
    [34] Hand, D. J. and Till R. J. (2001). A Simple Generalisation of the Area under the ROC Curve foe Multiple Class Classification Problems. Machine Learning, 45(2), 171-186.
    [35] Holland, J. H. (1975/1992). Adaptation in Natural and Artificial Systems. Cambridge, MA: MIT Press. (First edition, 1975; Second edition, 1992).
    [36] Hopfield, J. J. (1982). Neural Networks and Physical Systems with Emergent Collective Computational Abilities. Proc. Natl. Acad. Sci., 79(8), 2554-2558.
    [37] Hsieh, T. J., Hsiao, H. F. and Yeh, W. C. (2012). Mining financial distress trend data using penalty guided support vector machines based on hybrid of particle swarm optimization and artificial bee colony algorithm. Neurocomputing, 82, 196-206.
    [38] Huang, Y. C. (2010). Fundamental of Money, Banking, and Financial. Taipei City, Taiwan, ROC: Hwa Tai Publishing Company.
    [39] Jerome, T., Connor, R., Martin, D., Member, IEEE, and Atlas, L. E., Member IEEE. (1994). Recurrent Neural Networks and Robust Time Series Prediction, Transactions on Neural Networks, 5(2), 240-254.
    [40] Karaboga, D, (2005). An idea based on honey bee swarm for numerical optimization. Technical Report TR06, Erciyes University, Engineering Faculty, Computer Engineering Department.
    [41] Kennedy, J., & Eberhart, R. C. (1995). Particle swarm optimization. in: Proc. IEEE International Conference on Neural Networks, Perth, Australia, 4, 1942-1948.
    [42] Khashei, M., Rezvan, M. T., Hamadani, A. Z., & Bijari, M. (2013). A bi-level neural-based fuzzy classification approach for credit scoring problems. Complexity, 18, 46-57. doi: 10.1002/cplx.21458
    [43] Koh, H., & Tan, S. (1999). A Neural Network Approach to the Prediction of Going Concern Status. Accounting and Business Research, 29(3), 211-216.
    [44] Koza (1992). Genetic Programming: On the Programming of Computers by Mean of Natural Selection, MIT Press.
    [45] Marquez, L. & Hill, T., Function Approximation Using Backpropagation and General Regression Neural Networks. In Proceeding of the Twenty-Sixth Hawaii International Conference on System Science, 4, pp.607-615, 1993.
    [46] Li, H., Yu, J. L., Yu, L. A., & Sun, J. (2014). The clustering-based case-based reasoning for imbalanced business failure prediction: a hybrid approach through integrating unsupervised process with supervised process. International Journal of systems science, 45(5), 1225-1241.
    [47] Li, X. L. (2003). A New Intelligent Optimization-Artificial Fish Swarm Algorithm. In: PhD thesis, Zhejiang University, China.
    [48] Lu, C. J. (2013). Hybridizing nonlinear independent component analysis and support vector regression with particle swarm optimization for stock index forecasting. Neural Computing and Applications, 23, 2417–2427. doi 10.1007/s00521-012-1198-5.
    [49] Marcek, D. (2004). Stock price forecasting: Statistical, classical and fuzzy neural network approach. Lecture Notes in Artificial Intelligence, Subseries of Lecture Notes in Computer Science, 3131, 41-48.
    [50] Martin, D. (1977). Early warning of bank failure: A logit regression approach. Journal of Banking and Finance, 1(3), 249-276.
    [51] McMullen, P. R., & Strong, R. A. (1998). Selection of Mutual Funds Using Data Envelopment Analysis. Journal of Business and Economic Studies, 4(1), 1-12.
    [52] Merkevicius, E., Garsva, G., & Girdzijauskas, S. (2006). A Hybrid SOM-Altman Model for Bankruptcy Prediction. Lecture Notes in Computer Science, 3994, 364-371.
    [53] Minsky , M. and Papert, S. (1969). Perceptrons -An Essay in Computational Geometry, MIT Press, Cambridge, MA.
    [54] Murthi, B. P. S., Choi , Y. K., & Desai, P. (1997). Efficiency of Mutual Funds and Portfolio Performance Measurement: A Non-Parametric Approach. European Journal of Operational Research, 98(2), pp. 408-418.
    [55] Mustaffa, Z., Yusof, Y., & Kamaruddin, S. S. (2014). Enhanced Artificial Bee Colony for Training Least Squares Support Vector Machines in Commodity Price Forecasting. Journal of Computational Science, 5(2), 196-205. doi: dx.doi.org/10.1016/j.jocs.2013.11.004 (ISI-Q2 with IF:1.567 and SCOPUS indexed).
    [56] Odom, M. D., & Sharda, R. (1990). A Neural Network Model for Bankruptcy Prediction. IJCNN International Joint Conference on Neural Network, 2, 163-168.
    [57] Ohlson, J. A. (1980). Financial ratios and the probabilistic prediction of bankruptcy. Journal of Accounting Research, 18(1), 109-131.
    [58] Pan, W.T.(2009). Forecasting classification of operating performance of enterprises by ZSCORE combining ANFIS and genetic algorithm. Neural Computing and Applications, 18, 1005-1011.
    [59] Pan, W. T. (2010). Performing stock price prediction use of hybrid model. Chinese management studies, 4(1), 77-86.
    [60] Pan, W. T. (2011). Fruit Fly Optimization Algorithm, Taipei City, Taiwan, ROC: Hwa Tai Publishing Company.
    [61] Pan, W. T. (2012). A New Fruit Fly Optimization Algorithm: Taking the Financial Distress Model as An Example. Knowledge‐Based Systems, 26, 69-74.
    [62] Pan, W. T. (2014). Mixed modified fruit fly optimization algorithm with general regression neural network to build oil and gold prices forecasting model. Kybernetes, 43(7), 1053 - 1063.
    [63] Rosenblatt, F. (1957). The perceptron: A perceiving and recognizing automaton (Project PARA). Buffalo, New York Cornell Aeronautical Laboratory Report No. 85-460-1.
    [64] Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning Representations by Back-Propagating Errors. Letters To Nature, 323, 533-536.
    [65] Serrano-Cinca, C. (1996). Self organizing neural networks for financial diagnosis. Decision Support Systems, 17(3), 227-238.
    [66] Shao Y.E. (2013). Prediction of Currency Volume Issued in Taiwan Using a Hybrid Artificial Neural Network and Multiple Regression Approach. Mathematical Problems in Engineering, 2013, Article ID676742, 9 pages.
    [67] Sharpe, W. F. (1966). Mutual Fund Performance. Journal of Business, 39(1), Part 2, 119-138.
    [68] Shayanfar, H. A., Ghasemi, A., Abedinia, O., Izadfar, H. R. & Amjady, N. (2012). Optimal PID Power System Stabilizer Tuning Via Artificial Bee Colony. Technical and Physical Problems of Engineering, Issue 12, 4(3), 75-82.
    [69] Shin, K. S., Lee, K. J., & Kim, H. J.(2004). Support vector machines approach to pattern detection in bankruptcy prediction and its contingency. Lecture Notes In Computer Science, 3316, 1254-1259.
    [70] Specht, D. F. (1991). A General Regression Neural Network. IEEE Transactions on Neural Networks, 2(6), 568-576.
    [71] Tam, K. Y., & Kiang, M. (1992). Managerial Applications of Neural Networks: The Case of Bank Failure Predictions. Management Science, 38(7), 926-947.
    [72] Tien, H. C. (2003). Factors Contributing to an Increase in Currency in Circulation in Taiwan, Central Bank of China Quarterly, 25 (4), 65-72.
    [73] Treynor, J. L. (1965). How to Rate Management Investment Funds. Harvard 84 Business Review, 43, 63-75.
    [74] Yang, S. Y. (2011). Pattern Recognition and Intelligent Computing-Realization of Matlab Technology (2nd Version). China: Publishing House of Electronics Indstry.
    [75] Zadeh, L. A. (1965). Fuzzy sets. Information and Control 8(3), 338–353, doi:10.1016/s0019-9958(65)90241-x.
    [76] Zhang Y., Wang S., & Ji, G., (2013). A Rule-Based Model for Bankruptcy Prediction Based on an Improved Genetic Ant Colony Algorithm. Mathematical Problems in Engineering, 2013, 10 pages, doi: 10.1155/2013/753251.
    [77] Zhou, L., Lai, K.K. & Yen, J. (2014). Bankruptcy prediction using SVM models with a new approach to combine features selection and parameter optimisation. International Journal of Systems Science, 45(3), 241-253.
    [78] Zmijewski, M. (1984). Methodological issues related to the estimation of financial distress prediction models. Journal of Accounting Research, 22, 59-82.

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