## Wei Xu* and Daoli Yang**## |

No. | Variable |

[TeX:] $$x_{1}$$ | Current assets to current liabilities |

[TeX:] $$x_{2}$$ | Cash flow to assets |

[TeX:] $$x_{3}$$ | Cash flow to long-term liabilities |

[TeX:] $$x_{4}$$ | Cash flow to sales |

[TeX:] $$x_{5}$$ | Total liabilities to total assets |

[TeX:] $$x_{6}$$ | Market value of equity to total liabilities |

[TeX:] $$x_{7}$$ | Net working capital to total assets |

[TeX:] $$x_{8}$$ | Net working capital to sales |

[TeX:] $$x_{9}$$ | (Current asset-inventory) to current liabilities |

[TeX:] $$x_{10}$$ | (Current asset-inventory) to sales |

[TeX:] $$x_{11}$$ | Current liabilities to sales |

[TeX:] $$x_{12}$$ | Current assets to total asset |

[TeX:] $$x_{13}$$ | No-credit interval |

[TeX:] $$x_{14}$$ | Net income to total asset |

[TeX:] $$x_{15}$$ | Net earnings to total asset |

[TeX:] $$x_{16}$$ | Sales to total asset |

[TeX:] $$x_{17}$$ | Log (total assets to GNP price-level index) |

[TeX:] $$x_{18}$$ | Earnings before interest and taxes to total asset |

[TeX:] $$x_{E S}$$ | Comments of financial institutions |

The empirical experiment is used to verify whether UCSS can achieve an acceptable predicting performance. With considering the percentage of (25%, 75%), the percentage of (50%, 50%), and the percentage of (75%, 25%), we split the sample up into two groups: the training dataset and the testing dataset. According to the literature [12], it is much more challenge to predict business failure in a longer predicting horizon. Hence we try to challenge it by adopting the datasets of the year [TeX:] $$(t-2)$$, and [TeX:] $$(t-3)$$ to predict business failure at the year [TeX:] $$t$$. For comparison, three individual predicting models, and four combination predicting methods are included as benchmarks. The experiment framework is illustrated in Fig. 3.

Here we take 10-fold cross-validation technique to evaluate the out of sample performance of each method. All computations are performed by the MATLAB R2016 software.

According to the literature [12], the radial basis function (RBF) is adopted to be the kernel function of the SVM. Based on the training datasets, we can search out optimal parameters of kernel functions by the grid-search technique. Given features of BFP, the neural network (NN) is set up to be the back propagation NN algorithm. Thirty times verifications were conducted based on training datasets to select the optimal result as NN’s outputs. Meanwhile, the rule-based expert system with forward chaining is employed as the ES algorithm. Testing datasets are used to verify the out-of-sample performance of each method. Predicting results of the confidence intervals is 95% are illustrated in Figs. 4–9.

Here AUC of ROC curve is employed as the criterion to evaluate the predicting performance of each predicting method for BFP. To observe the changes of predicting performance of each method, we summarized the value of AUC based on the Figs. 4–9, and listed in Table 2. In the following, the predicting performance of each method are compared and analyzed from the horizontal perspective and the vertical perspective.

From Figs. 4, 6, 8, and Table 2, it is quite clearly that the proposed predicting method UCSS has the highest value of AUC. No matter what the sample percentage changes from (25%, 75%) to (75%, 25%), the value of AUC for UCSS is still around 0.84. It means that the UCSS not only has good predicting accuracy but also has reliable predicting stability. The superior performance is derived from the advantages of the uni-int decision making method on dealing with the small sample size. The individual predicting classifier ES and SVM of UCSS also have advantages on predicting with the small sample sizes. Moreover, without weighting determination, UCSS can reduce the interference in the process of calculation and obtain a better predicting performance. Also, the value of AUC for ES (around 0.81) does not have a lot changes with different sample sizes. This is easy to understand. It is because experts of the ES are actual practitioners. Risk management is a key work for them.

Table 2.

Year | Percentage | ES | LR | SVM | CMEW | CMNN | CMRD | CFBSS | UCSS |

(t-2) | (25%, 75%) | 0.8167 | 0.7986 | 0.8264 | 0.8097 | 0.7736 | 0.8319 | 0.8417 | 0.8514 |

(50%, 50%) | 0.8156 | 0.7281 | 0.8031 | 0.7875 | 0.7219 | 0.8000 | 0.8250 | 0.8344 | |

(75%, 25%) | 0.8125 | 0.6750 | 0.8000 | 0.7500 | 0.6625 | 0.7375 | 0.8125 | 0.8375 | |

(t-3) | (25%, 75%) | 0.7347 | 0.6875 | 0.7236 | 0.6972 | 0.6694 | 0.7556 | 0.7639 | 0.7778 |

(50%, 50%) | 0.7313 | 0.6469 | 0.7375 | 0.6969 | 0.6813 | 0.7281 | 0.7625 | 0.7719 | |

(75%, 25%) | 0.7375 | 0.6750 | 0.7250 | 0.6875 | 0.6500 | 0.6625 | 0.7500 | 0.7625 |

While, different from the UCSS, other benchmarks were suffering from the size changing of samples. Most of the rest predicting methods get a better predicting performance with the percentage changing from (75%, 25%) to (25%, 75%). The training sample size is bigger, the value of AUC is higher, the predicting performance is better. The obvious upheaval of results are LR, CMEW, CMNN. While, for SVM, CMRD, CFBSS, the result is different. When the sample size is changing, they always can obtain acceptable predicting results. This advantage is inherited from the superiority of SVM, evidence theory, and SS on dealing with small sample sizes.

Furthermore, from Figs. 5, 7, 9, and Table 2, according to the value of AUC, we can easily summarize a conclusion that the ranking results of each predicting method no matter what the data of the year is adopted do not have big difference. The proposed predicting method UCSS has the highest AUC. The AUC value of UCSS is still around 0.77.

From Figs. 4–9, and Table 2, for each selected predicting method in this study, it is easy to obtain a conclusion that the predicting with the datasets of the year [TeX:] $$(t-2)$$ has a better performance (bigger value of AUC) than predicting with the datasets of the year [TeX:] $$(t-3)$$. It is because that some unexpected incidents might have happened during the longer predicting term. The unexpected incidents may have impact on the firms’ development. This conclusion is same as the literatures [1] and [7].

More specially, for the proposed UCSS, the difference of the AUC value is the second smallest. The smallest one is the CFBSS. It means that both the CFBSS and the UCSS have an excellent fault-tolerant capability for BFP in long predicting term. The biggest is the LR. This because LR is a classical statistical method. The performance of LR depends on the quality of data.

To test the adaptability of the proposed UCSS model, we randomly select 360 listed firms in pair of the Taiwan Stock Exchange (TSE) from years 2010 to 2017 as samples to make a robustness test. According to the literature [24,25], if the stock is classified as “full delivery stock” by TSE, we view the firm is business failure. And “Yuanta Securities”, “KGI” and “Fubon Securities”, which are top three security institutions in Taiwan, are employed as experts of the ES. The “Taiwan Economic Journal Data Bank” database is the data sources. Then we run our new empirical experiment with Taiwan China samples again. The results, which are briefly showed in Table 3, are similar to the empirical results using data of mainland China, although the exact value is different. Because, the operational environment in Taiwan China is more complex than the mainland China. This demonstrates that our proposed predicting model can be widely used for BFP.

Table 3.

Year | Percentage | ES | LR | SVM | CMEW | CMNN | CMRD | CFBSS | UCSS |

(t-2) | (25%, 75%) | 0.8098 | 0.7854 | 0.8277 | 0.7974 | 0.7673 | 0.8304 | 0.8290 | 0.8470 |

(50%, 50%) | 0.8258 | 0.7228 | 0.8041 | 0.7995 | 0.7354 | 0.7983 | 0.8246 | 0.8304 | |

(75%, 25%) | 0.8118 | 0.6643 | 0.8120 | 0.7438 | 0.6542 | 0.7304 | 0.8132 | 0.8439 | |

(t-3) | (25%, 75%) | 0.7455 | 0.6770 | 0.7332 | 0.6991 | 0.6816 | 0.7490 | 0.7650 | 0.7799 |

(50%, 50%) | 0.7366 | 0.6560 | 0.7266 | 0.7002 | 0.6775 | 0.7394 | 0.7703 | 0.7664 | |

(75%, 25%) | 0.7490 | 0.6201 | 0.7286 | 0.6734 | 0.6103 | 0.6485 | 0.7571 | 0.7704 |

In this study, the research margin of combination models for predicting business failure was extended by introducing a novel unweighted combination method (UCSS). For UCSS, the combination method, which is used to integrate the results of each basal classifiers without weighting, is the novel uni-int decision making method. This method is developed based on the soft set theory. In such a way that the dilemma of weighting for most combination predicting methods can be effectively bypassed. Compared with other selected benchmark methods, UCSS demonstrates its excellent performance when it is applied to predict the business failure under all sample sizes in the age of big data. In years to come, for a better performance of BFP, we will make further efforts on the theoretical and systematical work about the individual predicting classifier. Besides, we will continue to focus on the combining or integrating method to construct some more excellent predicting models for BFP, especially with a large volume data.

He received Ph.D. degrees in School of Economics and Business Administration from Chongqing University in 2015. Since October 2016, he is with the School of Business from Jiangnan University as an associate professor. His current research interests include business failure prediction and failure management.

- 1 W. Xu, Z. Xiao, "Soft set theory oriented forecast combination method for business failure prediction,"
*Journal of Information Processing Systems*, vol. 12, no. 1, pp. 109-128, 2016.doi:[[[10.3745/JIPS.04.0016]]] - 2 X. Zhao, K. Yeung, Q. Huang, X. Song, "Improving the predictability of business failure of supply chain finance clients by using external big dataset,"
*Industrial Management & Data Systems*, vol. 115, no. 9, pp. 1683-1703, 2015.doi:[[[10.1108/IMDS-04-2015-0161]]] - 3 W. Xu, Z. Xiao, X. Dang, D. Yang, X. Yang, "Financial ratio selection for business failure prediction using soft set theory,"
*Knowledge-Based Systems*, vol. 63, pp. 59-67 2014. doi:[[[10.1016/j.knosys.2014.03.007]]] - 4 W. Xu, Y. Pan, W. Chen, H. Fu, "Forecasting corporate failure in the Chinese energy sector: a novel integrated model of deep learning and support vector machine,"
*Energies*, vol. 12, no. 12, 2019.doi:[[[10.3390/en12122251]]] - 5 E. I. Altman, "Financial ratios, discriminant analysis and the prediction of corporate bankruptcy,"
*Journal of Finance*, vol. 23, no. 4, pp. 589-609, 1968.doi:[[[10.2307/2978933]]] - 6 J. A. Ohlson, "Financial ratios and the probabilistic prediction of bankruptcy,"
*Journal of Accounting Research*, vol. 18, no. 1, pp. 109-131, 1980.doi:[[[10.2307/2490395]]] - 7 L. Wang, C. Wu, "Business failure prediction based on two-stage selective ensemble with manifold learning algorithm and kernel-based fuzzy self-organizing map,"
*Knowledge-Based Systems*, vol. 121, pp. 99-110, 2017.doi:[[[10.1016/j.knosys.2017.01.016]]] - 8 H. Li, J. Sun, B. L. Sun, "Financial distress prediction based on OR-CBR in the principle of k-nearest neighbors,"
*Expert Systems with Applications*, vol. 36, no. 1, pp. 643-659, 2009.doi:[[[10.1016/j.eswa.2007.09.038]]] - 9 D. Wang, X. Song, W. Yin, J. Yuan, "Forecasting core business transformation risk using the optimal rough set and the neural network,"
*Journal of Forecasting*, vol. 34, no. 6, pp. 478-491, 2015.doi:[[[10.1002/for.2349]]] - 10 Y. Zelenkov, E. Fedorova, D. Chekrizov, "Two-step classification method based on genetic algorithm for bankruptcy forecasting,"
*Expert Systems with Applications*, vol. 88, pp. 393-401, 2017.doi:[[[10.1016/j.eswa.2017.07.025]]] - 11 L. Zhou, Y. W. Si, H. Fujita, "Predicting the listing statuses of Chinese-listed companies using decision trees combined with an improved filter feature selection method,"
*Knowledge-Based Systems*, vol. 128, pp. 93-101, 2017.doi:[[[10.1016/j.knosys.2017.05.003]]] - 12 J. Sun, H. Fujita, P. Chen, H. Li, "Dynamic financial distress prediction with concept drift based on time weighting combined with AdaBoost support vector machine ensemble,"
*Knowledge-Based Systems*, vol. 120, pp. 4-14, 2017.doi:[[[10.1016/j.knosys.2016.12.019]]] - 13 J. M. Bates, C. W. Granger, "The combination of forecasts,"
*Journal of the Operational Research Society*, vol. 20, no. 4, pp. 451-468, 1969.doi:[[[10.2307/2982011]]] - 14 Z. Xiao, X. Yang, Y. Pang, X. Dang, "The prediction for listed companies’ financial distress by using multiple prediction methods with rough set and Dempster–Shafer evidence theory,"
*Knowledge-Based Systems*, vol. 26, pp. 196-206, 2012.doi:[[[10.1016/j.knosys.2011.08.001]]] - 15 D. Molodtsov, "Soft set theory: first results,"
*Computers & Mathematics with Applications*, vol. 37, no. 4-5, pp. 19-31, 1999.custom:[[[-]]] - 16 F. Feng, Y. Li, N. Cagman, "Generalized uni–int decision making schemes based on choice value soft sets,"
*European Journal of Operational Research*, vol. 220, no. 1, pp. 162-170, 2012.doi:[[[10.1016/j.ejor.2012.01.015]]] - 17 H. Li, Y. H. Xu, L. Yu, "Predicting hospitality firm failure: mixed sample modelling,"
*International Journal of Contemporary Hospitality Management*, vol. 29, no. 7, pp. 1770-1792, 2017.doi:[[[10.1108/IJCHM-03-2015-0092]]] - 18 A. I. Dimitras, S. H. Zanakis, C. Zopounidis, "A survey of business failures with an emphasis on prediction methods and industrial applications,"
*European Journal of Operational Research*, vol. 90, no. 3, pp. 487-513, 1996.doi:[[[10.1016/0377-2217(95)00070-4]]] - 19 N. Cagman, S. Enginoglu, "Soft set theory and uni–int decision making,"
*European Journal of Operational Research*, vol. 207, no. 2, pp. 848-855, 2010.custom:[[[-]]] - 20] S. Enginoglu, S. Memis, and B. Arslan, "Comment (2) on soft set theory and uni-int decision-making [European Journal of Operational Research, (2010) 207, 848-855 Comment (2) on soft set theory and uni-int decision-making [European Journal of Operational Research, (2010) 207, 848-855-sciedit-2-03"> Enginoglu , S. , Memis , S. , & Arslan , B. ( 2018 ). Comment (2) on soft set theory and uni-int decision-making [European Journal of Operational Research, (2010) 207, 848-855] .
*Journal of New Theory*,( 25 ), 84 - 102 , custom:[[[ - ]]].*2018* - 21 F. Feng, J. Cho, W. Pedrycz, H. Fujita, T. Herawan, "Soft set based association rule mining,"
*Knowledge-Based Systems*, vol. 111, pp. 268-282, 2016.doi:[[[10.1016/j.knosys.2016.08.020]]] - 22 J. H. Min, Y. C. Lee, "Bankruptcy prediction using support vector machine with optimal choice of kernel function parameters,"
*Expert Systems with Applications*, vol. 28, no. 4, pp. 603-614, 2005.doi:[[[10.1016/j.eswa.2004.12.008]]] - 23 A. P. Bradley, "The use of the area under the ROC curve in the evaluation of machine learning algorithms,"
*Pattern Recognition*, vol. 30, no. 7, pp. 1145-1159, 1997.doi:[[[10.1016/S0031-3203(96)00142-2]]] - 24 F. Lin, C. C. Yeh, M. Y. Lee, "The use of hybrid manifold learning and support vector machines in the prediction of business failure,"
*Knowledge-Based Systems*, vol. 24, no. 1, pp. 95-101, 2011.doi:[[[10.1016/j.knosys.2010.07.009]]] - 25 P. Ravisankar, V. Ravi, I. Bose, "Failure prediction of dotcom companies using neural network–genetic programming hybrids,"
*Information Sciences*, vol. 180, no. 8, pp. 1257-1267, 2010.doi:[[[10.1016/j.ins.2009.12.022]]]