Concluding the conformity of XBRL (eXtensible Business Reporting Language) instance documents law to the Benford's law yields apparently different results before and after a company's financial distress. These results bring an idea of finding fraudulent documents from the inspection of financial ratios since the unacceptable conformity implies a large likelihood of a fraudulent document. Fuzzy support vector machines models are developed to implement such an idea. The dependent variable is a fuzzy variable quantifying the conformity of an XBRL instance document to the Benford's law; whereas, independent variables are financial ratios. Nevertheless, insufficient data are available to define any membership function for describing the fuzziness in independent and dependent variables, but the interval factor method is introduced to express that fuzziness. Using the resulting fuzzy support vector machines model, it is suggested that the price-to-book ratio versus equity ratio may be used to classify the priority of auditing XBRL instance documents. The misclassification rate is less than 30 \%. In conclusion, a new and promising application of fuzzy support vector machines algorithm has been found in this study.
fuzzy support vector machines algorithm, XBRL, Benford's law
Full TextPDF - Viewed/Downloaded: 134 Times
 Sheu Guang Yih. “aXBRL: Search of fraudulent XBRL instance documents with an Android app SoftwareX, Vol. 9, 2019.
 Sheu Guang Yih, Chen, Y. X. “A Research of Integrating Fuzzy Support Vector Machines Model and an Android App to Assist the Audit of XBRL Instance Documents”, College Student Research Report, 107-2813-C-309-010-H, MOST, Taiwan, 2019 (in Chinese)
 Hoaglin D. C., Mosteller F., Tukey J. W. “Understanding Robust and Exploratory Data Analysis”, John Wiley & Sons, 2008.
 Greenwood. P. E., Nikulin, M. S. “A Guide to Chi-squared Testing”, John Wiley & Sons, 2008.
 Vapnik, V. “Estimation of Dependences based on Empirical Data”, Springer-Verlag, 1982.
 Kara, Y., Boyacioglu, M. A. Baykan, K. “Predicting direction of stock price index movement using artificial neural networks and support vector machines: The sample of the Istanbul stock exchange”, Expert Systems with Applications, 2011.
 Hua, Z., Xiaoyan, Y. W., Xu, X., Zhang, B. Liang, L. “Predicting corporate financial distress based on integration of support vector machine and logistic regression”, Expert Systems with Applications, 2008.
 Erdogan, B. E. “Prediction of bankruptcy using support vector machines: an application to bank bankruptcy”, Journal of Statistical Computation and Simulation}, 83, 2013.
 Lin, C.-F. and Wang, S. D. “Fuzzy support vector machines”, IEEE Transaction on Neutral Networks, 2002.
 Wei, G. “Interval finite element analysis using interval factor method”, Computational Mechanics, 2007.
 Nigrini, M. J. and Wells, J. T. “Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud Detection, New Jersey, USA: John Wiley & Sons, 2012.
 Kuiper, N. H. “Tests concerning random points on a circle”, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series A., 1960.
 Kolmogorov, A. “Sulla determination empirica di una legge di distribuzione”, Giornale dell’istituto italiano degli attuari, 1993
 Smirnov, N. “Table for estimating the goodness of fit of empirical distributions”, Annals of Mathematical Statistics, 1948.
 Hall, J. A. “Information Technology Auditing”, Cengage Learning, 2010.
 Turnbull, C. S. “Fraud Investigation Using IDEA”, Ekaros Analytical Inc., 2003.
 Hoffman, C. http:// http://xbrl.squarespace.com, 2010.
 Kecman, V. “Learning and Soft Computing, Support Vector Machines, Neural Networks and Fuzzy Logic Models”, The MIT Press, 2001.
 John, P. T. “Sequential Minimal Optimization: a Fast Algorithm for Training Support Vector Machines”, CiteSeerX 10.1.1.43.4376, 1998.
Copyright © 2019 Guang-Yih Sheu
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License