Abstract
In this study, we are concerned with the concept, properties and algorithms of differentiation of the Choquet integral. The differentiation of the Choquet integral of a nonnegative measurable function is studied in the setting of sensitivity analysis. It is shown that the differentiation of Choquet integral reflects a way in which the aggregation is sensitive to the function being aggregated. The aggregation function using fuzzy integral could be viewed central to data-mining, the business process mining, web-marketing, e-commerce and the other pattern-matching problems in economics. Next, the differentiation of the Choquet integral is extended to the differentiation of the generalized t-conorm integral. Four types of the differentiation of the generalized t-conorm integrals (namely, Choquet integral, Sugeno integral, and the other generalized t-conorm integrals) are discussed and compared with regard to their sensitivity properties. Lastly, the Choquet integral is applied to the credit risk analysis (long-term debt rating ) to make clear the significance of them, especially, this differentiation is shown to be an effective sensitivity analysis tool which gives us how much evaluation of each index influence to the total evaluation on the corporations.
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References
Altman, E.I.: Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance 23, 189–209 (1969)
Altman, E.I., Haldeman, R.G., Narayama, P.: ZETA analysis: a new model to identify bankruptcy risk of corporations. Journal of Banking and Finance 1, 29–54 (1977)
Chen, S.H., Yang, C.C., Lin, W.T., Yeh, T.M.: Performance evaluation for introducing statistical process control to the liquid crystal display industry. International Journal of Production Economics 111(1), 80–92 (2008)
Chen, X., Xiao, Z.J.G.: Nonlinear fusion for face recognition using fuzzy integral. Communications in Nonlinear Science and Numerical Simulation 12, 823–831 (2005)
Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–295 (1953)
Coats, P., Fant, K.: Recognizing financial distress patterns using a neural network tool. Financial Management 22(3), 142–155 (1993)
Daiamond Inc: Ranking of Japanese corporations. Daiamond Inc 18, 26–74 (1997)
Dubois, D., Prade, H.: A class of fuzzy measures based on triangular norms. Internat. J. Gen. Systems 8, 43–61 (1982)
Hand, D.J., Henley, W.E.: Statistical classification methods in consumer credit scoring: a review. J.R. Statist. Soc. A 3, 523–541 (1997)
Hu, Y.C., Tseng, F.M.: Functional-link net with fuzzy integral for bankruptcy prediction. Neurocomputing 70(16-18), 2959–2968 (2007)
Jarrow, A.R., Lando, D., Turnbull, S.M.: A Markov model for the term structure of credit risk spreads. Review of Financial Studies 10(2), 481–523 (1997)
Kaino, T., Hirota, K.: Differentiation of the Choquet integral of nonnegative measurable function.In: Proc. of FUZZ IEEE 1999, Seoul (1999)
Kaino, T., Hirota, K.: Y-CG derivative of fuzzy relations and its application to sensitivity analysis. The International Journal of Fuzzy Systems 1(2), 129–132 (1999)
Kaino, T., Hirota, K.: Differentiation of the Choquet integral and its application to long-term debt ratings. Journal of Advanced Computational Intelligence 4(1), 66–75 (2000)
Kaino, T., Hirota, K.: Composite fuzzy measure and its application to investment decision making problem. Journal of Advanced Computational Intelligence 8(3), 252–259 (2004)
Kaino, T., Urata, K., Yoshida, S., Hirota, K.: Improved debt rating model using Choquet integral. Journal of Advanced Computational Intelligence 9(6), 615–621 (2005)
KMV Corporation. Introduction credit monitor, version 4, San Francisco (1995)
Kobayashi: Testing the ordered profit model and its application to corporate bond rating data. institute for Monetary and Economic Studies Discussion, (2000) paper No.2000-J-17
Kwak, K., Pedrycz, W.: Face recognition: A study in information fusion using fuzzy integral. Pattern Recognition Letters 26, 719–733 (2005)
Liou, J.J.H., Tzeng, G.H.: A non-additive model for evaluating airline service quality. Journal of Air Transport Management. (2008) doi:10.1016/j.jairtraman.2006.12.002
Logstaff, A.F., Schwartz, E.S.: A simple approach to valuing risky fixed and floating rate debt. Journal of Finance 50(3), 790–819 (1995)
Marichal, J.L.: On Sugeno integral as an aggregation function. Fuzzy Sets and Systems 114, 347–365 (2000)
Merton, R.C.: On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance 28, 87–109 (1974)
Moody’s Investors Service, Default report (1999), http://www.moodysqra.com/.
Moody’s Japan, K.K.: The Moody’s ratings list (1999)
Murofushi, T., Sugeno, M.: Fuzzy t-conorm integral with respect to fuzzy measures: generalization of Sugeno integral and Choquet integral. Fuzzy Sets and Systems 41, 57–71 (1991)
Narukawa, Y., Torra, V.: Generalized transformed t-conorm integral and multifold integral. Fuzzy Sets and Systems 157, 1384–1392 (2006)
Nihon Keizai Shimbun Inc: All listed Japanese company version, Nikkei management index (2000)
Nihon Keizai Shimbun Inc: Nikkei top-rated company ranking (2000)
Nihon Keizai Shimbun Inc: All listed Japanese company version, Nikkei management index (2001)
Nihon Keizai Shimbun Inc: Nikkei top-rated company ranking (2001)
Scott, J.: The probability of bankruptcy: a comparison of empirical predictions and theoretical models. Journal of Banking and Finance 5(3), 317–344 (1981)
Standard & Poor’s Corporation, Debt ratings criteria: municipal overview (1986)
Sugeno, M.: Fuzzy measure and fuzzy integral. Journal of the Society of Instrument and Control Engineers 8(2), 218–226 (1972)
Toyo Keizai Inc: Toyo Keizai 1999 data bank (1998)
Vellido, A., Lisboa, P.J.G., Vaughan, J.: Neural networks in business: a survey of applications (1992-1998). Expert Systems with Applications 17, 51–70 (1999)
Wu, J.Q.C., Li, F.: On the restudy of fuzzy complex analysis: Part II. The continuity and differentiation of fuzzy complex functions. Fuzzy Sets and Systems 120(3), 517–521 (2001)
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Kaino, T., Hirota, K., Pedrycz, W. (2008). Fuzzy Sensitivity Analysis and Its Application. In: Kahraman, C. (eds) Fuzzy Engineering Economics with Applications. Studies in Fuzziness and Soft Computing, vol 233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70810-0_12
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DOI: https://doi.org/10.1007/978-3-540-70810-0_12
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