Fuzzy Sensitivity Analysis and Its Application

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.

[1]  Jean-Luc Marichal,et al.  On Sugeno integral as an aggregation function , 2000, Fuzzy Sets Syst..

[2]  Alfredo Vellido,et al.  Neural networks in business: a survey of applications (1992–1998) , 1999 .

[3]  Kaoru Hirota,et al.  Improved Debt Rating Model Using Choquet Integral , 2005, Journal of Advanced Computational Intelligence and Intelligent Informatics.

[4]  Edward I. Altman,et al.  FINANCIAL RATIOS, DISCRIMINANT ANALYSIS AND THE PREDICTION OF CORPORATE BANKRUPTCY , 1968 .

[5]  Kaoru Hirota,et al.  Differentiation of the Choquet Integral and Its Application to Long-term Debt Ratings , 2000, J. Adv. Comput. Intell. Intell. Informatics.

[6]  Michio Sugeno,et al.  Fuzzy t -conorm integral with respect to fuzzy measures: generalization of Sugeno integral and choquet integral , 1991 .

[7]  Zhongliang Jing,et al.  Nonlinear fusion for face recognition using fuzzy integral , 2007 .

[8]  R. C. Merton,et al.  On the Pricing of Corporate Debt: The Risk Structure of Interest Rates , 1974, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[9]  G. Choquet.  Theory of capacities , 1954 .

[10]  R. Jarrow,et al.  A Markov Model for the Term Structure of Credit Risk Spreads , 1997 .

[11]  Didier Dubois,et al.  A class of fuzzy measures based on triangular norms , 1982 .

[12]  Jiqing Qiu,et al.  On the restudy of fuzzy complex analysis: Part II. The continuity and differentiation of fuzzy complex functions , 2001, Fuzzy Sets Syst..

[13]  David J. Hand,et al.  Statistical Classification Methods in Consumer Credit Scoring: a Review , 1997 .

[14]  Toshihiro Kaino.  Composite Fuzzy Measure and Its Application to Investment Decision Making Problem , 2002 .

[15]  Gwo-Hshiung Tzeng,et al.  A Non-Additive Model for Evaluating Airline Service Quality , 2007 .

[16]  E. Altman,et al.  ZETATM analysis A new model to identify bankruptcy risk of corporations , 1977 .

[17]  James H. Scott.  The probability of bankruptcy: A comparison of empirical predictions and theoretical models , 1981 .

[18]  Pamela K. Coats,et al.  Recognizing Financial Distress Patterns Using a Neural Network Tool , 1993 .

[19]  Michio Sugeno,et al.  Fuzzy Measure and Fuzzy Integral , 1972 .

[20]  Vicenç Torra,et al.  Generalized transformed t-conorm integral and multifold integral , 2006, Fuzzy Sets Syst..

[21]  K. Hirota,et al.  Differentiation of the Choquet integral of a nonnegative measurable function , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[22]  Witold Pedrycz,et al.  Face recognition: A study in information fusion using fuzzy integral , 2005, Pattern Recognit. Lett..

[23]  Congxin Wu,et al.  On Henstock integral of fuzzy-number-valued functions (I) , 2001, Fuzzy Sets Syst..

[24]  Yi-Chung Hu,et al.  Functional-link net with fuzzy integral for bankruptcy prediction , 2007, Neurocomputing.

[25]  Eduardo S. Schwartz,et al.  A Simple Approach to Valuing Risky Fixed and Floating Rate Debt , 1995 .

[26]  Wen-Tsann Lin,et al.  Performance evaluation for introducing statistical process control to the liquid crystal display industry , 2008 .