Using Fuzzy Analytic Hierarchy Process and Hybrid of ...ijiepm.iust.ac.ir/article-1-857-en.pdf ·...

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Using Fuzzy Analytic Hierarchy Process and Hybrid of Higher Order Neural Network for Evaluation Credit Risk of Corporate S. H. Ghodsypour*, M. Salari & V. Delavari Seyed Hassan Ghodsypour, Professor of Industrial Engineering, Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran Meysam Salari, M.Sc. in Industrial Engineering, Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran Vahid Delavari, M.Sc. in Information Technology Management, Shahidbeheshti University, Tehran, Iran Keywords 1 ABSTRACT Banks as financial institutions must estimate the credit risk of their debtors. This is the basis of pricing a loan, determining appropriate interest rates and determining the mortgage required to each borrower. Since the continuity of bank activities largely depends on the amount of credit losses in a particular period, banks should consider the credit quality of their loan portfolio as a collection of debts. In this paper, the calculation of credit risk of corporates applying for loans has been investigated. Using fuzzy analytic hierarchy process, effective criteria for credit risk have been analyzed. The neural network is used to extract an open box model that describes the relationship between effective criteria and the credit risk of the companies who apply for a loan. Neural network model has been run with historical data. Observations have been based on 174 corporate who had taken out a loan from a major Iranian bank named Mellat (All loans had been made during 2005 to 2008). The output of the model can predict credit risk of a corporate by at least 84% accuracy. © 2012 IUST Publication, IJIEPM. Vol. 23, No. 1, All Rights Reserved * Corresponding author. Seyed Hassan Ghodsypour Email: [email protected] June 2012, Volume 23, Number 1 pp. 43-54 http://IJIEPM.iust.ac.ir/ International Journal of Industrial Engineering & Production Management (2012) Credit risk, Default rate, neural network, fuzzy analytic hierarchy process Downloaded from ijiepm.iust.ac.ir at 22:25 IRDT on Wednesday July 29th 2020

Transcript of Using Fuzzy Analytic Hierarchy Process and Hybrid of ...ijiepm.iust.ac.ir/article-1-857-en.pdf ·...

Page 1: Using Fuzzy Analytic Hierarchy Process and Hybrid of ...ijiepm.iust.ac.ir/article-1-857-en.pdf · the amount of credit losses in a particular period, banks should consider the credit

Using Fuzzy Analytic Hierarchy Process and Hybrid of

Higher Order Neural Network for Evaluation Credit Risk

of Corporate

S. H. Ghodsypour*, M. Salari & V. Delavari

Seyed Hassan Ghodsypour, Professor of Industrial Engineering, Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran Meysam Salari, M.Sc. in Industrial Engineering, Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran

Vahid Delavari, M.Sc. in Information Technology Management, Shahidbeheshti University, Tehran, Iran

Keywords 1ABSTRACT

Banks as financial institutions must estimate the credit risk of their

debtors. This is the basis of pricing a loan, determining appropriate

interest rates and determining the mortgage required to each

borrower. Since the continuity of bank activities largely depends on

the amount of credit losses in a particular period, banks should

consider the credit quality of their loan portfolio as a collection of

debts.

In this paper, the calculation of credit risk of corporates applying for

loans has been investigated. Using fuzzy analytic hierarchy process,

effective criteria for credit risk have been analyzed.

The neural network is used to extract an open box model that

describes the relationship between effective criteria and the credit risk

of the companies who apply for a loan. Neural network model has

been run with historical data. Observations have been based on 174

corporate who had taken out a loan from a major Iranian bank named

Mellat (All loans had been made during 2005 to 2008).

The output of the model can predict credit risk of a corporate by at

least 84% accuracy.

© 2012 IUST Publication, IJIEPM. Vol. 23, No. 1, All Rights Reserved

**

Corresponding author. Seyed Hassan Ghodsypour Email: [email protected]

JJuunnee 22001122,, VVoolluummee 2233,, NNuummbbeerr 11

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Credit risk, Default rate,

neural network,

fuzzy analytic hierarchy process

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[email protected]

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.

[5] Caouette, J., Altman, E., Narayanan, p., “Managing

Credit Risk: the NextGreat Financial Challenge” N.Y:

John Wiley & Sons, 1998.

[6] Baesens, B., Van Gestel, T., Viaene, S., Stepanova, M.,

Jsuyken, S., Jvanthienen, “ Benchmarking State-of-the-

Art Classification”, Journal of the Operational Research

Society, 54, 627–635, 2003.

[7] Zuranda, J., “Comparison Of The Performance Of

Several Data Mining Methods For Bad Debt

Recovery In The Healthcare Industry” , The Journal

of Applied Business Research –Volume 21, Number

2, 37-54 Spring 2005.

[8] Huang, C.L., Chen, M.C., Wang, C.J., “Credit Card

Scoring with a Data Mining Approach Based on

Support Vector Machine”, Expert Systems with

Applications 33, 847–856, 2007.

[9] Lee, T.S., Chiu, C.C., Lu, C.J., Chen, I.F., Credit

Scoring using the Hybrid Neural Discriminant

Technique. Expert System with Applications, 23,

2002, 245–254.

[10] Lee, T. S., Chen, I.F., A Two-Stage Hybrid Credit

Scoring Model using Artificial Neural Networks and

Multivariate Adaptive Regression Splines. Expert

Systems with Applications, 28, 2005, 743–752.

[11] Huang, Z., Chen, H., Hsu, C.J., Chen, W.H., Wu, S.,

Credit Rating Analysis with Support Vector

Machines and Neural networks: a Market

Comparative Study. Decision Support Systems,

37(4) , 2004, 543–558.

[12] Hoffmann, F., Baesens, B., Martens, J., Put, F.,

Vanthienen, J., Comparing a Genetic Fuzzy and a

Neurofuzzy Classifier for Credit Scoring.

International Journal of Intelligent Systems, 17(11) ,

2002, 1067–1083.

[13] West, D., Neural Network Credit Scoring Models.

Computers and Operations Research, 27, 2000,

1131–1152.

[14] Ertuğrul, İ.; Karakaşoğlu, N. “Performance

Evaluation of Turkish cement Firms with Fuzzy

Analytic Hierarchy Process and TOPSIS Methods”,

Expert Systems with Applications, 36, 2009, pp.

702–715.

[15] Chang, D.Y., “Applications of the Extent Analysis

Method on Fuzzy AHP”, European Journal of

Operational Research, 95, 1996, pp. 649–655.

[16] Lee, Y.C., Doolen, G., Chen, H., Sun, G., Maxwell,

T., Lee, H., Giles, C.L., Machine Learning using a

Higher order Correlation Network. Physica D 22:

1986, 276-306.

[17] Zhang, M., Artificial Higher Order Neural Networks for

Economics and Business. IGI Global, New York 2009.

[18] Fallahnezhad, M., M.H., Moradi, S., Zaferanlouei, "A

Hybrid Higher Order Neural Classifier for Handling

Classification Problems", Expert Systems with

Applications, 38, 2011, 386–393.

[19] Shin, K.S., Lee, T.s., 'An Application of Support

Vector Machines in Bankruptcy Prediction Model',

Expert systems with application, Vol.28, 2005,

pp.127-135.

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