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ic statistical methods require the datato have a specific distribution.In addition to the restriction on the distribution involved,multi-
collinearity,autocorrelation could lead to problems with the estimated model when statistical methodsare used.
Other kind of methods were used for credit granting:neural networks(Piramuthu,Shaw and Gentry,1994;Piramuthu,1999),hybrid models(Piramuthu,1999),expert system(Duchessi,Shawky andSeagle,1988;Shaw and Gentry,1988;Deng,1993),fuzzy sets(Levy,Mallach and Duchessi,1991;
Chen and Chiou,1999)or multi-criteria(Srinivasan and Kim,1987;Srinivasan and Ruparel,1990;Zopounidis,Matsatsinis and Doumpos,1996;Doumpos et al.,2000).Unfortunately,some methods arenot adapted to credit scoring(for example neural networks are unable to explain decisions,which is a
big drawback in credit evaluation)or too complicated to implement(for instance,knowledgeacquisition is often a bottleneck in building expert systems).
On the other hand,inductive methods like decision trees(Marais,Patell and Wolfson,1984;Srinivasan and Kim,1987;Cronan,Glorfield and Perry,1991;Piramuthu,Shaw and Gentry,1994;Tessmer,1997;Joos et al.,1998)or rough sets have better knowledge representational structure in the
sense that they can be used to derive decision rules.These rules represent not only the relationshipsbetween the description of objects by attributes and their assignment to particular classes,but can alsobe used for the classification of new objects(Krusinska etal.,1992).Another advantage of these twoinductive methods is that one can eliminate all superfluous attributes in order to find the mostsignificant attributes for the classification.Even if rough sets are an extensively used approach in many topics like evaluation of bankruptcyrisk(Slowinski and Zopounidis,1995),they have rarely been used for creditgranting.Consequently,
the aim of this paper is to use rough sets for this kind of issue and to compare the results obtained with
another very often used method,the decision tree.
Mak and Munakata(2002)compare the rule-extraction capability of neural networks,rough sets,anddecision trees in analyzing expert heuristics on new product entry.Other experiments to compare roughsets with probabilistic inductive learning techniques and rough sets with ordinal statistical methods hadbeen also carried out by Krusinska et al.(1992)and by Teghem and Benjelloun(1992),but on othertopics.
The remainder of the paper is organized as follows.Section 2 will be devoted to rough sets.We first
present the method and then we apply it to our database,before we present our database.Section 3
aims to present decision trees and to show the results obtained with our data.Before concluding we
will go further in the comparison of both methods.
682 M.Daubie,P.Levecq and N.Meskens/Intl.Trans.in Op.Res.9(2002)681–6942.Rough sets
2.1.Description of rough sets
For many years now,rough sets theory has been confirmed to be a very good tool to deal withvagueness and imprecision.More specifically,this method has proved to be efficient for solving themulti-attribute classification problem(Pawlak and Slowinski,1993).The rough sets theory developed by Pawlak(1982,1991)proved to be an effective tool for theanalysis of information describing a set of objects(credit loans)by a set of multi-valued attributes.Wedistinguish two kinds of attributes:condition attributes and decision attributes.
On the basis of the description of objects in