Credit scoring analysis by a partial probabilistic rough set model

Credit scoring analysis is an important issue, even more nowadays that a huge number of defaults has been one of the main cause of the financial crisis. Amongst the many different tools used to model credit risk, recently Rough Set has shown its effectiveness. Furthermore, original rough set theory has been widely generalized and contaminated by other uncertain reasoning approaches, especially probability and fuzzy set theories. In this paper we try to conjugate Fuzzy Rough Set with Coherent Partial Conditional Probability Assessments. In fact this last model has been shown to be a powerful tool to unify different uncertainty reasoning approaches. In particular, we propose to encompass experts partial probabilistic evaluations inside a gradual decision rule structure, with coherence of the conclusion as guideline. In line with Bayesian Rough Set models, we introduce credibility degrees of multiple premises through conditional probability assessments. Discernibility with this method remains anyhow too fine to reach reasonable graded classification rules. Hence we propose to coarsen the partition of the universe U by equivalence classes based on the arity of positively, negatively and neutrally related criteria. We will use data related to a sample of firms in order to build and test our model.