APPLICATION OF NEURO-FUZZY SYSTEMS IN BANK SCORING PROBLEMS

Abstract

As the generation of a neuro-fuzzy model from scratch by hand is complex and time consuming process, evolutionary computations are used for this. By virtue of genetic algorithms, the development of neuro-fuzzy systems is simplified and becomes automatic. The proposed scheme is applied to well-known Australian and German Credit Approval problems. Comparison of different algorithms is given.

Full Text

Neuro-fuzzy modeling is applied to soft computing paradigm. It combines the advantages of neural networks and fuzzy rule based systems. While fuzzy systems implement effective approximate reasoning in uncertain environment, neural networks provide efficient learning algorithms from data. Meanwhile, neuro-fuzzy systems chiefly represent a knowledge base with fuzzy rules and membership functions where neural network algorithms such are used for parameters learning. Typically, the learning phase of neuro-fuzzy modeling consists of two stages. The first one is an unsupervised mode where any clustering algorithm could by applied for determination of initial size of rule base, i. e. number of rules. Mamdani inference type Rk a °1 an a1 am ^m Y Input parameters Y Output parameters Takagi-Sugeno inference type Rk _Ж_ a1 an °n V V m j -v- Input parameters yv "v- Output parameters yv. Fig. 1. Chromosome coding schemes Comparison with different algorithms Australian Data Set Proposed algorithm LR Bayesian RSM k-NN CART 0.8696 0.8696 0.8470 0.8660 0.8744 0.8986 C4.5 CCEL 2SGP GP+SRF Boosting Bagging 0.8986 0.7150 0.9027 0.8889 0.7600 0.8470 German Data Set Proposed algorithm LR Bayesian RSM k-NN CART 0.8700 0.7837 0.6790 0.7460 0.7565 0.7618 C4.5 CCEL 2SGP GP+SRF Boosting Bagging 0.7773 0.7151 0.8015 0.7834 0.7000 0.6840 Here a competitive learning with rival penalized mechanism is used. In comparison with other clustering techniques (such as k-mean, fuzzy k-means, conventional competitive learning) where a specific number of clusters is to be set, competitive learning with rival penalized mechanism requires a maximum number of clusters. During the learning procedure it will eliminate extra clusters that are beyond the universe of discourse. After such a stage the “rough” fuzzy rule base is established. The second stage (supervised mode) consists in tuning of parameters of membership functions. At this stage the learning capabilities of neural networks are applied. As a rule, a modified version of steepest descent method is used. The drawbacks of gradient based techniques are well known. They could be trapped in a local extremum due to a complex shape of objective function, go to stagnation or, otherwise, pulse. Under these considerations it is rational to apply evolutionary algorithms as well-established technique in global multiextremal optimization. Genetic algorithms are robust stochastic search procedure based on principles of natural evolution. It possesses flexible coding structure making it applicable to problems in different areas of human life. The next paragraph presents the proposed coding schemes of bit strings in genetics algorithms for automatic adjustment of membership function parameters. Coding structure of neuro-fuzzy model parameters. There are three main evolutionary coding structures of fuzzy rule base while designing a system. In our case the Pittsburgh approach was implemented where each individual in population represents single rule base. The developed algorithmic scheme requires only settings parameters of a genetic algorithm to be set. As for membership function, Gaussian membership functions were used. The coding schemes are given below (Fig. 1). Application to bank credit assignment problems. There are two data sets concerning customer credit card applications. The first one (Australian data set) contains 690 instances and 14 attributes and the second one (German data set) - 1000 instances and 24 attributes. The sets are to be classified into two classes. 10 % of instances in every set were randomly picked out for test sample. In Table 1 the results obtained and comparison with other techniques are given. The results of other algorithms were found in [1] and [2]. As it can be seen from the table our proposed algorithm is comparable with well-known techniques and can be applied to many real-world applications in different areas of human life. In this paper evolutionary tuning technique of a neuro-fuzzy system is described. The method proposed was applied to Australian and German Credit Approval problems and showed comparable results in comparison with other algorithms found in the literature. Future work of investigation is aimed at conducting additional numeric experiments and solving other real-world problems.