Fuzzy clustering method and evaluation based on multi criteria decision making technique

In the financial sector, credit scoring is one of the most successful operational research techniques. Credit scoring is an evaluation of the risk connected with lending to clients (consumers) or an organization. In actual credit scoring-related problems, generally inaccurate parameters or input data are used due to incomplete or inaccessible information being provided. Thus, designing a successful credit scoring model is then becoming more complex. Furthermore, the fuzzy approach is more efficient than the others to handle imprecisions and uncertainties. Hence, fuzzy clustering analysis such as the Gustafson-Kessel (GK) algorithm is seen to be a very important tool in the field of credit scoring. In a credit scoring problem with cluster analysis, finding a subset of features from large data sets is a very important issue. In addition, two other important problems are the requiring predefined number of clusters and selecting initial centres of clusters. Thus in this study we intend to overcome these problems by determining a feature subset and the number of the cluster problems after developing an algorithm which simultaneously solved these issues. This proposed algorithm is developed based on heuristic method named modified binary particle swarm optimization (MBPSO) with kernel fuzzy clustering method as a fitness function. The proposed algorithm is used as a pre-processing method for data followed by Gustafson-Kessel (GK) algorithm to classify credit scoring data. For the third problem a modified of Kohonen Network (MKN) algorithm was proposed to select the initial centres of clusters. A similar degree between points was utilized to get similarity density, and then by means of maximum density points selecting them as weights of the Kohonen algorithm. After the optimization of the weights by modified version of the Kohonen Network method these weights will be set as the initial centres of the Gustafson-Kessel (GK) algorithm. Hence, we proposed a complete method by combining MBPSO, MKN and GK (MBPSO+MKN+GK). The new proposed method (MBPSO+MKN+GK) Gustafson- Kessel algorithm (GK)integrated with modified of Kohonen Network algorithm (MKN)and modified binary particle swarm optimization (MBPSO) was used to classify the credit scoring data. Multi-criteria decision making was used for measuring the overall preference values of these methods and considered all the criteria at the same time. The technique for order preference by similarity to ideal solution (TOPSIS) was used for ranking the fuzzy clustering processes having multiple criteria. Furthermore, the weights of the criteria were determined by using the modified fuzzy analytic hierarchy process (MFAHP) with ranking function. Simulation experiments were carried out to investigate the performance of methods with different number of samples and different number of features. Also these methods were applied on two credit scoring datasets of German and Australian. For a real problem application, we consider the data from Gulf Commercial Bank in Iraq. This study revealed that the GK along with the MBPSO algorithm showed a better performance as compared to the GK algorithm alone. Also, the GK and MKN algorithms together were better than GK alone. But the best performance of all will be the MBPSO+MKN+GK.

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