Comparative Research Of Condense Nearest Rules Based On Fuzzy Rough Sets

The NN algorithm is a simple and well-known learning scheme based on the instanceswhich classifies an unseen instance by finding its closest neighbor in training set. Due to itssimplicity and effectiveness, it is widely used in many fields, such as pattern recognition,machine learning and data mining. However, the main drawback of NN is the whole trainingset must be stored in the computer to classify an unseen instance, and its distance to each oneof the stored instances is computed, so that the time complexity and space complexity is high.Another problem encountered in NN is that all of instances in training set are consideredequally important. When the instances with different class labels are overlapped, theperformance of the NN algorithm will degrade greatly. To overcome the drawbacks above,reducing the dimensions of the datasets becomes hot.Fuzzy rough set is a mathematical theory which is combining fuzzy set and rough set anddealing with information with imprecision and vagueness. At the present time, the research offuzzy rough set focus on the definition and reduct methods. From the definition of upperapproximation, lower approximation and bound approximation, the important degree of aninstance could be obtained. In this paper, we propose two condensed fuzzy nearest rules basedon fuzzy rough sets (CF K-NN1and CF K-NN2) and a modified fuzzy nearest neighbor rule.The two condensed fuzzy nearest rules consists of tree steps.(1) Obtaining a fuzzy attribute reduct based on fuzzy rough set technique,(2) Finding two sets of prototypes, the one is selected from fuzzy positive region and theother is selected from fuzzy boundary region,(3) Extracting fuzzy classification rules with the modified fuzzy K-NN from the two setsof prototype.Extensive experiments and statistical analysis are conducted to verify the effectiveness ofour proposed method. The experimental results and the statistical analysis of the experimentalresults both demonstrate that the proposed methods outperform other related methods such asCNN, ENN, and ICF et al. The conclusions are drawn from the comparative study as follows:the number of instances selected by the algorithm CF K-NN1is less than the numbers ofinstances selected by the algorithm CF K-NN2, CNN, RNN and ENN, and more than thenumbers of instances selected by ICF and MCS. The test accuracy of the algorithm CFK-NN1is higher than CF K-NN2. However, the test accuracies of the two algorithms proposed in this paper is higher than the others.