Pattern Classification Based on New Interpretation of MFI and Floating Point Genetic Algorithm

Abstract

In this chapter we consider an alternative soft computing approach to pattern classification. Our basic tools for soft computing are fuzzy relational calculus (FRC) and floating point genetic algorithm (GA). We introduce a new interpretation of multidimensional fuzzy implication (MFI) (see Eq. (A.4) of Appendix-A) to represent our knowledge about the training data set. The said new interpretation and the notion of an induced fuzzy pattern vector to handle the fuzzy information granules of the quantized pattern space, were considered for the classifier design of Chap. 3. We have already experienced that the construction of the pattern classifier is essentially based on the estimate of a fuzzy relation $\Re_{i}$ between the antecedent clause and consequent clause of each one dimensional fuzzy implication. But the only difference between the design study of Chaps. 3 and 4 is that for the estimation of $\Re_{i}$ in this chapter we use floating point representation of genetic algorithm (GA) (Michalewicz in Genetic algorithm + data structures = evolution programs, Springer, New York, 1994). Thus, a set of fuzzy relations is formed from the new interpretation of MFI. This set of fuzzy relations is termed as the core of the pattern classifier. Once the classifier is constructed the non-fuzzy features of a test pattern can be classified. The performance of the proposed scheme is tested on synthetic data. Subsequently, we use the proposed scheme for the vowel classification problem of an Indian language. Finally, a benchmark of performance is established by considering MLP (Multilayer Perceptron), SVM (Support Vector Machine) and the present method. The Abalone, Hosse colic and Pima Indians data sets, obtained from UCL database repository are used for the said benchmark study. This new tool for pattern classification is very effective for classification of patterns under vegue and imprecise environment. It can provide multiple classification under overlapped classes.