Pattern Classification Based on Conventional Interpretation of MFI

Our aim is to design a pattern classifier using fuzzy relational calculus (FRC) which was initially proposed by Pedrycz (Pattern Recognition 23 (1/2), 121–146, 1990). In the course of doing so, we first consider a particular interpretation of the multidimensional fuzzy implication (MFI) to represent our knowledge about the training data set. Subsequently, we introduce the notion of a fuzzy pattern vector to represent a population of training patterns in the pattern space and to denote the antecedent part of the said particular interpretation of the MFI. We introduce a new approach to the computation of the derivative of the fuzzy max-function and min-function using the concept of a generalized function. During the construction of the classifier based on FRC, we use fuzzy linguistic statements (or fuzzy membership function to represent the linguistic statement) to represent the values of features (e.g., feature F1 is small and F2 is big) for a population of patterns. Note that the construction of the classifier essentially depends on the estimate of a fuzzy relation < between the input (fuzzy set) and output (fuzzy set) of the classifier. Once the classifier is constructed, the nonfuzzy features of a pattern can be classified. At the time of classification of the nonfuzzy features of the test patterns, we use the concept of fuzzy masking to fuzzify the nonfuzzy feature values of the test patterns. The performance of the proposed scheme is tested on synthetic data. Finally, we use the proposed scheme for the vowel classification problem of an Indian language.