Fuzzy relational calculus approach to multidimensional pattern classification

Our aim is to design a pattern classifier using fuzzy relational calculus ( FRC) which was initially proposed by W, Pedrycz. In the course of doing thi s we introduce a new interpretation of multidimensional fuzzy implication ( MFI) to represent our knowledge about the training data set. The new interp retation is basically a set of one-dimensional fuzzy implications. The cons equences of all one-dimensional Fuzzy implications are finally collected th rough one intersection operator 'boolean AND', Subsequently, we consider th e notion of a fuzzy pattern vector, which is formed by the cylindrical exte nsion of the antecedent part of each one-dimensional fuzzy implication. Thu s, we get a set of fuzzy pattern vectors for the new interpretation of MFI and represent the population of training patterns in the pattern space. We also introduce a new approach to the computation of the derivative of the f uzzy max and min functions using the concept of a generalized Function. Dur ing the construction of the classifier, based on FRC, we use fuzzy linguist ic statements (or fuzzy membership function to represent the linguistic sta tement) to represent the ranges of features (e.g, feature F-i is small/medi um/big, etc, For All i) for a population of patterns. Note that the constru ction of the classifier essential depends on the estimate of a fuzzy relati on R-i between the antecedent parr and consequent part of each one-dimensio nal fuzzy implication. Thus, a set of fuzzy relations is formed from the ne w interpretation of MFI. This set of fuzzy relations is termed as a core of the classifier. Once the classifier is constructed the non-fuzzy features of a pattern can be classified. At the time of classification of the test p atterns, we use the concept of fuzzy singleton to fuzzify the non-fuzzy fea ture values of the test patterns. The performance of the proposed scheme is tested on synthetic data. Finally, we use the proposed scheme for the vowe l classification problem of Indian languages. (C) 1999 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.