Dealing with Uncertainty: The Rough Set, the LVQ Neural Network, and the Bayesian Approaches

摘要

In solving pattern recognition problems, it is often advantageous to use hybrid systems that accommodate a number of different techniques and tools. The main objective of this study was to evaluate the rough set theory and the LVQ neural network approaches in terms of their classification measures of handling uncertainty in data, and their reasoning abilities to classify new patterns. The main purpose of this research was to find answers to the following principal questions: 1) Whether or not the rough sets theory and the LVQ neural network solve a patterns recognition problem equally well; 2) Can the measures used by rough sets for handling uncertain data be found in the LVQ solution for the same data; 3) Can fault-tolerance and generalization of the LVQ paradigm be described in terms of uncertainty measures used by the rough set theory? In order to achieve this goal, two procedures have been designed. The first procedure was designed in order: 1) to express the existing rough sets classification measures in terms of the statistical parameters of data, and to determine their potency for classifying new patterns; 2) to introduce a new approach of building a rough sets classifier based on the statistical parameters of data, if the existing classification measures are not sufficient to serve as a classifier. The second procedure was designed in order: 1) to determine what statistical parameters of data can be used to calculate LVQ weights, given that the decision surfaces of LVQ paradigm approximate the decision surfaces of the theoretical Bayesian classifier, and that data is presented in terms of the rough sets decision tables; 2) to introduce a new approach to re-express the LVQ weight matrix in terms of decision rules, similar to those used for rough sets.