Knowledge Discovery with Words Using Cartesian Granule Features: An Analysis for Classification Problems

Abstract

Cartesian granule features were originally introduced to address some of the shortcomings of existing forms of knowledge representation such as decomposition error and transparency, and also to enable the paradigm modelling with words through related learning algorithms. This chapter presents a detailed analysis of the impact of granularity on Cartesian granule features models that are learned from example data in the context of classification problems. This analysis provides insights on how to effectively model problems using Cartesian granule features using various levels of granulation, granule characterizations, granule dimensionalies and granule generation techniques. Other modelling with words approaches such as the data browser [1, 2] and fuzzy probabilistic decision trees [3] are also examined and compared. In addition, this chapter provides a useful platform for understanding many other learning algorithms that may or may not explicitly manipulate fuzzy events. For example, it is shown how a naive Bayes classifier is equivalent to crisp Cartesian granule feature classifiers under certain conditions.