Comparison of Algorithms for Fuzzy Decision Tree Induction

Abstract

The objective of the classification is to assign a class label to a data sample based on previous, learned experience. Despite the long tradition of classification algorithms research, there is not a unique technique that yields the best classification performance in all scenarios. Many real-world problems are uncertain. In this case, the crisp classification can be difficult to perform. The usage of fuzzy logic can be useful to describe real-world problems with higher accuracy. In this paper, we describe and compare algorithms of Fuzzy Decision Trees (FDTs), which are an extension of traditional decision trees. These algorithms are popular for their easy understandability and interpretability. But today there are many algorithms for FDT induction. These algorithms differ in many aspects. The most common difference is in information measures for selecting splitting attributes. Generally, the goal of decision tree induction is to create the smallest tree which is the most accurate as possible. In this paper, we use various information measures to induct FDTs and compare the accuracy and size of obtained FDTs. In comparison, information measures that are based on a generalization of the Shannon entropy and cumulative mutual information are included. The comparison shows that FDTs based on the cumulative mutual information acquired the best results. These results will also be included in a course on data mining that is taught at Faculty of Management Science and Informatics of University of Zilina.