Comparing different stopping criteria for fuzzy decision tree induction through IDFID3

Abstract

Fuzzy Decision Tree (FDT) classifiers combine decision trees with approximate reasoning offered by fuzzy representation to deal with language and measurement uncertainties. When a FDT induction algorithm utilizes stopping criteria for early stopping of the tree's growth, threshold values of stopping criteria will control the number of nodes. Finding a proper threshold value for a stopping criterion is one of the greatest challenges to be faced in FDT induction. In this paper, we propose a new method named Iterative Deepening Fuzzy ID3 (IDFID3) for FDT induction that has the ability of controlling the tree's growth via dynamically setting the threshold value of stopping criterion in an iterative procedure. The final FDT induced by IDFID3 and the one obtained by common FID3 are the same when the numbers of nodes of induced FDTs are equal, but our main intention for introducing IDFID3 is the comparison of different stopping criteria through this algorithm. Therefore, a new stopping criterion named Normalized Maximum fuzzy information Gain multiplied by Number of Instances (NMGNI) is proposed and IDFID3 is used for comparing it against the other stopping criteria. Generally speaking, this paper presents a method to compare different stopping criteria independent of their threshold values utilizing IDFID3. The comparison results show that FDTs induced by the proposed stopping criterion in most situations are superior to the others and number of instances stopping criterion performs better than fuzzy information gain stopping criterion in terms of complexity (i.e. number of nodes) and classification accuracy. Also, both tree depth and fuzzy information gain stopping criteria, outperform fuzzy entropy, accuracy and number of instances in terms of mean depth of generated FDTs.