Globally optimal fuzzy decision trees for classification and regression

Abstract

ÐA fuzzy decision tree is constructed by allowing the possibility of partial membership of a point in the nodes that make up the tree structure. This extension of its expressive capabilities transforms the decision tree into a powerful functional approximant that incorporates features of connectionist methods, while remaining easily interpretable. Fuzzification is achieved by superimposing a fuzzy structure over the skeleton of a CART decision tree. A training rule for fuzzy trees, similar to backpropagation in neural networks, is designed. This rule corresponds to a global optimization algorithm that fixes the parameters of the fuzzy splits. The method developed for the automatic generation of fuzzy decision trees is applied to both classification and regression problems. In regression problems, it is seen that the continuity constraint imposed by the function representation of the fuzzy tree leads to substantial improvements in the quality of the regression and limits the tendency to overfitting. In classification, fuzzification provides a means of uncovering the structure of the probability distribution for the classification errors in attribute space. This allows the identification of regions for which the error rate of the tree is significantly lower than the average error rate, sometimes even below the Bayes misclassification rate.

Multi-model decomposition of nonlinear dynamics using a fuzzy-CART approach

“…Here, we propose the use of the steady-state decomposition for establishing local relationships. We show that an extension of the CART methodology proposed by Jang et al [17] and subsequent fuzzification proposed by Suarez and Lutsko [18] could yield better results especially when there are gain sign changes and during transition regions.…”

Exploratory multivariate analysis for empirical information affected by uncertainty and modeled in a fuzzy manner: a review

“…Lertworaprachaya et al (2014) suggested an intervalvalued fuzzy decision trees with optimal neighborhood perimeter Recently, Cappelli et al (2015) suggested a regime change analysis of imprecise time series (i.e., interval-valued time series) based on regression trees. Useful references on decision trees in a fuzzy framework which can be considered for future studies are, e.g., Suarez and Lutsko (1999), Chiang and Hsu (2002), Olaru and Wehenkel (2003), Qin and Lawry (2005), Wang et al (2008), Zeinalkani and Eftekhari (2014). --Three-way analysis: in the last decades, increasing attention has also been paid to fuzzy clustering models for complex structures of fuzzy data.…”

Data-driven approach to machine condition prognosis using least square regression tree

“…Nevertheless, the average value of samples in each terminal node used as predicted result is the reason for reducing the accuracy of CART. Several approaches have been proposed to ameliorate that CART's limitation [14][15][16]. In this paper, least square method [17] to improve the prediction capability of CART model is proposed.…”