The seminal work of Zadeh (1965), namely fuzzy set theory (FST), has developed into a methodology fundamental to analysis that incorporates vagueness and ambiguity. With respect to the area of data mining, it endeavours to find potentially meaningful patterns from data (Hu & Tzeng, 2003). This includes the construction of if-then decision rule systems, which attempt a level of inherent interpretability to the antecedents and consequents identified for object classification (See Breiman, 2001). Within a fuzzy environment this is extended to allow a linguistic facet to the possible interpretation, examples including mining time series data (Chiang, Chow, & Wang, 2000) and multi-objective optimisation (Ishibuchi & Yamamoto, 2004). One approach to if-then rule construction has been through the use of decision trees (Quinlan, 1986), where the path down a branch of a decision tree (through a series of nodes), is associated with a single if-then rule. A key characteristic of the traditional decision tree analysis is that the antecedents described in the nodes are crisp, where this restriction is mitigated when operating in a fuzzy environment (Crockett, Bandar, Mclean, & O’Shea, 2006). This chapter investigates the use of fuzzy decision trees as an effective tool for data mining. Pertinent to data mining and decision making, Mitra, Konwar and Pal (2002) succinctly describe a most important feature of decision trees, crisp and fuzzy, which is their capability to break down a complex decision-making process into a collection of simpler decisions and thereby, providing an easily interpretable solution.
Learning fuzzy decision trees using integer programming
