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.
The development of fuzzy decision trees brings a linguistic form to the if-then rules constructed, offering a concise readability in their findings (see Olaru & Wehenkel, 2003). Examples of their successful application include in the areas of optimising economic dispatch (Roa-Serpulveda, Herrera, Pavez-Lazo, Knight, & Coonick, 2003) and the antecedents of company audit fees (Beynon, Peel, & Yang, 2004). Even in application based studies, the linguistic formulisation to decision making is continually investigated (Chakraborty, 2001; Herrera, Herrera-Viedma, & Martinez, 2000).
Appropriate for a wide range of problems, the fuzzy decision trees approach (with linguistic variables) allows a representation of information in a direct and adequate form. A linguistic variable is described in Herrera, Herrera-Viedma, & Martinez (2000), highlighting it differs from a numerical one, with it instead using words or sentences in a natural or artificial language. It further serves the purpose of providing a means of approximate characterization of phenomena, which are too complex, or too ill-defined to be amenable to their description in conventional quantitative terms.
The number of elements (words) in a linguistic term set which define a linguistic variable determines the granularity of the characterisation. The semantic of these elements is given by fuzzy numbers defined in the [0, 1] interval, which are described by their membership functions (MFs). Indeed, it is the role played by, and the structure of, the MFs that is fundamental to the utilization of FST related methodologies (Medaglia, Fang, Nuttle, & Wilson, 2002; Reventos, 1999). In this context, DeOliveria (1999) noted that fuzzy systems have the important advantage of providing an insight on the linguistic relationship between the variables of a system.