Constructing fuzzy graphs from examples

Abstract

Methods to build function approximators from example data have gained considerable interest in the past. Especially methodologies that build models that allow an interpretation have attracted attention. Most existing algorithms, however, are either complicated to use or infeasible for high-dimensional problems. This article presents an ecient and easy to use algorithm to construct fuzzy graphs from example data. The resulting fuzzy graphs are based on locally independent fuzzy rules that operate solely on selected, important attributes. This enables the application of these fuzzy graphs also to problems in high dimensional spaces. Using illustrative examples and a real world data set it is demonstrated how the resulting fuzzy graphs oer quick insights into the structure of the example data, that is, the underlying model. The underlying algorithm is demonstrated using several Java applets, which can be found under ÔElectronic annexesÕ on www.elsevier.com/locate/ida.

GNU Fuzzy

“…However, it must be taken into account that different learning algorithms may have different requirements for representing rules. Some algorithms may expect that rules share a common set of membership functions [19], while others may create fuzzy sets on the fly while creating fuzzy rules [40]. The fuzzy core should therefore provide a rule implementation that accommodates both types of rule learning approaches.…”

Intelligent data analysis with fuzzy decision trees

“…Hyperbox-oriented learning is a supervised learning approach, where the training data are covered by (eventually overlapping) hyperboxes, so that the dependency between output and input variables is described by fuzzy graphs (Berthold and Huber 1999). The fuzzy rules are produced from the hyperboxes and fuzzy sets by projecting the hyperboxes onto individual dimensions.…”

Hybrid learning-based neuro-fuzzy inference system: a new approach for system modeling

“…Many approaches (Cho and Wang 1996, Berthold and Huber 1999, Nauck and Kruse 1999, Su and Chang 2000, Gonzales et al 2002, Paul and Kumar 2002, Li and Lee 2003, Li et al 2004b, Tsekouras et al 2005, Velayutham and Kumar 2005 have addressed system structure and parameter learning with efficiency. The grid-type partitioning, in which the determination of rule number depends on the number of input variables and the number of membership functions of each input variable, is the most intuitive and widely used method.…”

“…The grid-type partitioning, in which the determination of rule number depends on the number of input variables and the number of membership functions of each input variable, is the most intuitive and widely used method. Besides grid-type partitioning, many clustering algorithms were exploited for generating rules by cluster-based partitioning (Berthold and Huber 1999, Nauck and Kruse 1999, Gonzales et al 2002, Li et al 2004a, Tsekouras et al 2005. In the parameter learning, the generated rules need to be refined by the applied algorithm for the purpose of higher accuracy.…”