On the Optimization of T-norm parameters within Fuzzy Decision Trees

The success of fuzzy decision trees when applied to classification problems is usually attributed to the selection and tuning of fuzzy sets to represent the problem domain. The impact of fuzzy inference in combining grades of membership throughout fuzzy trees has not been considered in-depth. A number of parameterized fuzzy operators based on the T-norm model have been proposed but not exploited in practical applications. This paper presents a comparative study which examines a number of T-norm and T-conorms and their application within Fuzzy Decision Trees. The methodology uses a Genetic Algorithm to tune the weights of T-norm operators and optimize fuzzy membership functions simultaneously in fuzzy trees. The paper applies the methodology to two Fuzzy Decision Tree algorithms known as FIA and Fuzzy CHAIRS. Six different T-norm models are investigated across five real world datasets. Experimental results indicate that significant improvements can be made in the performance of fuzzy trees when the most appropriate T-norm is optimised for a specific domain.