A Hierarchically ⊥-Decomposable Fuzzy Measure-Based Approach for Fuzzy Rules Aggregation

Abstract

A Fuzzy Decision Tree is a classification method consisting of a set of rules defined on fuzzy variables. The final class assignment is done according to the output of all the rules of the tree. Generally, the maximum operator is used to aggregate the results of the rules. However, some approaches based on more complex aggregation operators have appeared recently. In this work we propose to use Sugeno and Choquet integrals together with a Hierarchically ⊥-Decomposable Fuzzy Measure (HDFM) to aggregate the rules' values. The HDFM exploits the hierarchical structure of the fuzzy decision tree and takes into account the confidence value of the output together with the classification ambiguity of the rules. The HDFM is built using Sugeno-Weber t-conorms.We validate this approach on several classification problems and make a comparison of the performance with the state of art aggregation operators. Finally, a case study with a real dataset of diabetic patients is analyzed to predict the risk of suffering from diabetic retinopathy.