The development of fuzzy decision trees in the framework of Axiomatic Fuzzy Set logic

Decision trees are one among interesting and commonly encountered architectures used for learning, reasoning and organization of datasets. This study being positioned in the realm of decision trees is aimed at two main objectives. First, we propose a new algorithmic framework for building fuzzy sets (membership functions) and their logic operators based upon theoretical findings of the Axiomatic Fuzzy Set (logic) theory (AFS). Second, we cast the design processes of fuzzy decision trees in this framework. A number of illustrative examples are included. We demonstrate how the AFS setting results in the improvement of the performance of the resulting trees. The findings are contrasted with the outcomes produced by the decision trees studied by Janikow; in particular, we show the performance of different trees in the case of large number of fuzzy attributes.