Hierarchical Fuzzy Systems: Interpretability and Complexity

Abstract

Hierarchical fuzzy systems (HFSs) have been regarded as a useful solution for overcoming the major issues in fuzzy logic systems (FLSs), i.e., rule explosion due to the increase in the number of input variables. In HFS, the standard FLS are reformed into a low-dimensional FLS subsystem network. Moreover, the rules in HFS usually have antecedents with fewer variables than the rules in standard FLS with equivalent functions, because the number of input variables in each subsystem is less. Consequently, HFSs manage to decrease rule explosion, which minimises complexity and improves model interpretability. Nevertheless, the issues related to the question of “Does the complexity reduction of HFSs that have multiple subsystems, layers and different topologies really improve their interpretability?” are not clear and persist. In this paper, a comparison focusing on interpretability and complexity is made between two HFS’ topologies: parallel and serial. A detailed measurement of the interpretability and complexity with different configurations for both topologies is provided. This comparative study aims to examine the correlation between interpretability and complexity in HFS.