Decomposing Conventional Fuzzy Logic Systems to Hierarchical Fuzzy Systems

Hierarchical Fuzzy Systems (HFSs) have been viewed as a promising option to overcoming a fundamental problem in Fuzzy Logic Systems (FLSs), namely the rule explosion associated with an increase in input variables. In HFSs, the original FLS is decomposed into a number of low-dimensional fuzzy logic subsystems. As a result, rules in HFSs typically have antecedents with fewer variables than rules in FLSs which compute similar function mappings, given that the number of input variables of each subsystem is smaller. Consequently, HFSs tend to limit rule explosion, lowering complexity and enhancing model interpretability. However, developing the HFSs is difficult due to the added issue of designing suitable architecture (i.e., various subsystems, levels, topologies, and subsystem interactions) and rules for each subsystem. In fact, decomposing conventional fuzzy system is a challenging task. The difficulties include: "How to select the input variable for each subsystem", "How to improve the meaning of intermediate variable?", "How to link all the subsystems in HFSs?", and "How to design the rules for each subsystem?" Hence, this paper presents a method to convert conventional FLSs to hierarchical fuzzy systems using two key steps. This method contributes to the process or guidelines in overcoming the difficulties in the decomposition of FLS to HFS.