An Improved Complexity Measure in Hierarchical Fuzzy Systems
Tajul Rosli Razak, Jonathan M. Garibaldi, Christian Wagner · 2020
Interpretability is an important and necessary topic that needs to be discussed in relation to the fields of Artificial Intelligence and Machine Learning. Within fuzzy logic systems (FLSs), hierarchical fuzzy systems (HFSs) have been suggested as a key component to help improve the interpretability of FLSs. In this context, complexity is a key component in the interpretability of FLSs. In FLSs, the complexity is commonly expressed using in a rule-based manner, considering the number of rules, variables, and fuzzy terms. Several studies have used indicators (for example, the number of rules) to measure the complexity of FLSs. However, this is not a perfect way of assessing complexity in HFSs that have the structure of multiple subsystems, layers and different topologies. Thus far, complexity assessment associated with the structure of HFSs has not been discussed. In this paper, we aim to put forward a new approach in assessing the complexity of HFSs, which will combine rule-based complexity and structural complexity. A detailed measurement of complexity for different HFSs' topologies, namely parallel and serial, will be presented to showcase the features of the new approach. The contribution of this paper is the introduction of a combined rule-based and structural complexities-based approach in order to establish a comprehensive measurement of complexity in HFSs.