A Measure of Structural Complexity of Hierarchical Fuzzy Systems Adapted from Software Engineering

Hierarchical fuzzy systems (HFSs) have been seen as an effective approach to reduce the complexity of fuzzy logic systems (FLSs), largely as a result of reducing the number of rules. However, it is not clear completely how complexity of HFSs can be measured. In FLSs, complexity is commonly expressed using a multi-factorial approach, taking into consideration the number of rules, variables, and fuzzy terms. However, this may not be the best way to assess complexity in HFSs that have structures involving multiple subsystems, layers and different topologies. Thus far, structural complexity associated with the structure of HFSs has not been discussed. In the field of software engineering (SE), a complexity measure has been proposed to measure program complexity. This measure uses the concept of graph theory complexity, which considers the control structure complexity. The measure can also be applied to assess the complexity of a collection of programs known as a hierarchical nest. In this paper, we present an approach to mapping an SE complexity measure to HFS design. The approach includes several mapping alternatives that are outlined and illustrated using different HFS designs. This study contributes a new approach for the first time to assessing structural complexity in HFSs based on an approach from SE complexity measure.