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

Razak, Tajul Rosli; Garibaldi, Jonathan M; Wagner, Christian

Abstract

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.

Citation

Razak, T. R., Garibaldi, J. M., & Wagner, C. (2019). A Measure of Structural Complexity of Hierarchical Fuzzy Systems Adapted from Software Engineering. In 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). https://doi.org/10.1109/FUZZ-IEEE.2019.8859011

• Conference Name: International Conference on Fuzzy Systems (FUZZ-IEEE 2019)
• Conference Location: New Orleans, USA
• Start Date: Jun 23, 2019
• End Date: Jun 26, 2019
• Acceptance Date: Mar 7, 2019
• Online Publication Date: Oct 11, 2019
• Publication Date: 2019
• Deposit Date: Mar 27, 2019
• Publicly Available Date: Sep 28, 2022
• Publisher: Institute of Electrical and Electronics Engineers
• Book Title: 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
• ISBN: 978-1-5386-1729-8
• DOI: https://doi.org/10.1109/FUZZ-IEEE.2019.8859011
• Keywords: Hierarchical fuzzy systems; Complexity; Struc- tural complexity; Mapping Process
• Public URL: https://nottingham-repository.worktribe.com/output/1694629
• Publisher URL: https://ieeexplore.ieee.org/document/8859011