Advancing Fuzzy Logic: A Hierarchical Fuzzy System Approach
Main Article Content
Abstract
Fuzzy logic systems (FLS) are widely used in various engineering, medical, and scientific applications for modelling complex and uncertain systems. However, traditional FLS has limitations in handling complex and hierarchical structures due to their lack of scalability and interpretability. This paper proposes an approach to hierarchical fuzzy systems (HFS) that enhances the traditional FLS by providing a hierarchical structure with multiple levels of fuzzy rules. The main contribution of this paper is the proposal of HFS, which improves interpretability, scalability, and accuracy compared to traditional FLS, particularly for real-world applications. However, the question arises, "How can the FLS be converted into the HFS?" In this paper, the approach to HFS architecture will comprise two levels of FLS, where the first level determines the overall behaviour of the system, and the second level refines the output by considering the local behaviour. The proposed approach has been validated through experimental results on a case studies, such as the Iris flower classification. The results demonstrate that HFS provides more efficient and reliable solutions and can be applied to various complex and hierarchical systems in different domains, such as manufacturing, robotics, and decision-making.
Article Details
How to Cite
[1]
N. H. Anuar, T. R. Razak, and N. H. Kamis, “Advancing Fuzzy Logic: A Hierarchical Fuzzy System Approach”, AJSE, vol. 23, no. 1, pp. 64 - 70, Apr. 2024.
Section
Special Section on ISTEC – CoSQA 2023
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References
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[49] R. A. Fisher, “The use of multiple measurements in taxonomic problems,” Annals of Eugenics, vol. 7, no. 2, pp. 179–188, 9 1936.
[50] H. Hagras, “A Hierarchical Type-2 Fuzzy Logic Control Architecture for Autonomous Mobile Robots,” IEEE Trans. Fuzzy Syst., vol. 12, no. 4, pp. 524–539, 8 2004.
[51] M.-L. Lee, H.-Y. Chung, and F.-M. Yu, “Modeling of hierarchical fuzzy systems,” Fuzzy Sets Syst., vol. 138, no. 2, pp. 343–361, 9 2003.
[52] C. Mencar and A. Fanelli, “Interpretability constraints for fuzzy information granulation,” Inf. Sci., vol. 178, no. 24, pp. 4585–4618, 2008.
[53] T. Razak, J. M. Garibaldi, and C. Wagner, “An Improved Complexity Measure in Hierarchical Fuzzy Systems,” in Proc. IEEE Int. Conf. Fuzzy Systems (FUZZ-IEEE), 2020, pp. 1–8.
[54] T. R. Razak, S. S. M. Fauzi, R. A. J. Gining, M. H. Ismail, and R. Maskat, “Hierarchical Fuzzy Systems: Interpretability and Complexity,” Indonesian Journal of Electrical Engineering and Informatics (IJEEI), vol. 9, no. 2, 6 2021. [Online]. Available: http://section.iaesonline.com/index.php/IJEEI/article/view/2813
[2] G. V. S. Raju, J. Zhou, and R. Kisner, “Hierarchical fuzzy control,” Int. J. Contr., vol. 54, no. 5, pp. 1201–1216, 11 1991.
[3] L. Magdalena, “Semantic interpretability in hierarchical fuzzy systems: Creating semantically decouplable hierarchies,” Inf. Sci., vol. 496, pp.109–123, 9 2019.
[4] L. Zadeh, “Fuzzy sets,” Inf. and Control, vol. 8, no. 3, pp. 338–353, 6 1965.
[5] R. John and S. Coupland, “Type-2 Fuzzy Logic: A Historical View,” IEEE Computational Intelligence Magazine, vol. 2, no. 1, pp. 57–62, 2007.
[6] L. Zadeh, “The role of fuzzy logic in the management of uncertainty in expert systems,” Fuzzy Sets and Systems, vol. 11, no. 1-3, pp. 199–227, 1983.
[7] ——, “The concept of a linguistic variable and its application to approximate reasoning—I,” Inf. Sci., vol. 8, no. 3, pp. 199–249, 1 1975.
[8] M. Tavana and V. Hajipour, “A practical review and taxonomy of fuzzy expert systems: methods and applications,” Benchmarking, vol. 27, no. 1, pp. 81–136, 1 2020.
[9] G. Casalino, R. Grassi, M. Iannotta, V. Pasquadibisceglie, and G. Zaza, “A Hierarchical Fuzzy System for Risk Assessment of Cardiovascular Disease,” in 2020 IEEE Conference on Evolving and Adaptive Intelligent
Systems (EAIS). IEEE, 2020.
[10] N. Krichen, M. S. Masmoudi, and N. Derbel, “Autonomous omnidirectional mobile robot navigation based on hierarchical fuzzy systems,” Engineering Computations, 2020.
[11] O. Samuel, M. Omisore, and B. Ojokoh, “A web based decision support system driven by fuzzy logic for the diagnosis of typhoid fever,” Expert Systems with Applications, vol. 40, no. 10, pp. 4164–4171, 8 2013.
[12] R. Naranjo and M. Santos, “A fuzzy decision system for money investment in stock markets based on fuzzy candlesticks pattern recognition,” Expert Systems with Applications, vol. 133, pp. 34–48, 11 2019.
[13] Y. Jin, “Decentralized adaptive fuzzy control of robot manipulators,” IEEE Trans. Syst. Man Cybern. - Part B, vol. 28, no. 1, pp. 47–57, 1998.
[14] A. Waldock and B. Carse, “Learning a robot controller using an adaptive hierarchical fuzzy rule-based system,” Soft Computing, vol. 20, no. 7, pp. 2855–2881, 7 2016.
[15] T. R. Razak, J. M. Garibaldi, and C. Wagner, “A Measure of Structural Complexity of Hierarchical Fuzzy Systems Adapted from Software Engineering,” in Proc. IEEE Int. Conf. Fuzzy Systems (FUZZ-IEEE), 2019, pp. 1–7.
[16] R. Mikut, J. J¨akel, and L. Gr¨oll, “Interpretability issues in data-based learning of fuzzy systems,” Fuzzy Sets Syst., vol. 150, pp. 179–197, 2005.
[17] D. Nauck and R. Kruse, “Obtaining interpretable fuzzy classification rules from medical data,” Artif. Intell. Med, vol. 16, no. 2, pp. 149–169, 1999.
[18] T. R. Razak, J. M. Garibaldi, C. Wagner, A. Pourabdollah, and D. Soria, “Interpretability indices for hierarchical fuzzy systems,” in Proc. IEEE Int. Conf. Fuzzy Systems (FUZZ-IEEE). IEEE, 7 2017, pp. 1–6.
[19] D. Wang, X.-J. Zeng, and J. A. Keane, “A Survey of Hierarchical Fuzzy Systems (Invited Paper),” Tech. Rep. 1, 2006.
[20] T. Razak, J. Garibaldi, C. Wagner, A. Pourabdollah, and D. Soria, “Towards a Framework for Capturing Interpretability of Hierarchical Fuzzy Systems - A Participatory Design Approach,” IEEE Transactions
on Fuzzy Systems, vol. 29, no. 5, pp. 1160 – 1172, 2021.
[21] L.-X. Wang, “Universal approximation by hierarchical fuzzy systems,” Fuzzy Sets Syst., vol. 93, no. 2, pp. 223–230, 1 1998.
[22] R. Bellman, Adaptive Control Processes: A Guided Tour. Princeton University Press, 1961.
[23] X.-J. Zeng and J. Keane, “Separable Approximation Property of Hierarchical Fuzzy Systems,” in The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ ’05. IEEE, 2005, pp. 951–956.
[24] H. Ishibuchi, K. Nozaki, N. Yamamoto, and H. Tanaka, “Selecting fuzzy if-then rules for classification problems using genetic algorithms,” IEEE Trans. Fuzzy Syst., vol. 3, no. 3, pp. 260–270, 1995.
[25] H. Ishibuchi, T. Murata, and I. T¨urks¸en, “Single-objective and twoobjective genetic algorithms for selecting linguistic rules for pattern classification problems,” Fuzzy Sets Syst., vol. 89, no. 2, pp. 135–150, 7 1997.
[26] O. Cord´on, M. J. Del Jesus, F. Herrera, L. Magdalena, and P. Villar, “A Multiobjective Genetic Learning Process for joint Feature Selection and Granularity and Contexts Learning in Fuzzy Rule-Based Classification Systems,” in Interpretability issues in fuzzy modeling. Springer Berlin Heidelberg, 2003, pp. 79–99.
[27] L. Koczy, K. Hirota, and L. Muresan, “Interpolation in hierarchical fuzzy rule bases,” in The Ninth IEEE International Conference on Fuzzy Systems, 2000. FUZZ IEEE 2000., vol. 1. IEEE, 2000, pp. 471–477.
[28] Q. Liang and J. M. Mendel, “Designing interval type-2 fuzzy logic systems using an SVD-QR method: Rule reduction,” Int. J. Intell. Syst., vol. 15, no. 10, pp. 939–957, 10 2000.
[29] Y. Jin, “Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement,” IEEE Trans. Fuzzy Syst., vol. 8, no. 2, pp. 212–221, 4 2000.
[30] S.-M. Zhou and J. Gan, “Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling,” Fuzzy Sets Syst., vol. 159, no. 23, pp. 3091–3131, 12 2008.
[31] G. Raju and J. Zhou, “Adaptive Hierarchical Fuzzy Controller,” IEEE Trans. Syst., Man, and Cybern., vol. 23, no. 4, pp. 973–980, 1993.
[32] T. Zhao, H. Cao, and S. Dian, “A Self-Organized Method for a Hierarchical Fuzzy Logic System Based on a Fuzzy Autoencoder,” IEEE Transactions on Fuzzy Systems, vol. 30, no. 12, pp. 5104–5115, 12 2022.
[33] T. R. Razak, N. H. Kamis, N. H. Anuar, J. M. Garibaldi, and C. Wagner, “Decomposing Conventional Fuzzy Logic Systems to Hierarchical Fuzzy Systems,” IEEE International Conference on Fuzzy Systems, 2023.
[34] C. W. Chang and C. W. Tao, “A simplified implementation of hierarchical fuzzy systems,” Soft Computing, vol. 23, no. 12, pp. 4471–4481, 6 2019. [Online]. Available: https://link.springer.com/article/10.1007/s00500-018-3111-3
[35] T. R. Razak, N. H. Anuar, J. M. Garibaldi, and C. Wagner, “Modelling Hierarchical Fuzzy Systems for Mango Grading via FuzzyR Toolkit,” in 2022 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2022, pp. 1–8.
[36] X. J. Wei, D. Q. Zhang, and S. J. Huang, “A variable selection method for a hierarchical interval type-2 TSK fuzzy inference system,” Fuzzy Sets and Systems, vol. 438, pp. 46–61, 6 2022.
[37] R. Holve, “Rule generation for hierarchical fuzzy systems,” in Proc. Annu.Conf. North American Fuzzy Information Processing. IEEE, 1997, pp. 444–449.
[38] L.-X. Wang, “Analysis and Design of Hierarchical Fuzzy Systems,” IEEE Transactions on Fuzzy Systems, vol. 7, no. 5, pp. 617–624, 1999.
[39] R. Campello and W. Caradori do Amaral, “Hierarchical fuzzy relational models: linguistic interpretation and universal approximation,” IEEE Trans. Fuzzy Syst., vol. 14, no. 3, pp. 446–453, 6 2006.
[40] M. Brown and C. Harris, Neurofuzzy adaptive modelling and control. Prentice Hall, 1994.
[41] W. Rattasiri and S. Halgamuge, “Computational complexity of hierarchical fuzzy systems,” in PeachFuzz 2000. 19th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.00TH8500). IEEE, 2000, pp. 383–387. [Online]. Available: http://ieeexplore.ieee.org/document/877457/
[42] R. Alcal´a, J. Ram´on Cano, O. Cord´on, F. Herrera, P. Villar, and I. Zwir, “Linguistic modeling with hierarchical systems of weighted linguistic rules,” Int. J. Approx. Reas., vol. 32, no. 2-3, pp. 187–215, 2 2003.
[43] P. Salgado and J. Cunha, “Greenhouse climate hierarchical fuzzy modelling,” Control Engineering Practice, vol. 13, no. 5, pp. 613–628, 2005.
[44] A. D. Ben´ıtez and J. Casillas, “Multi-objective genetic learning of serial hierarchical fuzzy systems for large-scale problems,” Soft Comput., vol. 17, no. 1, pp. 165–194, 2013.
[45] P. K. Shukla and S. P. Tripathi, “A Survey on Interpretability-Accuracy (I-A) Trade-Off in Evolutionary Fuzzy Systems,” in 2011 Fifth Interna-tional Conference on Genetic and Evolutionary Computing. IEEE, 8 2011, pp. 97–101.
[46] M. Delgado, F. Von Zuben, and F. Gomide, “Multi-objective decision making: towards improvement of accuracy, interpretability and design autonomy in hierarchical genetic fuzzy systems,” in Proc. Int. Conf.
FUZZ-IEEE, vol. 2. IEEE, 2002, pp. 1222–1227.
[47] O. Cordon, F. Herrera, and I. Zwir, “Linguistic modeling by hierarchical systems of linguistic rules,” IEEE Trans. Fuzzy Syst., vol. 10, no. 1, pp. 2–20, 2002.
[48] M. Joo and J. Lee, “A class of hierarchical fuzzy systems with constraints on the fuzzy rules,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 2, pp. 194–203, 4 2005.
[49] R. A. Fisher, “The use of multiple measurements in taxonomic problems,” Annals of Eugenics, vol. 7, no. 2, pp. 179–188, 9 1936.
[50] H. Hagras, “A Hierarchical Type-2 Fuzzy Logic Control Architecture for Autonomous Mobile Robots,” IEEE Trans. Fuzzy Syst., vol. 12, no. 4, pp. 524–539, 8 2004.
[51] M.-L. Lee, H.-Y. Chung, and F.-M. Yu, “Modeling of hierarchical fuzzy systems,” Fuzzy Sets Syst., vol. 138, no. 2, pp. 343–361, 9 2003.
[52] C. Mencar and A. Fanelli, “Interpretability constraints for fuzzy information granulation,” Inf. Sci., vol. 178, no. 24, pp. 4585–4618, 2008.
[53] T. Razak, J. M. Garibaldi, and C. Wagner, “An Improved Complexity Measure in Hierarchical Fuzzy Systems,” in Proc. IEEE Int. Conf. Fuzzy Systems (FUZZ-IEEE), 2020, pp. 1–8.
[54] T. R. Razak, S. S. M. Fauzi, R. A. J. Gining, M. H. Ismail, and R. Maskat, “Hierarchical Fuzzy Systems: Interpretability and Complexity,” Indonesian Journal of Electrical Engineering and Informatics (IJEEI), vol. 9, no. 2, 6 2021. [Online]. Available: http://section.iaesonline.com/index.php/IJEEI/article/view/2813