Grid Partitioning And Rough Set Method Approach For Fuzzy Rule Generation
DOI:
https://doi.org/10.35335/emod.v13i1.6Keywords:
Grid partitioning, Rough set method, Fuzzy rule generation, Accuracy, InterpretabilityAbstract
The generation of accurate and interpretable fuzzy rules plays a crucial role in various data analysis and decision-making systems. In this research, we propose a mathematical model based on grid partitioning and the rough set method for fuzzy rule generation. The model combines the advantages of grid partitioning, which enables localized analysis, and the rough set method, which captures the uncertainty in the dataset. By partitioning the input space into grids and determining the lower and upper approximations within each grid, the model generates accurate and representative fuzzy rules. These rules provide meaningful insights into the relationships between input variables and output variables, enhancing interpretability. The model is applied in a case example of temperature control to demonstrate its effectiveness. Additionally, a numerical example showcases the predictive performance and applicability of the model. The limitations of the research, such as dependency on data quality and scalability issues, are also discussed. Despite these limitations, the mathematical model contributes to the field of data analysis and decision-making systems by offering an approach that integrates grid partitioning and rough set method for fuzzy rule generation. It holds promise for applications in various domains, providing accurate and interpretable fuzzy rules for decision support systems and intelligent automation.
References
Abdulraheem, A., Sabakhy, E., Ahmed, M., Vantala, A., Raharja, I., & Korvin, G. (2007, March). Estimation of permeability from wireline logs in a middle eastern carbonate reservoir using fuzzy logic. In SPE middle east oil and gas show and conference. OnePetro.
Alcalá, R., Casillas, J., Cordón, O., & Herrera, F. (2001). Building fuzzy graphs: features and taxonomy of learning for non-grid-oriented fuzzy rule-based systems. Journal of Intelligent & Fuzzy Systems, 11(3-4), 99-119.
Beaubouef, T., Ladner, R., & Petry, F. (2004). Rough set spatial data modeling for data mining. International Journal of Intelligent Systems, 19(7), 567-584.
Chen, T., Shen, Q., Su, P., & Shang, C. (2016). Fuzzy rule weight modification with particle swarm optimisation. Soft Computing, 20, 2923-2937.
Chiang, J. H., & Hao, P. Y. (2004). Support vector learning mechanism for fuzzy rule-based modeling: a new approach. IEEE Transactions on Fuzzy systems, 12(1), 1-12.
Dehzangi, O., Zolghadri, M. J., Taheri, S., & Fakhrahmad, S. M. (2007, August). Efficient fuzzy rule generation: a new approach using data mining principles and rule weighting. In Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007) (Vol. 2, pp. 134-139). IEEE.
Esfahanipour, A., & Aghamiri, W. (2010). Adapted neuro-fuzzy inference system on indirect approach TSK fuzzy rule base for stock market analysis. Expert Systems with Applications, 37(7), 4742-4748.
Hassanien, A. E., Abraham, A., Peters, J. F., Schaefer, G., & Henry, C. (2009). Rough sets and near sets in medical imaging: A review. IEEE Transactions on Information Technology in Biomedicine, 13(6), 955-968.
Ho, S. Y., Chen, H. M., Ho, S. J., & Chen, T. K. (2004). Design of accurate classifiers with a compact fuzzy-rule base using an evolutionary scatter partition of feature space. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 34(2), 1031-1044.
Hu, Q., Yu, D., Liu, J., & Wu, C. (2008). Neighborhood rough set based heterogeneous feature subset selection. Information sciences, 178(18), 3577-3594.
Jensen, R., & Shen, Q. (2007). Fuzzy-rough sets assisted attribute selection. IEEE Transactions on fuzzy systems, 15(1), 73-89.
Khan, M. A., Khan, M. A. I., Aref, M., & Khan, S. F. (2016). Cluster & rough set theory based approach to find the reason for customer churn. Int. J. Appl. Bus. Econ. Res, 14(1), 439-455.
Kostek, B. (2013). Soft computing in acoustics: applications of neural networks, fuzzy logic and rough sets to musical acoustics (Vol. 31). Physica.
Lazar, A. (2002). Heuristic knowledge discovery for archaeological data using genetic algorithms and rough sets. In Heuristic and optimization for knowledge discovery (pp. 263-278). IGI Global.
Leung, Y., Wu, W. Z., & Zhang, W. X. (2006). Knowledge acquisition in incomplete information systems: a rough set approach. European Journal of Operational Research, 168(1), 164-180.
Liang, J., Wang, F., Dang, C., & Qian, Y. (2012). A group incremental approach to feature selection applying rough set technique. IEEE Transactions on Knowledge and Data Engineering, 26(2), 294-308.
Lin, T. Y., & Cercone, N. (Eds.). (2012). Rough sets and data mining: Analysis of imprecise data. Springer Science & Business Media.
Majak, M., & Żołnierek, A. (2016). Rough Sets and Fuzzy Logic Approach for Handwritten Digits and Letters Recognition. In Proceedings of the 9th International Conference on Computer Recognition Systems CORES 2015 (pp. 713-722). Springer International Publishing.
Mitra, S., & Hayashi, Y. (2000). Neuro-fuzzy rule generation: survey in soft computing framework. IEEE transactions on neural networks, 11(3), 748-768.
Pawlak, Z. (2004). Some issues on rough sets. In Transactions on Rough Sets I: James F. Peters-Andrzej Skowron, Editors-in-Chief (pp. 1-58). Springer Berlin Heidelberg.
Pawlak, Z., & Skowron, A. (2007). Rudiments of rough sets. Information sciences, 177(1), 3-27.
Polkowski, L. (Ed.). (2013). Rough sets in knowledge discovery 2: applications, case studies and software systems (Vol. 19). Physica.
Samantaray, S. R., El-Arroudi, K., Joos, G., & Kamwa, I. (2010). A fuzzy rule-based approach for islanding detection in distributed generation. IEEE transactions on power delivery, 25(3), 1427-1433.
Sharma, D. (2011). Designing and modeling fuzzy control Systems. International Journal of Computer Applications, 16(1), 46-53.
Suo, M., An, R., Zhou, D., & Li, S. (2018). Grid-clustered rough set model for self-learning and fast reduction. Pattern Recognition Letters, 106, 61-68.
Thangavel, K., & Pethalakshmi, A. (2009). Dimensionality reduction based on rough set theory: A review. Applied soft computing, 9(1), 1-12.
Vluymans, S., D'eer, L., Saeys, Y., & Cornelis, C. (2015). Applications of Fuzzy Rough Set Theory in Machine Learning: a Survey. Fundam. Informaticae, 142(1-4), 53-86.
Wang, X., Yang, J., Teng, X., Xia, W., & Jensen, R. (2007). Feature selection based on rough sets and particle swarm optimization. Pattern recognition letters, 28(4), 459-471.
Zhu, W. (2007). Generalized rough sets based on relations. Information Sciences, 177(22), 4997-5011.
Zhu, W. (2007). Topological approaches to covering rough sets. Information sciences, 177(6), 1499-1508.
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 Chris Kornelisius, Eyvan Caeyso, Ching-Ghiang Feh
This work is licensed under a Creative Commons Attribution 4.0 International License.
