e-ISSN 2231-8526
ISSN 0128-7680
Farah Liyana Azizan, Saratha Sathasivam and Majid Khan Majahar Ali
Pertanika Journal of Science & Technology, Volume 31, Issue 4, July 2023
DOI: https://doi.org/10.47836/pjst.31.4.06
Keywords: 3SAT, alpha-cut, defuzzification, fuzzification, fuzzy logic, Hopfield network
Published on: 3 July 2023
This study presents a new way of increasing 3SAT logic programming’s efficiency in the Hopfield network. A new model of merging fuzzy logic with 3SAT in the Hopfield network is presented called HNN-3SATFuzzy. The hybridised dynamic model can avoid locally minimal solutions and lessen the computing burden by utilising fuzzification and defuzzification techniques in fuzzy logic. In addressing the 3SAT issue, the proposed hybrid approach can select neuron states between zero and one. Aside from that, unsatisfied neuron clauses will be changed using the alpha-cut method as a defuzzifier step until the correct neuron state is determined. The defuzzification process is a mapping stage that converts a fuzzy value into a crisp output. The corrected neuron state using alpha-cut in the defuzzification stage is either sharpening up to one or sharpening down to zero. A simulated data collection was utilised to evaluate the hybrid techniques’ performance. In the training phase, the network for HNN-3SATFuzzy was weighed using RMSE, SSE, MAE and MAPE metrics. The energy analysis also considers the ratio of global minima and processing period to assess its robustness. The findings are significant because this model considerably impacts Hopfield networks’ capacity to handle 3SAT problems with less complexity and speed. The new information and ideas will aid in developing innovative ways to gather knowledge for future research in logic programming. Furthermore, the breakthrough in dynamic learning is considered a significant step forward in neuro-symbolic integration.
Abdullah, W. A. T. W. (1992). Logic programming on a neural network. International Journal of Intelligent Systems, 7(6), 513-519. https://doi.org/10.1002/int.4550070604
Abdullah, W. A. T. W. (1993). The logic of neural networks. Physics Letters A, 176(3-4), 202-206. https://doi.org/10.1016/0375-9601(93)91035-4
Alzaeemi, S. A., & Sathasivam, S. (2021). Examining the forecasting movement of palm oil price using RBFNN-2SATRA metaheuristic algorithms for logic mining. IEEE Access, 9, 22542-22557. https://doi.org/10.1109/ACCESS.2021.3054816
Alzaeemi, S. A., Sathasivam, S., & Velavan, M. (2021). Agent-based modeling in doing logic programming in fuzzy hopfield neural network. International Journal of Modern Education and Computer Science, 13(2), 23-32. https://doi.org/10.5815/IJMECS.2021.02.03
Badawi, M. B., Awad, T. H., & Fahham, I. M. E. (2022). Application of artificial intelligence for the prediction of plain journal bearings performance. Alexandria Engineering Journal, 61(11), 9011-9029. https://doi.org/10.1016/j.aej.2022.02.041
Bilal, M., Masud, S., & Athar, S. (2012). FPGA design for statistics-inspired approximate sum-of-squared-error computation in multimedia applications. IEEE Transactions on Circuits and Systems II: Express Briefs, 59(8), 506-510. https://doi.org/10.1109/TCSII.2012.2204841
Bodjanova, S. (2002). A generalized α-cut. Fuzzy Sets and Systems, 126(2), 157-176. https://doi.org/10.1016/S0165-0114(01)00062-8
Brys, T., Hauwere, Y. M. D., Cock, M. D., & Nowé, A. (2012, August 6-8). Solving satisfiability in fuzzy logics with evolution strategies. [Paper presentation]. 2012 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), Berkeley, California. https://doi.org/10.1109/NAFIPS.2012.6290998
Fung, C. H., Wong, M. S., & Chan, P. W. (2019). Spatio-temporal data fusion for satellite images using hopfield neural network. Remote Sensing, 11(18), Article 2077. https://doi.org/10.3390/rs11182077
Garcez, A. S. A., & Zaverucha, G. (1999). Connectionist inductive learning and logic programming system. Applied Intelligence, 11(1), 59-77. https://doi.org/10.1023/A:1008328630915
Halaby, M. E., & Abdalla, A. (2016, May 9-11). Fuzzy maximum satisfiability. [Paper presentation]. INFOS ‘16: The 10th International Conference on Informatics and Systems, Giza, Egypt. https://doi.org/10.1145/2908446.2908476
Kubat, M. (1999). Neural networks: A comprehensive foundation by Simon Haykin, Macmillan, 1994, ISBN 0-02-352781-7. The Knowledge Engineering Review, 13(4), 409-412. https://doi.org/10.1017/s0269888998214044
Hopfield, J. J., & Tank, D. W. (1985). “Neural” computation of decisions in optimization problems. Biological Cybernetics, 52(3), 141-152. https://doi.org/10.1007/BF00339943
Kho, L. C., Kasihmuddin, M. S. M., Mansor, M. A., & Sathasivam, S. (2020). Logic mining in league of legends. Pertanika Journal of Science and Technology, 28(1), 211-225.
Kowalski, R., & Sergot, M. (1986). A logic-based calculus of events. New Generation Computing, 4(1), 67-95. https://doi.org/10.1007/BF03037383
Lee, C. C., & Gyvez, J. P. (1996). Color image processing in a cellular neural-network environment. IEEE Transactions on Neural Networks, 7(5), 1086-1098. https://doi.org/10.1109/72.536306
Little, W. A. (1974). The existence of persistent states in the brain. Mathematical Biosciences, 19(1-2), 101-120. https://doi.org/10.1016/0025-5564(74)90031-5
Maandag, P. (2012). Solving 3-SAT [Bachelor dissertation]. Radboud University Nijmegen, Netherlands. https://www.cs.ru.nl/bachelors-theses/2012/Peter_Maandag___3047121___Solving_3-Sat.pdf
Mansor, M. A., & Sathasivam, S. (2021). Optimal performance evaluation metrics for satisfiability logic representation in discrete hopfield neural network. International Journal of Mathematics and Computer Science, 16(3), 963-976.
Mansor, M. A., Sathasivam, S., & Kasihmuddin, M. S. M. (2018). 3-satisfiability logic programming approach for cardiovascular diseases diagnosis. AIP Conference Proceedings, 1974(1), Article 020022. https://doi.org/10.1063/1.5041553
De Myttenaere, A., Golden, B., Le Grand, B., & Rossi, F. (2016). Mean absolute percentage error for regression models. Neurocomputing, 192, 38-48. https://doi.org/10.1016/j.neucom.2015.12.114
Nasir, M., Sadollah, A., Grzegorzewski, P., Yoon, J. H., & Geem, Z. W. (2021). Harmony search algorithm and fuzzy logic theory: An extensive review from theory to applications. Mathematics, 9(21), 1-46. https://doi.org/10.3390/math9212665
Novák, V., Perfilieva, I., & Močkoř, J. (1999). Mathematical principles of fuzzy logic. Springer. https://doi.org/10.1007/978-1-4615-5217-8
Pan, J., Pottimurthy, Y., Wang, D., Hwang, S., Patil, S., & Fan, L. S. (2020). Recurrent neural network based detection of faults caused byparticle attrition in chemical looping systems. Powder Technology, 367, 266-276. https://doi.org/10.1016/j.powtec.2020.03.038
Pourabdollah, A., Mendel, J. M., & John, R. I. (2020). Alpha-cut representation used for defuzzification in rule-based systems. Fuzzy Sets and Systems, 399, 110-132. https://doi.org/10.1016/j.fss.2020.05.008
Rhodes, P. C., & Menani, S. M. (1992). Towards a fuzzy-logic programming system: A 1st-order fuzzy logic. Knowledge-Based Systems, 5(2), 106-116. https://doi.org/10.1016/0950-7051(92)90001-V
Sathasivam, S. (2006). Logic mining in neural networks. [Unpublished Doctoral Dissertation] Universiti Malaya, Malaysia.
Sathasivam, S. (2010). Upgrading logic programming in hopfield network. Sains Malaysiana, 39(1), 115-118.
Sathasivam, S., & Abdullah, W. A. T. W. (2008). Logic learning in hopfield networks. Modern Applied Science, 2(3), 57-63. https://doi.org/10.5539/mas.v2n3p57
Sathasivam, S., Mamat, M., Kasihmuddin, M. S. M., & Mansor, M. A. (2020). Metaheuristics approach for maximum k satisfiability in restricted neural symbolic integration. Pertanika Journal of Science and Technology, 28(2), 545-564.
Velavan, M., Yahya, R. Z., Halif, M. N. A., & Sathasivam, S. (2015). Mean field theory in doing logic programming using hopfield network. Modern Applied Science, 10(1), 154-160. https://doi.org/10.5539/mas.v10n1p154
Wang, L. X. (1996). A course in fuzzy systems and control. Prentice-Hall Inc.
Willmott, C. J., & Matsuura, K. (2005). Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Climate Research, 30(1), 79-82. https://doi.org/10.3354/cr030079
Zadeh, L. A. (1973). Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man and Cybernetics, SMC-3(1), 28-44. https://doi.org/10.1109/TSMC.1973.5408575
Zadeh, L. A. (1974). The concept of a linguistic variable and its application to approximate reasoning. In K. S. Fu & J. T. Tou (Eds.), Learning Systems and Intelligent Robots (pp. 1-10). Springer. https://doi.org/10.1007/978-1-4684-2106-4_1
Zadeh, L. A. (1979). A theory of approximation reasoning. In J. E. Hayes, D. Mishie & L. I. Mikulish (Eds.), Machine Intelligence (pp. 149-194). Elservier.
Zamri, N. E., Alway, A., Mansor, M. A., Kasihmuddin, M. S. M., & Sathasivam, S. (2020). Modified imperialistic competitive algorithm in hopfield neural network for boolean three satisfiability logic mining. Pertanika Journal of Science and Technology, 28(3), 983-1008.
ISSN 0128-7680
e-ISSN 2231-8526