{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T19:15:41Z","timestamp":1782933341136,"version":"3.54.5"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T00:00:00Z","timestamp":1677628800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Higher Education Malaysia (MOHE) through the Fundamental Research Grant Scheme (FRGS)","award":["FRGS\/1\/2022\/STG06\/USM\/02\/11"],"award-info":[{"award-number":["FRGS\/1\/2022\/STG06\/USM\/02\/11"]}]},{"name":"Universiti Sains Malaysia","award":["FRGS\/1\/2022\/STG06\/USM\/02\/11"],"award-info":[{"award-number":["FRGS\/1\/2022\/STG06\/USM\/02\/11"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This work proposed a new hybridised network of 3-Satisfiability structures that widens the search space and improves the effectiveness of the Hopfield network by utilising fuzzy logic and a metaheuristic algorithm. The proposed method effectively overcomes the downside of the current 3-Satisfiability structure, which uses Boolean logic by creating diversity in the search space. First, we included fuzzy logic into the system to make the bipolar structure change to continuous while keeping its logic structure. Then, a Genetic Algorithm is employed to optimise the solution. Finally, we return the answer to its initial bipolar form by casting it into the framework of the hybrid function between the two procedures. The suggested network\u2019s performance was trained and validated using Matlab 2020b. The hybrid techniques significantly obtain better results in terms of error analysis, efficiency evaluation, energy analysis, similarity index, and computational time. The outcomes validate the significance of the results, and this comes from the fact that the proposed model has a positive impact. The information and concepts will be used to develop an efficient method of information gathering for the subsequent investigation. This new development of the Hopfield network with the 3-Satisfiability logic presents a viable strategy for logic mining applications in future.<\/jats:p>","DOI":"10.3390\/axioms12030250","type":"journal-article","created":{"date-parts":[[2023,3,2]],"date-time":"2023-03-02T02:10:59Z","timestamp":1677723059000},"page":"250","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Hybridised Network of Fuzzy Logic and a Genetic Algorithm in Solving 3-Satisfiability Hopfield Neural Networks"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8070-8206","authenticated-orcid":false,"given":"Farah Liyana","family":"Azizan","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia"},{"name":"Centre for Pre-University Studies, Universiti Malaysia Sarawak, Kota Samarahan 94300, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2843-7082","authenticated-orcid":false,"given":"Saratha","family":"Sathasivam","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5558-5929","authenticated-orcid":false,"given":"Majid Khan Majahar","family":"Ali","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nurshazneem","family":"Roslan","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia"},{"name":"Institute of Engineering Mathematics, Universiti Malaysia Perlis, Arau 02600, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Caicai","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/BF00339943","article-title":"\u201cNeural\u201d Computation of Decisions in Optimization Problems","volume":"52","author":"Hopfield","year":"1985","journal-title":"Biol. Cybern."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1002\/int.4550070604","article-title":"Logic Programming on a Neural Network","volume":"7","author":"Abdullah","year":"1992","journal-title":"Int. J. Intell. Syst."},{"key":"ref_3","first-page":"115","article-title":"Upgrading Logic Programming in Hopfield Network","volume":"39","author":"Sathasivam","year":"2010","journal-title":"Sains Malays."},{"key":"ref_4","first-page":"453","article-title":"Robust Artificial Bee Colony in the Hopfield Network for 2-Satisfiability Problem","volume":"25","author":"Kasihmuddin","year":"2017","journal-title":"Pertanika J. Sci. Technol."},{"key":"ref_5","first-page":"1173","article-title":"Artificial Immune System Paradigm in the Hopfield Network for 3-Satisfiability Problem","volume":"25","author":"Mansor","year":"2017","journal-title":"Pertanika J. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Agrawal, H., Talwariya, A., Gill, A., Singh, A., Alyami, H., Alosaimi, W., and Ortega-Mansilla, A. (2022). A Fuzzy-Genetic-Based Integration of Renewable Energy Sources and E-Vehicles. Energies, 15.","DOI":"10.3390\/en15093300"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Nasir, M., Sadollah, A., Grzegorzewski, P., Yoon, J.H., and Geem, Z.W. (2021). Harmony Search Algorithm and Fuzzy Logic Theory: An Extensive Review from Theory to Applications. Mathematics, 9.","DOI":"10.3390\/math9212665"},{"key":"ref_8","first-page":"1056","article-title":"A Fuzzy-Based Prediction Approach for Blood Delivery Using Machine Learning and Genetic Algorithm","volume":"12","author":"Qbadou","year":"2022","journal-title":"Int. J. Electr. Comput. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"106275","DOI":"10.1016\/j.asoc.2020.106275","article-title":"Fuzzy Neural Networks and Neuro-Fuzzy Networks: A Review the Main Techniques and Applications Used in the Literature","volume":"92","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_10","first-page":"1146","article-title":"A Comparative Analysis of Metaheuristic Algorithms in Fuzzy Modelling for Phishing Attack Detection","volume":"23","author":"Nordin","year":"2021","journal-title":"Indones. J. Electr. Eng. Comput. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"100172","DOI":"10.1109\/ACCESS.2020.2997939","article-title":"Artificial Immune Systems and Fuzzy Logic to Detect Flooding Attacks in Software-Defined Networks","volume":"8","author":"Scaranti","year":"2020","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Torres-Salinas, H., Rodr\u00edguez-Res\u00e9ndiz, J., Cruz-Miguel, E.E., and \u00c1ngeles-Hurtado, L.A. (2022). Fuzzy Logic and Genetic-Based Algorithm for a Servo Control System. Micromachines, 13.","DOI":"10.3390\/mi13040586"},{"key":"ref_13","unstructured":"Holland, J.H. (1975). Adaptation in Natural and Artificial Systems, University of Michigan Press."},{"key":"ref_14","first-page":"545","article-title":"Metaheuristics Approach for Maximum k Satisfiability in Restricted Neural Symbolic Integration","volume":"28","author":"Sathasivam","year":"2020","journal-title":"Pertanika J. Sci. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy Sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1585","DOI":"10.1049\/piee.1974.0328","article-title":"Application of Fuzzy Algorithms for Control of Simple Dynamic Plant","volume":"121","author":"Mamdani","year":"1974","journal-title":"Proc. Inst. Electr. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.fss.2020.05.008","article-title":"Alpha-cut representation used for defuzzification in rule-based systems","volume":"399","author":"Pourabdollah","year":"2020","journal-title":"Fuzzy Sets Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"19283","DOI":"10.1007\/s00521-022-07541-6","article-title":"Multi-discrete genetic algorithm in Hopfield neural network with weighted random k satisfiability","volume":"34","author":"Zamri","year":"2022","journal-title":"Neural Comput. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s12518-020-00297-5","article-title":"Multiple Criteria Decision-Making for Hospital Location-Allocation Based on Improved Genetic Algorithm","volume":"12","author":"Kaveh","year":"2020","journal-title":"Appl. Geomat."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.eswa.2018.12.020","article-title":"A novel multi-stage hybrid model with enhanced multi-population niche genetic algorithm: An application in credit scoring","volume":"121","author":"Zhang","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"8091","DOI":"10.1007\/s11042-020-10139-6","article-title":"A Review on Genetic Algorithm: Past, Present, and Future","volume":"80","author":"Katoch","year":"2021","journal-title":"Multimed Tools Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"55012","DOI":"10.1109\/ACCESS.2020.2981689","article-title":"An Empirical Evaluation of Machine Learning Techniques for Chronic Kidney Disease Prophecy","volume":"8","author":"Khan","year":"2020","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"100399","DOI":"10.1016\/j.rineng.2022.100399","article-title":"A hybrid chaotic-based discrete wavelet transform and Aquila optimisation tuned-artificial neural network approach for wind speed prediction","volume":"14","author":"Ziggah","year":"2022","journal-title":"Results Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"103169","DOI":"10.1016\/j.advengsoft.2022.103169","article-title":"YRAN2SAT: A Novel Flexible Random Satisfiability Logical Rule in Discrete Hopfield Neural Network","volume":"171","author":"Guo","year":"2022","journal-title":"Adv. Eng. Softw."},{"key":"ref_25","first-page":"506","article-title":"FPGA Design for Statistics-Inspired Approximate Sum-of-Squared-Error Computation in Multimedia Applications","volume":"59","author":"Bilal","year":"2012","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1224","DOI":"10.1016\/j.egyr.2020.05.006","article-title":"Parameter estimation of PEMFC based on Improved Fluid Search Optimization Algorithm","volume":"6","author":"Qin","year":"2020","journal-title":"Energy Rep."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.neucom.2015.12.114","article-title":"Mean Absolute Percentage Error for Regression Models","volume":"192","author":"Golden","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/j.asej.2020.07.012","article-title":"Global Performance of Metaheuristic Optimization Tools for Water Distribution Networks","volume":"12","author":"Djebedjian","year":"2021","journal-title":"Ain Shams Eng. J."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"50831","DOI":"10.1109\/ACCESS.2021.3068998","article-title":"Random satisfiability: A higher-order logical approach in discrete hopfield neural network","volume":"9","author":"Karim","year":"2021","journal-title":"IEEE Access"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"e1106","DOI":"10.7717\/peerj-cs.1106","article-title":"On component-wise dissimilarity measures and metric properties in pattern recognition","volume":"8","author":"Martino","year":"2022","journal-title":"PeerJ Comput. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Bazuhair, M.M., Mohd Jamaludin, S.Z., Zamri, N.E., Mohd Kasihmuddin, M.S., Mansor, M.A., Alway, A., and Karim, S.A. (2021). Novel Hopfield Neural Network Model with Election Algorithm for Random 3 Satisfiability. Processes, 9.","DOI":"10.3390\/pr9081292"},{"key":"ref_32","unstructured":"Abdullahi, S., Mansor, M.A., Sathasivam, S., Kasihmuddin, M.S.M., and Zamri, N.E. (2020). AIP Conference Proceedings 2266, American Institute of Physics."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1590\/S1415-47572004000100014","article-title":"Comparison of Similarity Coefficients Used for Cluster Analysis with Dominant Markers in Maize","volume":"27","author":"Meyer","year":"2004","journal-title":"Genet. Mol. Biol."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Gao, Y., Guo, Y., Romli, N.A., Kasihmuddin, M.S.M., Chen, W., Mansor, M.A., and Chen, J. (2022). GRAN3SAT: Creating Flexible Higher-Order Logic Satisfiability in the Discrete Hopfield Neural Network. Mathematics, 11.","DOI":"10.3390\/math10111899"},{"key":"ref_35","first-page":"27","article-title":"Enhanced Hopfield Network for Pattern Satisfiability Optimization","volume":"11","author":"Mansor","year":"2016","journal-title":"Int. J. Intell. Syst. Appl."},{"key":"ref_36","first-page":"22","article-title":"VLSI Circuit Configuration Using Satisfiability Logic in Hopfield Network","volume":"9","author":"Mansor","year":"2016","journal-title":"Int. J. Intell. Syst. Appl."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/3\/250\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:45:09Z","timestamp":1760121909000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/3\/250"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,1]]},"references-count":36,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["axioms12030250"],"URL":"https:\/\/doi.org\/10.3390\/axioms12030250","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,1]]}}}