Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm
Discrete Hopfield Neural Network is widely used in solving various optimization problems and logic mining. Boolean algebras are used to govern the Discrete Hopfield Neural Network to produce final neuron states that possess a global minimum energy solution. Non-systematic satisfiability logic is pop...
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AIMS Press
2023-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231145?viewType=HTML |
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| author | Muhammad Aqmar Fiqhi Roslan Nur Ezlin Zamri Mohd. Asyraf Mansor Mohd Shareduwan Mohd Kasihmuddin |
| author_facet | Muhammad Aqmar Fiqhi Roslan Nur Ezlin Zamri Mohd. Asyraf Mansor Mohd Shareduwan Mohd Kasihmuddin |
| author_sort | Muhammad Aqmar Fiqhi Roslan |
| collection | DOAJ |
| description | Discrete Hopfield Neural Network is widely used in solving various optimization problems and logic mining. Boolean algebras are used to govern the Discrete Hopfield Neural Network to produce final neuron states that possess a global minimum energy solution. Non-systematic satisfiability logic is popular due to the flexibility that it provides to the logical structure compared to systematic satisfiability. Hence, this study proposed a non-systematic majority logic named Major 3 Satisfiability logic that will be embedded in the Discrete Hopfield Neural Network. The model will be integrated with an evolutionary algorithm which is the multi-objective Election Algorithm in the training phase to increase the optimality of the learning process of the model. Higher content addressable memory is proposed rather than one to extend the measure of this work capability. The model will be compared with different order logical combinations $ k = \mathrm{3, 2} $, $ k = \mathrm{3, 2}, 1 $ and $ k = \mathrm{3, 1} $. The performance of those logical combinations will be measured by Mean Absolute Error, Global Minimum Energy, Total Neuron Variation, Jaccard Similarity Index and Gower and Legendre Similarity Index. The results show that $ k = \mathrm{3, 2} $ has the best overall performance due to its advantage of having the highest chances for the clauses to be satisfied and the absence of the first-order logic. Since it is also a non-systematic logical structure, it gains the highest diversity value during the learning phase. |
| first_indexed | 2024-03-12T20:52:02Z |
| format | Article |
| id | doaj.art-5354213442994eaaa10a07ca3b48964a |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-12T20:52:02Z |
| publishDate | 2023-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-5354213442994eaaa10a07ca3b48964a2023-08-01T01:14:18ZengAIMS PressAIMS Mathematics2473-69882023-07-0189224472248210.3934/math.20231145Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election AlgorithmMuhammad Aqmar Fiqhi Roslan0Nur Ezlin Zamri 1Mohd. Asyraf Mansor2Mohd Shareduwan Mohd Kasihmuddin31. School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia2. School of Distance Education, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia2. School of Distance Education, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, MalaysiaDiscrete Hopfield Neural Network is widely used in solving various optimization problems and logic mining. Boolean algebras are used to govern the Discrete Hopfield Neural Network to produce final neuron states that possess a global minimum energy solution. Non-systematic satisfiability logic is popular due to the flexibility that it provides to the logical structure compared to systematic satisfiability. Hence, this study proposed a non-systematic majority logic named Major 3 Satisfiability logic that will be embedded in the Discrete Hopfield Neural Network. The model will be integrated with an evolutionary algorithm which is the multi-objective Election Algorithm in the training phase to increase the optimality of the learning process of the model. Higher content addressable memory is proposed rather than one to extend the measure of this work capability. The model will be compared with different order logical combinations $ k = \mathrm{3, 2} $, $ k = \mathrm{3, 2}, 1 $ and $ k = \mathrm{3, 1} $. The performance of those logical combinations will be measured by Mean Absolute Error, Global Minimum Energy, Total Neuron Variation, Jaccard Similarity Index and Gower and Legendre Similarity Index. The results show that $ k = \mathrm{3, 2} $ has the best overall performance due to its advantage of having the highest chances for the clauses to be satisfied and the absence of the first-order logic. Since it is also a non-systematic logical structure, it gains the highest diversity value during the learning phase.https://www.aimspress.com/article/doi/10.3934/math.20231145?viewType=HTMLdiscrete hopfield neural networknon-systematic logicflexible logical rulemajor 3 satisfiability logicelection algorithm |
| spellingShingle | Muhammad Aqmar Fiqhi Roslan Nur Ezlin Zamri Mohd. Asyraf Mansor Mohd Shareduwan Mohd Kasihmuddin Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm AIMS Mathematics discrete hopfield neural network non-systematic logic flexible logical rule major 3 satisfiability logic election algorithm |
| title | Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm |
| title_full | Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm |
| title_fullStr | Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm |
| title_full_unstemmed | Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm |
| title_short | Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm |
| title_sort | major 3 satisfiability logic in discrete hopfield neural network integrated with multi objective election algorithm |
| topic | discrete hopfield neural network non-systematic logic flexible logical rule major 3 satisfiability logic election algorithm |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231145?viewType=HTML |
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