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Open AccessArticle

Systematic Boolean Satisfiability Programming in Radial Basis Function Neural Network

1
School of Distance Education, Universiti Sains Malaysia, Penang 11800 USM, Malaysia
2
School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800 USM, Malaysia
3
Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru 81310, Malaysia
*
Author to whom correspondence should be addressed.
Processes 2020, 8(2), 214; https://doi.org/10.3390/pr8020214 (registering DOI)
Received: 3 November 2019 / Revised: 15 December 2019 / Accepted: 30 December 2019 / Published: 10 February 2020
(This article belongs to the Special Issue Advances in Sustainable Supply Chains)
Radial Basis Function Neural Network (RBFNN) is a class of Artificial Neural Network (ANN) that contains hidden layer processing units (neurons) with nonlinear, radially symmetric activation functions. Consequently, RBFNN has extensively suffered from significant computational error and difficulties in approximating the optimal hidden neuron, especially when dealing with Boolean Satisfiability logical rule. In this paper, we present a comprehensive investigation of the potential effect of systematic Satisfiability programming as a logical rule, namely 2 Satisfiability (2SAT) to optimize the output weights and parameters in RBFNN. The 2SAT logical rule has extensively applied in various disciplines, ranging from industrial automation to the complex management system. The core impetus of this study is to investigate the effectiveness of 2SAT logical rule in reducing the computational burden for RBFNN by obtaining the parameters in RBFNN. The comparison is made between RBFNN and the existing method, based on the Hopfield Neural Network (HNN) in searching for the optimal neuron state by utilizing different numbers of neurons. The comparison was made with the HNN as a benchmark to validate the final output of our proposed RBFNN with 2SAT logical rule. Note that the final output in HNN is represented in terms of the quality of the final states produced at the end of the simulation. The simulation dynamic was carried out by using the simulated data, randomly generated by the program. In terms of 2SAT logical rule, simulation revealed that RBFNN has two advantages over HNN model: RBFNN can obtain the correct final neuron state with the lowest error and does not require any approximation for the number of hidden layers. Furthermore, this study provides a new paradigm in the field feed-forward neural network by implementing a more systematic propositional logic rule. View Full-Text
Keywords: Radial Basis Function Neural Network; Hopfield Neural Network; satisfiability; optimization; logic programming Radial Basis Function Neural Network; Hopfield Neural Network; satisfiability; optimization; logic programming
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Mansor, M.A.; Mohd Jamaludin, S.Z.; Mohd Kasihmuddin, M.S.; Alzaeemi, S.A.; Md Basir, M.F.; Sathasivam, S. Systematic Boolean Satisfiability Programming in Radial Basis Function Neural Network. Processes 2020, 8, 214.

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