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PublicationApplication of resampling techniques in Orthogonal regression(International Research Publication House, 2020)The classical Orthogonal Regression analysis relies heavily on the normality assumption. However, sometimes we might be uncertain of the underlying distribution of our dataset or the sample size might be small, which would cause an inaccurate inference on the parameter if the data is not normally distributed. This leads to the main objective of this paper which is to examine alternative methods to the parametric OR analysis which do not rely on the normality assumption. In this paper, the nonparametric jackknife and bootstrap resampling techniques were applied to assess the bias, standard errors and confidence intervals for the parameters of the model. We studied on the method of delete-one jackknife and bootstrapping the observations and made comparisons between the two methods as well. Under bootstrapping, three methods were considered to construct the confidence intervals which include percentile interval, bias-corrected (BC) interval and bias-corrected and accelerated (BCa) interval. Based on the results, it was found that the bootstrap estimators were closer to the values of classical OR analysis compared to jackknifed estimators. Besides, the jackknife estimates of bias and standard errors were slightly larger than that of bootstrap. Furthermore, we also found that the confidence intervals for the parameters constructed from jackknife have longer lengths and closer to that of OR. This showed that jackknife performed better in constructing confidence interval than the bootstrap.
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PublicationHybridised network of fuzzy logic and a genetic algorithm in solving 3-satisfiability hopfield neural networks(MDPI, 2023)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’s 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.
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PublicationFuzzy method based on the removal effects of criteria (MEREC) for determining objective weights in multi-criteria decision-making problems(MDPI, 2023)In multi-criteria decision-making (MCDM) research, the criteria weights are crucial components that significantly impact the results. Many researchers have proposed numerous methods to establish the weights of the criterion. This paper provides a modified technique, the fuzzy method based on the removal effects of criteria (MEREC) by modifying the normalization technique and enhancing the logarithm function used to assess the entire performance of alternatives in the weighting process. Since MCDM problems intrinsically are ambiguous or complex, fuzzy theory is used to interpret the linguistic phrases into triangular fuzzy numbers. The comparative analyses were conducted through the case study of staff performance appraisal at a Malaysian academic institution and the simulation-based study is used to validate the effectiveness and stability of the presented method. The results of the fuzzy MEREC are compared with those from a few different objective weighting techniques based on the correlation coefficients, outlier tests and central processing unit (CPU) time. The results of the comparative analyses demonstrate that fuzzy MEREC weights are verified as the correlation coefficient values are consistent throughout the study. Furthermore, the simulation-based study demonstrates that even in the presence of outliers in the collection of alternatives, fuzzy MEREC is able to offer consistent weights for the criterion. The fuzzy MEREC also requires less CPU time compared to the existing MEREC techniques. Hence, the modified method is a suitable alternative and efficient for computing the objective criteria weights in the MCDM problems.
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PublicationDual solutions of boundary layer flow and heat transfer in hybrid nanofluid over a stretching/shrinking cylinder(Semarak Ilmu Publishing, 2023)The boundary layer flow over a stretching/shrinking cylinder in hybrid nanofluid with the effects of suction, partial slip and convective boundary condition is studied. Hybrid nanoparticles Al2O3 and TiO2 with water as based fluid are considered in the study. The partial differential equations are transformed to ordinary differential equations by employing the similarity variables. The numerical results are obtained using the bvp4c solver in MATLAB software. The influence of nanoparticles volume fraction (Al2O3-TiO2 in water-based fluid), curvature parameter, suction parameter, partial slip parameter and Biot number on the velocity profile, temperature profile, skin friction coefficient and heat transfer rate are discussed. The numerical results indicate that for shrinking surface case, the dual solutions exist for a certain range of curvature parameter and suction parameter.
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PublicationMulti-unit discrete hopfield neural network for higher order supervised learning through logic mining: optimal performance design and attribute selection(Springer/King Saud University, 2023)In the perspective of logic mining, the attribute selection, and the objective function of the best logic is the two main factors that identifies the effectiveness of our proposed logic mining model. The non-significant attributes selected will cause the Discrete Hopfield Neural Network to learned and obtain wrong synaptic weight. Thus, this will result to suboptimal solution. Although we might select the correct attributes, the conventional objective function of the best logic limits the search space to obtained more induced logic during the retrieval phase of Discrete Hopfield Neural Network. Therefore, this paper proposes a novel logic mining by integrating statistical analysis in the pre-processing phase to ensure that only optimal attributes will be selected. Supervised learning approach via correlation analysis is implemented for the purpose of attribute selection. Additionally, permutation operator serves to enhance the probability of the higher order satisfiability logical rule to be satisfied by having finite arrangement of attributes. During the learning phase, we proposed multi-unit Discrete Hopfield Neural Network to enhance the search space which leads to optimal solution. The efficiency of the proposed model is tested on 15 real-life datasets by comparing the performance of the model with existing works in logic mining using five performance metrics including accuracy, sensitivity, precision, Matthews Correlation Coefficient (MCC) and F1 Score. According to the results, the proposed model has its own strength by dominating most of the average rank of the performance metrics. This demonstrates that the proposed model can differentiate across all domains in the confusion matrix. Additionally, the p-value obtained based on the five-performance metrics indicate that there is a significantly difference between the proposed model and all existing works since the value obtained for accuracy (0.000), sensitivity (0.001), precision (0.000), F1 score (0.000) and MCC (0.000) are less than 0.05. This finding statistically prove that the proposed model is more effective compared with existing works in logic mining.