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Publication

Analytical and numerical solutions of fuzzy differential equations

( 2013-02-26)

;

M.K. Hasan

;

B. De Baets

In this paper, we study analytical and numerical solutions of fuzzy differential equations based on the extension principle. For linear fuzzy differential equations, we state some results on the behaviour of the solutions and study their relationship with the generalised Hukuhara derivative. In order to approximate the solutions of linear and non-linear fuzzy differential equations, we propose a new fuzzification of the classical Euler method and then incorporate an unconstrained optimisation technique. This combination offers a powerful tool to tackle uncertainty in any numerical method. An efficient computational algorithm is also provided to guarantee the convexity of fuzzy solutions on the time domain. Several illustrative examples are given.

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Publication

Application of hybrid cubic B-Spline collocation approach for solving a generalized nonlinear Klien-Gordon equation

( 2014)

Shazalina Mat Zin

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Ahmad Abd Majid

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Ahmad Izani Md. Ismail

;

Muhammad Abbas

The generalized nonlinear Klien-Gordon equation is important in quantum mechanics and related fields. In this paper, a semi-implicit approach based on hybrid cubic B-spline is presented for the approximate solution of the nonlinear Klien-Gordon equation. The usual finite difference approach is used to discretize the time derivative while hybrid cubic B-spline is applied as an interpolating function in the space dimension. The results of applications to several test problems indicate good agreement with known solutions.

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Publication

Flow past a permeable stretching/shrinking sheet in a nanofluid using two-phase model

( 2014-11)

Wan Mohd Khairy Adly Wan Zaimi

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Anuar Ishak

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Ioan Pop

;

James P. Brody

The steady two-dimensional flow and heat transfer over a stretching/shrinking sheet in a nanofluid is investigated using Buongiorno’s nanofluid model. Different from the previously published papers, in the present study we consider the case when the nanofluid particle fraction on the boundary is passively rather than actively controlled, which make the model more physically realistic. The governing partial differential equations are transformed into nonlinear ordinary differential equations by a similarity transformation, before being solved numerically by a shooting method. The effects of some governing parameters on the fluid flow and heat transfer characteristics are graphically presented and discussed. Dual solutions are found to exist in a certain range of the suction and stretching/shrinking parameters. Results also indicate that both the skin friction coefficient and the local Nusselt number increase with increasing values of the suction parameter.

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Publication

Applications of the fuzzy sumudu transform for the solution of first order fuzzy differential equations

( 2015)

Norazrizal Rahman

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Muhammad Zaini Ahmad

In this paper, we study the classical Sumudu transform in fuzzy environment, referred to as the fuzzy Sumudu transform (FST). We also propose some results on the properties of the FST, such as linearity, preserving, fuzzy derivative, shifting and convolution theorem. In order to show the capability of the FST, we provide a detailed procedure to solve fuzzy differential equations (FDEs). A numerical example is provided to illustrate the usage of the FST.

Publication

Boundary layer flow and heat transfer over a permeable stretching/shrinking sheet with a convective boundary condition

( 2015)

Wan Mohd Khairy Adly Wan Zaimi

;

Anuar Ishak

This paper concerns with the boundary layer flow and heat transfer over a permeable stretching/shrinking sheet in a viscous fluid, with the bottom surface of the plate is heated by convection from a hot fluid. The partial differential equations governing the flow and heat transfer are converted into ordinary differential equations using a similarity transformation, before being solved numerically. The effects of the suction, convection and stretching/shrinking parameters on the skin friction coefficient and the local Nusselt number are examined and graphically illustrated. Dual solutions are found to exist for a certain range of the suction and stretching/shrinking parameters. The numerical results also show that suction widens the range of the stretching/shrinking parameter for which the solution exists.

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Publication

Shape preserving data interpolation using rational cubic ball functions

( 2015)

Ayser Nasir Hassan Tahat

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Abd Rahni Mt Piah

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Zainor Ridzuan Yahya

A smooth curve interpolation scheme for positive, monotone, and convex data is developed.This scheme uses rational cubic Ball representation with four shape parameters in its description. Conditions of two shape parameters are derived in such a way that they preserve the shape of the data, whereas the other two parameters remain free to enable the user to modify the shape of the curve. The degree of smoothness is 𝐶1.The outputs from a number of numerical experiments are presented.

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Publication

Statistical modeling for nanofluid flow: a stretching sheet with thermophysical property data

(MDPI, 2020)

Alias Jedi

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Azhari Shamsudeen

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Noorhelyna Razali

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Haliza Othman

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Nuryazmin Ahmat Zainuri

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Noraishikin Zulkarnain

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Nor Ashikin Abu Bakar

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Kafi Dano Pati

;

Thanoon Y. Thanoon

This paper reports the use of a numerical solution of nanofluid flow. The boundary layer flow over a stretching sheet in combination of two nanofluids models is studied. The partial differential equation that governs this model was transformed into a nonlinear ordinary differential equation by using similarity variables, and the numerical results were obtained by applying the shooting technique. Copper (Cu) nanoparticles (water-based fluid) were used in this study. This paper presents and discusses all numerical results, including those for the local Sherwood number and the local Nusselt number. Additionally, the effects of the nanoparticle volume fraction, Brownian motion Nb, and thermophoresis Nt on the performance of heat transfer are discussed. The results show that the stretching sheet has a unique solution: as the nanoparticle volume fraction φ (φ = 0), Nt (Nt = 0.1), and Nb decrease, the rate of heat transfer increases. Furthermore, as φ (φ = 0) and Nb decrease, the rate of mass transfer increases. The data of the Nusselt and Sherwood numbers were tested using different statistical distributions, and it is found that both datasets fit the Weibull distribution for different values of Nt and rotating φ.

Publication

Pattern selection for Darcy-Bénard convection with local thermal nonequilibrium

(Elsevier, 2020)

Biliana Bidin

;

D. Andrew S. Rees

A weakly nonlinear analysis is performed on the classical Darcy-Bénard problem to determine the effects of local thermal nonequilibrium on the planform of convection immediately post-onset. It is found that two-dimensional rolls are always favoured. Although disturbances which are perpendicular to the roll whose stability is being assessed usually form the most dangerous mode of instability, it is also found that there are regions of parameter space where the cross-roll instability becomes inoperative as an instability mechanism.

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Publication

Application of resampling techniques in Orthogonal regression

(International Research Publication House, 2020)

Fitrianto, Anwar

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Yun, Tan Sin

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Wan Zuki Azman Wan Muhamad

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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Publication

Engineering students' performances in mathematics through project-based learning

(Horizon Research Publishing, 2020)

N. Razali

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N. A. Zainuri

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H. Othman

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Z. M. Nopiah

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Nor Ashikin Abu Bakar

Project-based learning is an example of active learning and is student-driven, interdisciplinary, collaborative and technology-based. To test the hypothesis that project-based learning maximises course performance, we analysed a difficulty index of examination scores or failure rates and compared between 422 students in the 2016/2017 session, who took the Vector Calculus course and project-based learning with 342 students from the 2015/2016 session without project-based learning. The analysis of the difficulty index is used to investigate the achievement of the course outcome and the analysis on the correlation between the project-based learning scores and the final exam scores are identified using Pearson's product-moment correlation. The effect sizes indicate that on average examination scores improved by about 12% with project-based learning and students in classes with project-based learning were 3.4 times more likely to get as than students in classes without project-based learning. It is observed that the difficulty index for all course outcomes are achieved and distributed between a good range of 0.3–0.8. It is also proven that the students find it easier to answer the exam questions after the project-based learning is implemented based on the results of their mid and final semester exams.

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Publication

Effect of extraction conditions on the phytochemical properties of Clinacanthus nutans using Pressurized Hot Water Extraction (PHWE) technique

(IOP Publishing Ltd, 2020)

M.K. Abduljabbar

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Khairul Farihan Kasim

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Akmal Hadi Ma’Radzi

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N.S. Sofian-Seng

Clinacanthus nutan is an important herb species from the family Acanthaceae and is commonly found in Southeast Asia. It is also known as snake grass, or 'belalai gajah' in malay. The leaves of C. nutan can be used to make a refreshing juice or tea, or even consumed raw as 'ulam', a traditional malay salad. In this work, the leaves, stems, and a mixture of both leaves and stems of C. nutan are first dried in an oven at 50 C for 24 hours and then grounded into a powder. Then, pressurized hot water extraction (PHWE) is used to extract phytochemicals from the powdered samples at 120 C for 20 minutes. This work investigates the effects of three important parameters for extraction; the sample particle size (<63 to 500μm), solventto-sample ratio (10:2 to 50:2 v/w), and sample weight (0.5 to 3.0g) on the extracted phytochemicals' total phenolic compounds (TPC), total flavonoid compounds (TFC), and 2,2-dipheny1-1picrylhydrazyl (DPPH) scavenging activity. The experiments are carried out in triplicate and the results are analyzed using Minitab. Phytochemicals extracted from 2g leaf powder samples of particle size <63μm using a solvent-tosample ratio of 50:2 (v/w) resulted in the most favorable results for TPC, TFC, and DPPH scavenging activity.

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Publication

The effects of internal heat generation or absorption on mixed convection in a lid-driven rectangular cavity using finite volume method

(Akademia Baru Publishing (M) Sdn Bhd, 2020)

Norhaliza Abu Bakar

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Rozaini Roslan

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Mohd Kamalrulzaman Md Akhir

Mixed convection heat transfer in cavities is a significant phenomenon in numerous engineering fields, such as nuclear reactors, solar energy storage, and heat exchangers. Despite acknowledging that a square is a basic shape found in these systems, not all the figures are geometrical. Less attention was given to the rectangle cavity even though it could be found in these systems. Various internal reactions could occur inside the systems, especially in geothermal heat exchangers. Therefore, this research aims to analyze the effect of internal heat generation or absorption in a two-dimensional (2D) horizontal cavity to the fluid flow and heat transfer process numerically. The vertical walls are well insulated. Meanwhile, the top and bottom walls are kept at and , respectively, where . The top wall moves at a constant speed from left to right. The finite volume method (FEM) and SIMPLE algorithm are employed to discretize the governing equations. Next, the algebraic equations are solved iteratively using the tri-diagonal matrix algorithm (TDMA). The influences of heat generation or absorption parameters are investigated in terms of the flow, heat transfer, and Nusselt number. The numerical results are plotted in the form of streamlines and isotherms. It is found that the presence of heat generation or absorption has a significant effect on the fluid flow and heat transfer process in the horizontal cavity. Overall, for internal heat generation, the heat transfer rate decreases, while the opposite pattern can be observed for the case of internal heat absorption. However, for Ri = 10.0, as the heat generation's value increases from 2 to 4, the heat transfer rate is the same.

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Publication

Mathematical model of dengue virus with predator-prey interactions

(Penerbit UKM, 2020)

Sarinah Banu Mohamed Siddik

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Farah Aini Abdullah

;

Ahmad Izani Md. Ismail

In this paper, a mathematical model of dengue incorporating two sub-models that: describes the linked dynamics between predator-prey of mosquitoes at the larval stage, and describes the dengue spread between humans and adult mosquitoes, is formulated to simulate the dynamics of dengue spread. The effect of predator-prey dynamics in controlling the dengue disease at the larval stage of mosquito populations is investigated. Stability analysis of the equilibrium points are carried out. Numerical simulations results indicate that the use of predator-prey dynamics of mosquitoes at the larval stage as biological control agents for controlling the larval stage of dengue mosquito assists in combating dengue virus contagion

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Publication

The performances of mixed ewma-cusum control charts based on median-based estimators under non-normality

( 2023)

Nor Fashihah Mohd Noor

;

Ayu Abdul-Rahman

;

Abdu Mohammed Ali Atta

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts have been regularly used to monitor small process mean shifts. More recently, a mixture of EWMA and CUSUM charts known as mixed EWMA-CUSUM (MEC) control chart has been introduced for better small shift detection. However, like its predecessor, the MEC chart requires the normality assumption to ensure optimal performances. In the presence of outliers, which is the cause of non-normality, the parameters of the chart may be overestimated, leading to an unreliable monitoring process. To mitigate this problem, this paper employed median-based estimators namely, the median and modified one-step M-estimator (MOM), to control the location parameter via the MEC control chart. In this study, the performance of robust MEC charts for Phase II monitoring of location was compared with the standard MEC chart that is based on the sample mean. The performance of the robust MEC charts in terms of the average run length (ARL) on various g-and-h distributions clearly shows that a robust MEC chart based on the MOM estimator performs well regardless of the distributional shapes.

Publication

Preformation probability and kinematics of cluster emission yielding Pb-daughters

(IOP Publishing and Chinese Physical Society, 2023)

Joshua T. Majekodunmi

;

Muruthujaya Bhuyan

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Khairul Anwar Mohamad Khazali

;

Nooraihan Abdullah

;

Raj Kumar

In the present study, the newly established preformation formula is applied for the first time to study the kinematics of the cluster emission from various radioactive nuclei, especially those that decay to the double shell closure Pb nucleus and its neighbors as daughters. The recently proposed universal cluster preformation formula has been established based on the concepts that underscore the influence of mass and charge asymmetry ( and ), cluster mass , and the Q-value, paving the way to quantify the energy contribution during preformation as well as during the tunneling process separately. The cluster-daughter interaction potential is obtained by folding the relativistic mean-field (RMF) densities with the recently developed microscopic R3Y using the NL and the phenomenological M3Y NN potentials to compare their adaptability. The penetration probabilities are calculated from the WKB approximation. With the inclusion of the new preformation probability , the predicted half-lives of the R3Y and M3Y interactions are in good agreement with the experimental data. Furthermore, a careful inspection reflects slight differences in the decay half-lives, which arise from their respective barrier properties. The for systems with double magic shell closure Pb daughter are found to be an order of higher than those with neighboring Pb daughter nuclei. By exploring the contributions of the decay energy, the recoil effect of the daughter nucleus is evaluated, in contrast to several other conjectures. Thus, the centrality of the -value in the decay process is demonstrated and redefined within the preformed cluster-decay model. Additionally, we have introduced a simple and intuitive set of criteria that governs the estimation of recoil energy in the cluster radioactivity.

Publication

The effect of different distance matrix on goodness-of-fit test for multinomial logistic regression

(AIP Publishing, 2023)

Hamzah Abdul Hamid

;

Yap Bee Wah

In a previous study, the performance of goodness-of-fit test based on clustering partitioning strategy for multinomial logistic regression has been investigated by using different type of clustering techniques. It is known that the clustering technique involves distance calculation to identify which cluster a data belongs to. There are several distance matrices available, but the most popular one is the Euclidean distance. Thus the previous study only considered the Euclidean distance in the process of clustering the data. In this study, the effect of different distance matrix has been investigated. Four different distance matrices, which are Maximum, Manhattan, Minkowski and Canberra were used to investigate the effect on the performance of the test. The results were then compared with the results from previous studies, which used Euclidean distance. The results show that Canberra distance produced different mean value and rejection rate while the other distance measurements produced the same mean value and rejection rate as Euclidean distance.

Publication

Multi-unit discrete hopfield neural network for higher order supervised learning through logic mining: optimal performance design and attribute selection

(Springer/King Saud University, 2023)

Nur' Afifah Rusdi

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Mohd Shareduwan Mohd Kasihmuddin

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Nurul Atiqah Romli

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Gaeithry Manoharam

;

Mohd. Asyraf Mansor

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.

Publication

Dual solutions of boundary layer flow and heat transfer in hybrid nanofluid over a stretching/shrinking cylinder

(Semarak Ilmu Publishing, 2023)

Nor Ashikin Abu Bakar

;

Rohana Abdul Hamid

;

Najwa Najib

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.

Publication

Fuzzy method based on the removal effects of criteria (MEREC) for determining objective weights in multi-criteria decision-making problems

(MDPI, 2023)

Mohamad Shahiir Saidin

;

Lai Soon Lee

;

Siti Mahani Marjugi

;

Muhammad Zaini Ahmad

;

Hsin-Vonn Seow

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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Publication

The α-particle clustering and half-lives of the newly discovered 207,208Th decay chains within relativistic-Hartree-Bogoliubov approach

(Elsevier, 2023)

Joshua T. Majekodunmi

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Deepika Jain

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Khairul Anwar Mohamad Khazali

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Theeb Y.T. Alsultan

;

Raj K.

;

Nujud Mohammed Badawi

;

M. Bhuyan

The structural and decay properties of the ground state of recently discovered neutron-deficient 207Th and remeasured 208Th isotopes Yang et al. (2022) [26] is examined using the Relativistic-Hartree-Bogoliubov (RHB) formalism using the DD-ME2 parameter set within the preformed cluster-decay model (PCM). The relativistic medium-dependant R3Y so-called DD-R3Y NN potentials are for the first time used to obtain the nucleus-nucleus potential as input into the PCM. The penetration probability is calculated using the WKB approximation, and the preformation probability (Pα) is estimated using our newly derived formula, which is based on parameters well known to influence the α -particle radioactivity. A close correlation is observed between the α-preformation factor and the crucial role of the pairing correlation in the α-decay process. Furthermore, the Pα values for the even-even nuclei are generally found to be of higher magnitude than those for the odd-A nuclei. Our results further affirm that the odd-even staggering effect on the Qα values and its accompanying effects on other observables such as the charge radii and the decay half-lives, which can be largely attributed to the pairing correlation and Pauli blocking of the unpaired valence nucleons.

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