Displaying publications 1 - 20 of 88 in total

  1. Mamuda M, Sathasivam S
    MATEMATIKA, 2017;33(1):11-19.
    Medical diagnosis is the extrapolation of the future course and outcome of a disease and a sign of the likelihood of recovery from that disease. Diagnosis is important because it is used to guide the type and intensity of the medication to be administered to patients. A hybrid intelligent system that combines the fuzzy logic qualitative approach and Adaptive Neural Networks (ANNs) with the capabilities of getting a better performance is required. In this paper, a method for modeling the survival of diabetes patient by utilizing the application of the Adaptive NeuroFuzzy Inference System (ANFIS) is introduced with the aim of turning data into knowledge that can be understood by people. The ANFIS approach implements the hybrid learning algorithm that combines the gradient descent algorithm and a recursive least square error algorithm to update the antecedent and consequent parameters. The combination of fuzzy inference that will represent knowledge in an interpretable manner and the learning ability of neural network that can adjust the membership functions of the parameters and linguistic rules from data will be considered. The proposed framework can be applied to estimate the risk and survival curve between different diagnostic factors and survival time with the explanation capabilities.
  2. Mohd Bakri Adam
    MATEMATIKA, 2017;33(1):21-34.
    The constraint of two ordered extreme minima random variables when one
    variable is consider to be stochastically smaller than the other one has been carried
    out in this article. The quantile functions of the probability distribution have been
    used to establish partial ordering between the two variables. Some extensions and
    generalizations are given for the stochastic ordering using the important of sign of the
    shape parameter.
  3. Sagir, Abdu Masanawa, Sathasivam, Saratha
    MATEMATIKA, 2017;33(1):1-10.
    In the recent economic crises, one of the precise uniqueness that all stock
    markets have in common is the uncertainty. An attempt was made to forecast future
    index of the Malaysia Stock Exchange Market using artificial neural network (ANN)
    model and a traditional forecasting tool – Multiple Linear Regressions (MLR). This
    paper starts with a brief introduction of stock exchange of Malaysia, an overview of
    artificial neural network and machine learning models used for prediction. System
    design and data normalization using MINITAB software were described. Training
    algorithm, MLR Model and network parameter models were presented. Best training
    graphs showing the training, validation, test and all regression values were analyzed.
  4. Ahmad Razin Zainal Abidin, Shaymaa Mustafa, Zainal Abdul Aziz and, Kamarudin Ismail
    MATEMATIKA, 2018;34(2):173-186.
    Subsea cable laying process is a difficult task for an engineer due to many
    uncertain situations which occur during the operation. It is very often that the cable being
    laid out is not perfectly fit on the route being planned, which results in the formation of
    slack. In order to control wastages during installation, the slack needs to be minimized
    and the movement of a ship/vessel needs to be synchronized with the cable being laid out.
    The current problem was addressed using a mathematical model by considering a number
    of defining parameters such as the external forces, the cable properties and geometry. Due
    to the complexity, the model is developed for a steady-state problem assuming velocity
    of the vessel is constant, seabed is flat and the effect of wind and wave is insignificant.
    Non-dimensional system is used to scale the engineering parameters and grouped them
    into only two main parameters which are the hydrodynamic drag of the fluid and the
    bending stiffness of the cable. There are two solutions generated in this article; numerical
    and asymptotic solutions. The result of these solutions suggests that the percentage of
    slack can be reduced by the increase of the prescribed cable tension, and also the increase
    in either the drag coefficient of the sea water or the bending stiffness of the cable, similarly
    will result in lower slack percentage
  5. Mohd Bakri Adam, Babangida Ibrahim Babura, Kathiresan Gopal
    MATEMATIKA, 2018;34(2):187-204.
    The box plot has been used for a very long time since 70s in checking the existence
    of outliers and the asymmetrical shape of data. The existing box plot is constructed
    using five values of statistics calculated from either the discrete or continous data. Many
    improvement of box plots have deviated from the elegant and simplier approach of exploratory
    data analysis by incorporating many other statistic values resulting the turning
    back of the noble philosophy behind the creation of box plot. The modification using
    range value with the minimum and maximum values are being incorporated to suit the
    need of selected discrete distribution when outliers is not an important criteria anymore.
    The new modification of box plot is not based on the asymmetrical shape of distribution
    but more on the spreading and partitioning data into range measure. The new propose
    name for the box plot with only three values of statistics is called range-box plot.
  6. Yusof, F. M., Md. Ismail, A. I. B., Abu Hasan, Y.
    MATEMATIKA, 2018;34(2):205-226.
    Hantaviruses are etiological agents of zoonotic diseases and certain other dis-
    eases, which pose a serious threat to human health. When rodent and predator popula-
    tions share in an ecology, the competitive force of the populations can lead to a reduction
    or elimination of a hantavirus outbreak. The effect of the predator eliminating rodents
    and predator populations that tends to reduce or eliminate hantavirus infection is investi-
    gated. The existence of several equilibrium points of the model is identified and local and
    global stabilities of the model at these equilibrium points are analysed in detail. Numerical
    simulations are carried out to illustrate our model results.
  7. Siti Rohani Mohd Nor, Fadhilah Yusof, Arifah Bahar
    MATEMATIKA, 2018;34(2):227-233.
    The incorporation of non-linear pattern of early ages has led to new research
    directions on improving the existing stochastic mortalitymodel structure. Several authors
    have outlined the importance of encompassing the full age range in dealing with longevity
    risk exposure, by not ignoring the dependence between young and old ages. In this study,
    we consider the two extensions of the Cairns, Blake and Dowd model that incorporate the
    irregularity profile seen at the mortality of lower ages, which are the Plat, and the O’Hare
    and Li models respectively. The models’ performances in terms of in-sample fitting and
    out-sample forecasts were examined and compared. The results indicated that the O’Hare
    and Li model performs better as compared to the Plat model.
  8. Azmirul Ashaari, Tahir Ahmad, Wan Munirah Wan Mohamad
    MATEMATIKA, 2018;34(2):235-244.
    Pressurized water reactor (PWR) type AP1000 is a third generation of a nuclear
    power plant. The primary system of PWR using uranium dioxide to generate heat energy
    via fission process. The process influences temperature, pressure and pH value of water
    chemistry of the PWR. The aim of this paper is to transform the primary system of PWR
    using fuzzy autocatalytic set (FACS). In this work, the background of primary system
    of PWR and the properties of the model are provided. The simulation result, namely
    dynamic concentration of PWR is verified against published data.
  9. Chai, Jin Sian, Hoe, Yeak Su, Ali H. M. Murid
    MATEMATIKA, 2018;34(2):0-0.
    A mathematical model is considered to determine the effectiveness of disin-
    fectant solution for surface decontamination. The decontamination process involved the
    diffusion of bacteria into disinfectant solution and the reaction of the disinfectant killing
    effect. The mathematical model is a reaction-diffusion type. Finite difference method and
    method of lines with fourth-order Runge-Kutta method are utilized to solve the model
    numerically. To obtain stable solutions, von Neumann stability analysis is employed to
    evaluate the stability of finite difference method. For stiff problem, Dormand-Prince
    method is applied as the estimated error of fourth-order Runge-Kutta method. MATLAB
    programming is selected for the computation of numerical solutions. From the results
    obtained, fourth-order Runge-Kutta method has a larger stability region and better ac-
    curacy of solutions compared to finite difference method when solving the disinfectant
    solution model. Moreover, a numerical simulation is carried out to investigate the effect
    of different thickness of disinfectant solution on bacteria reduction. Results show that
    thick disinfectant solution is able to reduce the dimensionless bacteria concentration more
  10. Shaymaa Mustafa, Zainal Abdul Aziz, Arifah Bahar, Mohd Khairul Nizar Shamsuddin
    MATEMATIKA, 2018;34(2):261-269.
    Riverbank filtration (RBF) system is a surface water technology that is based
    on the natural treatment of filtration instead of the use of chemicals, to pre-treat sur-
    face water and provides public water supplies. Hydraulic conductivity value is one of the
    significant factors affecting the water quality in RBF systems. In this article, an analyti-
    cal modelling is developed to investigate the effect of this parameter on one dimensional
    contaminant transport in RBF system. The model is solved by using Green’s function
    approach. The model is applied for the first RBF system conducted in Malaysia. Gener-
    ally, the results show that increasing the hydraulic conductivity value lead to an increase
    in contaminant concentration in pumping well area.
  11. Yahaya Shagaiya Daniel, Zainal Abdul Aziz, Zuhaila Ismail, Faisal Salah
    MATEMATIKA, 2018;34(2):393-417.
    Analyzed the effects of thermal radiation, chemical reaction, heat gener-
    ation/absorption, magnetic and electric fields on unsteady flow and heat transfer of
    nanofluid. The transport equations used passively controlled. A similarity solution is
    employed to transformed the governing equations from partial differential equations to
    a set of ordinary differential equations, and then solve using Keller box method. It was
    found that the temperature is a decreasing function with the thermal stratification due to
    the fact the density of the fluid in the lower vicinity is much higher compared to the upper
    region, whereas the thermal radiation, viscous dissipation and heat generation enhanced
    the nanofluid temperature and thermal layer thickness.
  12. Amir S. A. Hamzah, Ali H. M. Murid
    MATEMATIKA, 2018;34(2):293-311.
    This study presents a mathematical model examining wastewater pollutant removal through
    an oxidation pond treatment system. This model was developed to describe the reaction
    between microbe-based product mPHO (comprising Phototrophic bacteria (PSB)), dissolved
    oxygen (DO) and pollutant namely chemical oxygen demand (COD). It consists
    of coupled advection-diffusion-reaction equations for the microorganism (PSB), DO and
    pollutant (COD) concentrations, respectively. The coupling of these equations occurred
    due to the reactions between PSB, DO and COD to produce harmless compounds. Since
    the model is nonlinear partial differential equations (PDEs), coupled, and dynamic, computational
    algorithm with a specific numerical method, which is implicit Crank-Nicolson
    method, was employed to simulate the dynamical behaviour of the system. Furthermore,
    numerical results revealed that the proposed model demonstrated high accuracy when
    compared to the experimental data.
  13. Hooi, M.H., Tiong, W. K., Tay, K. G., Chiew,K. L., Sze, S. N.
    MATEMATIKA, 2018;34(2):333-350.
    In this paper, we look at the propagation of internal solitary waves over three
    different types of slowly varying region, i.e. a slowly increasing slope, a smooth bump and
    a parabolic mound in a two-layer fluid flow. The appropriate mathematical model for this
    problem is the variable-coefficient extended Korteweg-de Vries equation. The governing
    equation is then solved numerically using the method of lines. Our numerical simulations
    show that the internal solitary waves deforms adiabatically on the slowly increasing slope.
    At the same time, a trailing shelf is generated as the internal solitary wave propagates
    over the slope, which would then decompose into secondary solitary waves or a wavetrain.
    On the other hand, when internal solitary waves propagate over a smooth bump or a
    parabolic mound, a trailing shelf of negative polarity would be generated as the results of
    the interaction of the internal solitary wave with the decreasing slope of the bump or the
    parabolic mound. The secondary solitary waves is observed to be climbing the negative
    trailing shelf.
  14. Bako Sunday Samuel, Mohd Bakri Adam, Anwar Fitrianto
    MATEMATIKA, 2018;34(2):365-380.
    Recent studies have shown that independent identical distributed Gaussian
    random variables is not suitable for modelling extreme values observed during extremal
    events. However, many real life data on extreme values are dependent and stationary
    rather than the conventional independent identically distributed data. We propose a stationary
    autoregressive (AR) process with Gumbel distributed innovation and characterise
    the short-term dependence among maxima of an (AR) process over a range of sample
    sizes with varying degrees of dependence. We estimate the maximum likelihood of the
    parameters of the Gumbel AR process and its residuals, and evaluate the performance
    of the parameter estimates. The AR process is fitted to the Gumbel-generalised Pareto
    (GPD) distribution and we evaluate the performance of the parameter estimates fitted
    to the cluster maxima and the original series. Ignoring the effect of dependence leads to
    overestimation of the location parameter of the Gumbel-AR (1) process. The estimate
    of the location parameter of the AR process using the residuals gives a better estimate.
    Estimate of the scale parameter perform marginally better for the original series than the
    residual estimate. The degree of clustering increases as dependence is enhance for the AR
    process. The Gumbel-AR(1) fitted to the threshold exceedances shows that the estimates
    of the scale and shape parameters fitted to the cluster maxima perform better as sample
    size increases, however, ignoring the effect of dependence lead to an underestimation of
    the parameter estimates of the scale parameter. The shape parameter of the original
    series gives a superior estimate compare to the threshold excesses fitted to the Gumbel
    distributed Generalised Pareto ditribution.
  15. Kerk, Lee Chang, Rohanin Ahmad
    MATEMATIKA, 2018;34(2):381-392.
    Optimization is central to any problem involving decision making. The area
    of optimization has received enormous attention for over 30 years and it is still popular
    in research field to this day. In this paper, a global optimization method called Improved
    Homotopy with 2-Step Predictor-corrector Method will be introduced. The method in-
    troduced is able to identify all local solutions by converting non-convex optimization
    problems into piece-wise convex optimization problems. A mechanism which only consid-
    ers the convex part where minimizers existed on a function is applied. This mechanism
    allows the method to filter out concave parts and some unrelated parts automatically.
    The identified convex parts are called trusted intervals. The descent property and the
    global convergence of the method was shown in this paper. 15 test problems have been
    used to show the ability of the algorithm proposed in locating global minimizer.
  16. Fauzi Mohamed Yusof, Mohd Hafiz Mohd, Yazariah Mohd Yatim, Ahmad Izani Md. Ismail
    MATEMATIKA, 2020;36(1):1-14.
    In this paper, the combined influences of biotic interactions, environmental components and harvesting strategy on the spread of Hantavirus are investigated. By employing a multi-species model consisting of (susceptible and infected) rodents and alien species, we show that interspecific competition from alien species has an effect in reducing the spread of infection, and this species could be employed as a potential biocontrol agent. Our analysis using numerical continuation and simulation also reveals the conditions under which Hantavirus infection occurs and disappears as the environmental conditions and the intensity of harvesting change. Without harvesting, infection emerges when environments are conducive. Inclusion of moderate harvesting in favourable environments can lead to disappearance of infection among rodent species. However, as the intensity of harvesting increases, this situation can cause extinction of all rodents species and consequently, jeopardise biodiversity. Overall, our results demonstrate how the interplay of different factors can combine to determine the spread of infectious diseases.
  17. 'Aaishah Radziah Jamaludin, Fadhilah Yusof, Suhartono
    MATEMATIKA, 2020;36(1):15-30.
    Johor Bahru with its rapid development where pollution is an issue that needs to be considered because it has contributed to the number of asthma cases in this area. Therefore, the goal of this study is to investigate the behaviour of asthma disease in Johor Bahru by count analysis approach namely; Poisson Integer Generalized Autoregressive Conditional Heteroscedasticity (Poisson-INGARCH) and Negative Binomial INGARCH (NB-INGARCH) with identity and log link function. Intervention analysis was conducted since the outbreak in the asthma data for the period of July 2012 to July 2013. This occurs perhaps due to the extremely bad haze in Johor Bahru from Indonesian fires. The estimation of the parameter will be done by quasi-maximum likelihood estimation. Model assessment was evaluated from the Pearson residuals, cumulative periodogram, the probability integral transform (PIT) histogram, log-likelihood value, Akaike’s Information Criterion (AIC) and Bayesian information criterion (BIC). Our result shows that NB-INGARCH with identity and log link function is adequate in representing the asthma data with uncorrelated Pearson residuals, higher in log likelihood, the PIT exhibits normality yet the lowest AIC and BIC. However, in terms of forecasting accuracy, NB-INGARCH with identity link function performed better with the smaller RMSE (8.54) for the sample data. Therefore, NB-INGARCH with identity link function can be applied as the prediction model for asthma disease in Johor Bahru. Ideally, this outcome can assist the Department of Health in executing counteractive action and early planning to curb asthma diseases in Johor Bahru.
  18. Khairur Rijal Jamaludin, Nolia Harudin, Faizir Ramlie, Mohd Nabil Muhtazaruddin, Che Munira Che Razali, Wan Zuki Azman Wan Muhamad
    MATEMATIKA, 2020;36(1):69-84.
    Prediction analysis has drawn significant interest in numerous field. Taguchi’s T-Method is a prediction tool that developed practically but not limited to small sample analysis. It was developed explicitly for multidimensional system prediction by relying on historical data as the baseline model and adapting the signal to noise ratio (SNR) as well as zero proportional concepts in strengthening its robustness. Orthogonal array (OA) in T-Method is a variable selection optimization technique in improving the prediction accuracy as well as help in eliminating variables that may deteriorate the overall performance. However, the limitation of OA in dealing with higher multidimensionality restraint the optimization accuracy. Binary particle swarm optimization used in this study helps to cater to the limitation of OA as well as optimizing the variable selection process to better prediction accuracy. The results show that if the historical data consist of samples with higher correlation of determination (R2) value for the model creation, the optimization process in reducing the number of variables would be much reliable and accurate. Comparing between T-Method+OA and T-Method+BPSO in four different case study, it shows that T-Method+BPSO performing better with greater R2 and means relative error (MRE) value compared to T-Method+OA.
  19. Lloyd Wen Feng Lee, Mohd Hafiz Mohd
    MATEMATIKA, 2020;36(2):85-98.

    2 (UKM)43600 Bangi, Selangor, Malaysia
    ∗Corresponding author:

    Numerous studies have linked biodiversity with zoonotic disease control. However, researchers have warned against simply believing that the increase in biodiversity can reduce the infection disease in the community. They proposed that amplification effect (increase in biodiversity accompanied by an increase in disease prevalence) might sometimes occur. Thus, we formulated a deterministic model to consider the impact of an amplification or dilution agent on the SNV transmission in the deer mouse population. Bifurcation analysis was carried out to examine the combined influences of the environmental carrying capacity, the interspecific competition strength and the impact of amplification or dilution agent on the deer mouse population. Our results showed that the system with amplification agent required a higher carrying capacity or stronger interspecific strength to compensate for its amplification effect in suppressing the SNV prevalence; this situation explains the lack of reduction in SNV prevalence despite the presence of high biodiversity in some empirical studies. In this study, we highlight the importance of investigating the roles of the additional species in an assemblage to better understand their relationship with the SNV prevalence in deer mouse population.
  20. Nurul Nadiah Abdul Halim, S. Sarifah Radiah Shariff, Siti Meriam Zahari
    MATEMATIKA, 2020;36(2):113-126.
    Preventive maintenance (PM) planning becomes a crucial issue in the real world of the manufacturing process. It is important in the manufacturing industry to maintain the optimum level of production and minimize its investments. Thus, this paper focuses on multiple jobs with a single production line by considering stochastic machine breakdown time. The aim of this paper is to propose a good integration of production and PM schedule that will minimize total completion time. In this study, a hybrid method, which is a genetic algorithm (GA), is used with the Monte Carlo simulation (MCS) technique to deal with the uncertain behavior of machine breakdown time. A deterministic model is adopted and tested under different levels of complexity. Its performance is evaluated based on the value of average completion time. The result clearly shows that the proposed integrated production with PM schedule can reduce the average completion time by 11.68% compared to the production scheduling with machine breakdown time.
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