Pusat Pengajian Sains Matematik - Tesis
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- PublicationA Weighted Least Squares Estimation Of The Polynomial Regression Model On Paddy Production For The Muda Agriculture And Development Authority (Mada) Area(2016-01)Musa, RoslizaThe curvilinear relationship between a dependent variable and several independent variables can be represented by a polynomial regression model. This model is used to study the relationship between response variable and predictor variable which contain square and higher-order term. Polynomial regression model is a special case of multiple regression model. The building of polynomial regression model has the same characteristics as multiple linear regressions in term of parameter estimation, regression inference, variable selection and model diagnostic. Weighted least square estimation is used as a remedy for non-constant variance. This study used polynomial regression model with weighted least square estimation to investigate paddy production of different paddy lots based on environmental and cultivation characteristics in Muda Agriculture and Development Authority (MADA) area.
- PublicationAn Improved Training Method For Wavelet Neural Networks For Solving Ordinary And Partial Differential Equations(2022-10)Tan Lee SenDifferential equations (DEs) have been widely used for modelling countless studies and applications in various disciplines. In recent years, artificial neural networks (ANNs) have gained attention in solving DEs in a more efficient way to approximate solutions of DEs. In this thesis, wavelet neural networks (WNNs) were employed and programmed to solve ordinary differential equations (ODEs) and partial differential equations (PDEs).
- PublicationApplication Of Two-Stage Game Cross- Efficiency Approach To Primary Health Care In Nigeria(2023-04)Adejoh Friday OduhThis study aims to analyse the performance of primary health care (PHC) in Nigeria by using two states (Benue and Lagos) as case studies and the game theory-based data envelopment analysis (DEA) technique is introduced. Game theory helps to uncover the dominant (leader) stage of an unobservable two-stage decision making unit (DMU) in the absence of prior knowledge.
- PublicationArrangement Of Letters In Words Using Parikh Matrices(2019-04)Poovanandran, GhajendranThe Parikh matrix mapping is an ingenious generalization of the classical Parikh mapping in the aim to arithmetize words by numbers. Two words are M-equivalent if and only if they share the same Parikh matrix. The characterization of M-equivalent words remains open even for the case of the ternary alphabet. Due to the dependency of Parikh matrices on the ordering of the alphabet, the notion of strong M-equivalence was proposed as an order-independent alternative to M-equivalence. In this work, we introduce a new symmetric transformation that justifies strong M-equivalence for the ternary alphabet. We then extend certain work of §erbanuja to the context of strong ^-equivalence and show that the number of strongly M-unambiguous prints for any alphabet is always finite.
- PublicationAssessment Of Hydraulic Response Due To Flood Mitigation Measures In Sg. Pinang Catchment, Penang(1995-02)Low Chee SoonThe current study aims to assess the hydraulic response of Sg. Pinang catchment under both existing and proposed conditions, by means of the advanced flow simulation model SWMM developed by the USEPA.
- PublicationB-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation(2021-01)Saiful Anuar, Hanis Safirah BintiIn this study, the Coupled Nonlinear Schrödinger Equation (CNLSE) which models the propagation of light waves in optical fiber is solved using numerical methods namely Finite Difference Method (FDM) and B-Spline collocation methods. The equation was discretized in space and time. We propose the discretization of the nonlinear terms in the CNLSE following the Taylor approach and a newly developed approach called Besse. The theta-weighted method is used to generalize the scheme whereby the Crank-Nicolson scheme (i.e θ = 0.5) is chosen. The time derivatives are discretized by forward difference approximation. For each approach, the space dimension is then discretized by five different collocation methods independently. The first method for Taylor approach is based on FDM whereby the space derivatives are replaced by central difference approximation.
- PublicationBayesian Networks With Greedy Backward Elimination In Feature Selection For Data Classification(2019-03)Ang, Sau LoongNaive Bayes (NB) is an efficient Bayesian classifier with wide range of applications in data classification. Having the advantage with its simple structure. Naive Bayes gains attention among the researchers with its good accuracy in classification result. Nevertheless, the major drawback of Naive Bayes is the strong independence assumption among the features which is restrictive. This weakness causes not only confusion in the causal relationships among the features but also doubtful representation of the real structure of Bayesian Network for classification. Further development of Naive Bayes in augmenting extra links or dependent relationships between the features such as the Tree Augmented Naive Bayes (TAN) end up with slight improvement in accuracy of classification result where the main problems stated above remain unsolved.
- PublicationBinary Artificial Bee Colony Optimization For Weighted Random 2 Satisfiability In Discrete Hopfield Neural Network(2023-05)Muhammad Sidik, Siti SyatirahOne of the alternatives to improve the modeling of the Discrete Hopfield Neural Network is by implementing different variants of logical rules. In this context, Satisfiability is suitable as a logical rule in Discrete Hopfield Neural Network due to the simplicity of the structure, and fault tolerance. Hence, this thesis will utilize Non-Systematic Weighted Random 2 Satisfiability incorporating with Binary Artificial Bee Colony algorithm in Discrete Hopfield Neural Network. The Binary Artificial Bee Colony will be utilized to optimize the logical structure according to the ratio of negative literals by capitalizing the features of the exploration mechanism of the algorithm. Then, the Election algorithm will be utilized to obtain a satisfied interpretation of the correct logical structure in the training phase of the Discrete Hopfield Neural Network. This proposed model will be employed in the Improved Reverse Analysis method to extract the relationship between various fields of real-life data sets based on logical representation. This thesis will be presented by implementing simulated, and benchmark data sets with multiple performance evaluation metrics. Based on the findings, the proposed model outperforms other models.
- PublicationDevelopment Of Variable Sampling Interval Run Sum T Chart And Triple Sampling X ̅ Chart With Estimated Process Parameters(2022-03)Nahar Mim, FaijunThe Shewhart x ̅ control chart is a useful chart in process monitoring. However, the Shewhart x ̅ chart’s performance is significantly affected if the process standard deviation is erroneously estimated. To circumvent this problem, the t chart is commonly used as an alternative to the Shewhart x ̅ chart. The first and second objectives of this thesis aim at enhancing the performance of the basic t chart by proposing the variable sampling interval run sum (VSI RS) t charts for monitoring the mean of a process from a normal distribution, based on known and estimated process mean, respectively. The Markov chain technique is used to compute the optimal parameters for the new charts.
- PublicationDouble Sampling Auxiliary Information Chart And Exponentially Weighted Moving Average Auxiliary Information Chart, Both Based On Variable Sampling Interval, And Measurement Errors Based Triple Sampling Chart(2022-09)Umar, Adamu AbubakarThe concept of using auxiliary information (AI) in control charts is growing in popularity among researchers. Control charts using the AI technique have been found to be more effective than control charts without the AI technique. The first objective of this thesis is to develop a variable sampling interval (VSI) double sampling (DS) chart using the AI technique (called VSI DS-AI chart) for monitoring the process mean. The charting statistics, optimal designs and implementation of the VSI DS-AI chart are discussed. The steady-state average time to signal (ssATS) and steady-state expected average time to signal (ssEATS) criteria are used as the performance measures of the proposed VSI DS-AI chart. The ssATS and ssEATS results of the VSI DS-AI chart are compared with those of the double sampling AI, variable sample size and sampling interval AI, exponentially weighted moving average AI (EWMA-AI) and run sum AI (RS-AI) charts. The comparison reveals that the VSI DS-AI chart performs better than the competing charts for all shift sizes, except the EWMA-AI and RS-AI charts for small shifts.
- PublicationEconomic And Economic-Statistical Designs Of Variable Sample Size And Sampling Interval Coefficient Of Variation Chart And Development Of Variable Sample Size Multivariate Coefficient Of Variation Chart For Short Runs(2023-05)Chew, YiyingControl charts are one of the most useful statistical process control tools that have been adopted for process monitoring in numerous fields. Traditional control charts are ineffective in process monitoring when the process being monitored does not have the process mean and variance that are independent of one another. Under such a circumstance, the coefficient of variation (CV) is used in process monitoring, where the ratio of the standard deviation to the mean is monitored. The variable sample size and sampling interval CV (VSSI CV) chart was shown to be more effective than the Shewhart CV (SH CV) chart in the literature but only in terms of the statistical performance. Thus, the first objective of this thesis is to investigate the economic and the economic-statistical performance of the VSSI CV chart. By minimizing the cost via the economic and economic-statistical designs, the VSSI CV chart can be implemented more economically. The economic and economical-statistical performance of the VSSI CV chart is studied using numerical examples, where comparisons with the SH CV chart are made. The results show that the VSSI CV chart outperforms the SH CV chart, in terms of both economic and economic-statistical performance. A study on the misspecification of the shift size is also conducted to study the effect of wrongly specifying the shift size on the optimal cost.
- PublicationEfficient Entropy-Based Decoding Algorithms For Higher-Order Hidden Markov Model(2019-03)Chan, Chin TiongHigher-order Hidden Markov model (HHMM) has a higher prediction accuracy than the first-order Hidden Markov model (HMM). This is due to more exploration of the historical state information for predicting the next state found in HHMM. State sequence for HHMM is invisible but the classical Viterbi algorithm is able to track the optimal state sequence. The extended entropy-based Viterbi algorithm is proposed for decoding HHMM. This algorithm is a memory-efficient algorithm due to its required memory space that is time independent. In other words, the required memory is not subjected to the length of the observational sequence. The entropybased Viterbi algorithm with a reduction approach (EVRA) is also introduced for decoding HHMM. The required memory of this algorithm is also time independent. In addition, the optimal state sequence obtained by the EVRA algorithm is the same as that obtained by the classical Viterbi algorithm for HHMM.
- PublicationEvaluating The Effectiveness Of Monetary Versus Fiscal Policies In Malaysia Using Macroeconometric Approaches(2022-09)Ismail, Siti FatimahThe purpose of this thesis is to examine the roles of monetary and fiscal policies in achieving Malaysia's basic macroeconomic goals of price stability and long-term growth. This thesis is divided into two main parts. The first part employs nonlinear modelling techniques to investigate the nonlinear effect of policy stances on GDP growth and inflation using Malaysian data from 1980Q1 to 2018Q1. The results of the STAR and TAR approaches reveal the existence of a nonlinear relationship. The results show that no single policy tool can lead to the policy objectives of high GDP growth and low inflation at once. Both STAR and TAR results evident that the fiscal tools of government expenditure, current account balance and debt are harmful to the economic growth and the impact on inflation is either negative or not significant. In terms of monetary policy, the policy rate is a less effective tool to stimulate GDP growth but is a better option to control or reduce inflation. Meanwhile, real effective exchange rate encourages GDP growth but it does not influence price level significantly. The STAR model is a preferred model in capturing the gradual threshold adjustment in economic variables. In the second part of the analysis, a macroeconometric model is developed to evaluate the performance of Malaysia's monetary and fiscal policies as well as to project different economic outcomes and scenarios through numerical simulations.
- PublicationForecasting The Decision Based On Risk Perception Using Bayesian Game Theory Approach In Preventing Hand, Foot And Mouth Disease (Hfmd) In Pulau Pinang, Malaysia(2023-07)Abu Mansor, Siti NurleenaHand, foot, and mouth disease (HFMD) is amongst common diseases which often occurs in outbreaks and up to now, there is no effective vaccine yet to be found. Known to be caused by enterovirus usually typed Coxsackie virus A16 and Enterovirus 71, this disease is common among infants and children below the age of five. In this research, the HFMD epidemic models in Seberang Perai Tengah, Pulau Pinang are examined. Number of cases in epidemic week are used to compare HFMD epidemic model with and without virus shedding in the environment and contemplate their reproduction numbers. Furthermore, human behaviour has become the main factor in HFMD disease transmission systems. The effectiveness of interventions is largely dependent on the behaviour of the population. Risk perception shapes human behaviours in many ways, especially in decision making. Here, the factors that determine parents’ risk perception on HFMD disease and how they quantify their level of risk are explored. Factors such as knowledge of HFMD, health beliefs, preventive behaviour, and experienced with HFMD are put together and analysed to develop a framework to show the relationship with risk perception. Moreover, when making decisions related to health behaviours, one's decisions do not influence the decisions of others.
- PublicationGeometrical Analysis Of Quintic Trigonometric Bézier Surface(2023-05)Mohd Kamarudzaman, Anis Solehah BintiThe quintic trigonometric Bézier curve with two shape parameters has been extensively investigated due to its flexibility. Commonly, the Bézier curve has been widely used as a curve or surface designing tool in manufacturing industries. Hence, the study of surface curvature is required in design analysis. In this research, the quintic trigonometric Bézier curve has been implemented to generate various adjustable surfaces such as tensor product, swept, swung, ruled, and developable surfaces by using various value of shape parameters. The effect of the shape parameters on the surfaces has been demonstrated. Gaussian curvature, mean curvature, and Shape Index-Curvedness (SC Curvature) will be used to examine the geometric characteristics of surfaces. The Gaussian and mean curvature plots for each surface are visualised and evaluated. In addition, this study presents an alternate method for inspecting the geometrical properties of a surface using algebraic invariants. Surface curvature can be compared using differential geometry and algebraic invariants approach, leading to interesting discoveries. Additionally, the numerical data are presented to support the surface’s geometrical analysis that has been demonstrated by the 3D plot display. In conclusion, different surfaces will produce different curvature value, however, the shape parameters will alter the curvature’s intensity.
- PublicationHierarchical Gaussian Process Models For Loss Reserving(2021-12)Ang,Zi QingLoss reserving is one of the main activities of actuaries in the insurance industry and is done to ensure the financial health of companies as well as protecting consumers’ interest. Techniques applied by the practitioners are highly regulated, but researchers are still ongoing in the pursuit of finding methods to improve predictive accuracy and to establish a measure of predictive uncertainties. Diverting from the link ratio methods, researchers have experimented with parametric models such as growth-curve models and models involving dynamical systems, as well as nonparametric models. Researchers in this field have increasingly shown interests in utilizing Bayesian methods to measure predictive uncertainties.
- PublicationHybrid Model In Machine Learning With Robust Regression For Handling Multicollinearity Outlier In Big Data And Its Application To Agriculture(2023-01)MukhtarIn this research, 29 independent single variables and 435 independent interaction variables were identified. The limitation of this research were to address the problems such as irrelevant variables, multicollinearity and outliers.
- PublicationHybridization Model For Capturing Long Memory And Volatility Of Brent Crude Oil Price Data(2022-07)Al-Gounmeein, Remal Shaher HussienThe Brent crude oil price indices are typically nonlinear, nonstationary, and non-normal behavior with a long memory and high heteroscedasticity; hence, capturing the controlling properties of their changes is difficult. Subsequently, these phenomena weaken the validity and the accuracy of the result of the forecasting methods. Therefore, this study focuses on the hybridization method to capture long memory behavior and heteroscedasticity in the dataset and improve Brent crude oil price forecasting accuracy. Recently, the hybridization method for the autoregressive fractionally integrated moving average (ARFIMA) model has been introduced as an effective technique for overcoming the nonlinear, nonstationary, and non-normal behavior with high heteroscedasticity in a time series dataset. ARFIMA hybridization method presents several characteristics that other traditional methods do not have. Thus, this thesis proposed three new models and employed 12 different techniques based on combining and hybridizing the ARFIMA model with traditional forecasting techniques to forecast the Brent crude oil price. The three new models, namely, ARFIMA with the asymmetric power autoregressive conditional heteroscedasticity (ARFIMA-APARCH), ARFIMA with the Glosten, Jagannathan, and Runkle generalized autoregressive conditional heteroscedasticity (ARFIMA-GJRGARCH), and ARFIMA with the component standard GARCH (ARFIMA-csGARCH) are proposed. This proposal aims to obtain improved forecasting results and solve the forecasting inaccuracy problem in oil price series.
- PublicationInterpolasi Data Berselerak(1994-03)Rahmita WirzaTesis ini bertujuan untuk meninjau teknik-teknik bagi memodelkan permukaan yang licin bagi data berselerak dan penganggaran data berselerak tiga dimensi yang diberikan. Kaedah yang akan dibincangkan melibatkan tiga langkah iaitu, penyegitigaan data domain; penganggaran terbitan separa pada setiap data yang diberi untuk menghasilkan permukaan yang licin dan penakrifan skema interpolasi.
- PublicationLaplace Transform With Modified Analytical Approximate Methods For Fractional Differential Equations(2022-10)Hailat Ibrahim Yousef JaberIn this study, approximate analytical methods are highlighted. These methods are: the combination of the Laplace transformation with homotopy perturbation method (HPM) namely Laplace transform homotopy perturbation method (LT-HPM), Adomian decomposition method (ADM) namely Laplace transform Adomian decomposition method (LTADM), variational iteration method (VIM) namely Laplace transform variational iteration method (LT-VIM). The main target of this thesis is to improve and apply these methods to avoid the drawbacks and find the analytical approximate solutions for some cases of linear and nonlinear ordinary FDEs.