Pusat Pengajian Sains Matematik - Tesis

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A Resolution Based Automated Theorem Proving System Using Concurrent Processing Approach
(1994-05)
Natarajan, Surash
The research reported in this thesis is devoted to the use of concurrent processing for developing a resolution based automated theorem proving system, an application in the area of artificial intelligence. Our purpose in doing this is to study the usefulness of concurrent processing in enhancing the problem solving process in a resolution based automated theorem proving system. During our research here we investigated which component of the theorem prover can be decomposed into introducing concurrent processing and how this should be done. Our main aim in building this theorem prover was not mainly in producing a high performance theorem prover but to build a system that can be considered to be a prototype that would illustrate the idea of introducing concurrent processing in resolution based theorem provers. We believe that concurrent processing is the intermediate step in moving from sequential processing towards parallel processing. Concurrent processing provides the simplicity of sequential system design with efficient processing capabilities of parallel system. In our discussion here we present a novel design of the system and how we propose to implement it.
A Weighted Least Squares Estimation Of The Polynomial Regression Model On Paddy Production For The Muda Agriculture And Development Authority (Mada) Area
(2016-01)
Musa, Rosliza
The 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.
An Improved Training Method For Wavelet Neural Networks For Solving Ordinary And Partial Differential Equations
(2022-10)
Tan Lee Sen
Differential 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).
An Integrated Fuzzy Model For Pattern Recognition
(2016-02)
Sagir, Abdu Masanawa
Medical diagnosis is a process of investigating which medical condition, disease or disorder describes signs and symptoms of a patient. Medical diagnosis helps to obtain different features representing the different variation of the disease. The decision about presence or absence of diseases of patients is a challenging task because many signs and symptoms are non-specific; and many tests might be required. To recognise an accurate diagnosis of symptom analysis, the physician may need efficient diagnosis system that can predict and classify patient condition. This thesis describes a methodology for developing an integrated fuzzy model by utilising the application of adaptive neuro fuzzy inference system (ANFIS) that can be used by physicians to accelerate diagnosis process. Feature selection approach was used to identify and remove unneeded, irrelevant and redundant attributes from the data that do not contribute to the accuracy of a predictive model. The proposed method used Hold-out validation technique, which divides the training and test data sets into twothirds to one-third, respectively. The proposed method uses grid partition technique to cope with seven input attributes and Gaussian membership functions than conventional method built-in Matlab, which uses small number of input attributes usually less than five. For robustness, twelve benchmarked datasets obtained from University of California at Irvine’s (UCI) machine learning repository were used in this research.
Application Of Two-Stage Game Cross- Efficiency Approach To Primary Health Care In Nigeria
(2023-04)
Adejoh Friday Oduh
This 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.
Approximation Methods For Solving Hiv Infection Models In Fuzzy Environment
(2024-05)
Almismaery, Hafed H Saleh
Fuzzy differential equations (FDEs) have a wide range of applications in physics, applied sciences, and engineering and has become undeniably an essential tool for modelling a wide range of real-life phenomena and even more so, those involved with uncertainties such as HIV infection models. Nevertheless, the majority of mathematical representations for fuzzy HIV infection, as depicted in nonlinear models, suffer from a deficiency in analytical solutions whereby these solutions are frequently elusive. Consequently, the prevalent approach to address fuzzy HIV models involves employing approximation methods, typically through numerical techniques. Such numerical methods yield solutions in numeric values. However, it's important to note that these approximate numerical methods face limitations in directly resolving fuzzy HIV infection models and necessitate the use of discretization or linearization. In contrast, approximate analytical methods prove versatile, as they not only apply to fuzzy HIV models without requiring linearization or discretization but also furnish continuous solutions. Therefore, in this thesis, the approximate analytical methods fuzzy homotopy perturbation method (FHPM), fuzzy variational iteration method (FVIM), and their modified versions are considered for solving several linear and nonlinear fuzzy HIV infection models under the concept of Hukuhara differentiability approach to provide approximate analytical solutions in the form of convergence series solution. The existence and uniqueness of the solution for linear and nonlinear fuzzy HIV infection models in this work have also been investigated.
Arrangement Of Letters In Words Using Parikh Matrices
(2019-04)
Poovanandran, Ghajendran
The 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.
Assessment Of Hydraulic Response Due To Flood Mitigation Measures In Sg. Pinang Catchment, Penang
(1995-02)
Low Chee Soon
The 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.
B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation
(2021-01)
Saiful Anuar, Hanis Safirah Binti
In 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.
Bayesian Networks With Greedy Backward Elimination In Feature Selection For Data Classification
(2019-03)
Ang, Sau Loong
Naive 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.
Binary Artificial Bee Colony Optimization For Weighted Random 2 Satisfiability In Discrete Hopfield Neural Network
(2023-05)
Muhammad Sidik, Siti Syatirah
One 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.
Detection Of Outliers And Structural Breaks In Structural Time Series Model Using Indicator Saturation Approach
(2023-03)
Rose, Farid Zamani Che
The presence of structural changes, specifically outliers and structural breaks, adversely affects the estimation of economic and financial indicators in terms of the model accuracy and forecasting performance. Focusing on the detection of outliers and structural breaks, which has recently gained growing research interest, this study aimed to examine the performance of indicator saturation, as an extension of the general-to-specific (GETS) modelling, in detecting these structural changes in structural time series model framework. The proposed technique is capable to detect the location, duration, magnitude and number of structural changes in time series data. To date, prior studies only considered using Autometrics embodied in OxMetrics to apply this approach in static data generating process (DGP). Addressing this gap, this study used the gets package in R to examine the performance of indicator saturation in dynamic model viz state space model. Through Monte Carlo simulations, the performance of indicator saturation was evaluated in terms of potency and gauge. Based on the simulation results, the sequential selection algorithm outperformed the non-sequential selection approach in the automatic GETS model selection procedure. The results also suggested α = 1/T as the optimum level of significance level.
Development Of Robust Memory-Type Charts Under Repetitive Sampling And Triple Sampling Charts For The Gamma Process
(2024-04)
Mahmood, Yasar
Production processes in modern industries usually produce products with small variations due to technological advancement. The Shewhart-type charts are insensitive in detecting small process shifts. By developing memory-type and adaptive-type charts, researchers have solved the shortcomings of the Shewhart-type charts in detecting small shifts. Also, due to high sampling costs and destructive testing, quality engineers use individual control charts to monitor the process mean. There are three objectives in this thesis. Firstly, the triple exponentially weighted moving average (TEWMA) scheme and Tukey control chart (TCC) are combined to develop the TEWMA-TCC and repetitive sampling (RS) based RS-TEWMA-TCC, to monitor the mean of normal and non-normal distributed processes. The TEWMA-TCC, RS-TEWMA-TCC and competing charts are compared based on average run length (ARL), standard deviation of the run length (SDRL) and median run length (MRL) metrics under both zero-state (ZS) and steady-state (SS) conditions. The TEWMA-TCC and RS-TEWMA-TCC display dominance in detecting mean shifts in both directions. They are also robust to skewed distributions in that they are devoid of the ARL-biased problem. Secondly, the RS for cumulative sum (CUSUM)-type statistics discussed by Riaz et al. (2017) is coupled with the Shewhart chart to propose the RS Shewhart exponentially weighted moving average CUSUM TCC (RS-SEC-TCC).
Development Of Variable Sampling Interval Run Sum T Chart And Triple Sampling X ̅ Chart With Estimated Process Parameters
(2022-03)
Nahar Mim, Faijun
The 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.
Double 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 Abubakar
The 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.
Dynamics Of Co-Infectious Childhood Respiratory Diseases: Pertussis And Pneumonia
(2023-02)
Yakubu, Aisha Aliyu
Pertussis is a vaccine-preventable respiratory disease that affects humans of all age groups, yet there are reported cases of resurgence. The disease is highly contagious and has posed detrimental effects on the lives of infants globally. The impact of pertussis worsened with the presence of viral infections such as pneumonia. Therefore, it is imperative to study the behavior of these diseases and suggest control strategies using a mathematical modeling approach. The study area and literature of mathematical models on pertussis and pneumonia co-infection dynamics is rather scanty. Therefore, this study is aimed at obtaining model equations using a system of nonlinear ordinary differential equations for a better understanding of the transmission dynamics and control of these diseases in the infant population. Further, the models are used to evaluate the intervention strategies for disease control. The first model is the general model describing the transmission dynamics of pertussis which incorporates a maternally derived immunity compartment. The dynamical behavior of the basic model is analyzed analytically and numerically. Numerical simulations were carried out using mathematical software. The basic reproduction number of the model is obtained and its behavior is analyzed by varying parameters.
Economic 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, Yiying
Control 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.
Efficient Entropy-Based Decoding Algorithms For Higher-Order Hidden Markov Model
(2019-03)
Chan, Chin Tiong
Higher-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.
Estimation Of Weibull Parameters Using Simulated Annealing As Applied In Financial Data
(2023-03)
Hamza, Abubakar
An accurate analysis of financial data is vital to justify sustainability for investment potential in a company. Weibull distributions can be used to examine investment behaviour due to their flexibility to be transformed into other types of distribution. However, the selection of the most suitable estimators is still a challenging task. The present study proposes a simulated annealing algorithm (SA) in estimating the parameters of Weibull distribution with application to modified internal rate of return data (MIRR).The objective is to examine the investment potential of the shari’ah compliance companies of the Malaysia property sector (MPS). The MIRR were computed based on the data extracted from the companies’ financial reports from 2010 to 2018. The performance of the SA algorithm has been explored in terms of accuracies and estimation errors. The finding reveals that the Weibull distribution is well-suited to describing the investment behaviour of the MPS based on the estimates via the SA algorithm. Therefore, purchasing shares in this sector is very attractive for a long-term investment period, but may have a high risk of committing it as a result of fluctuations in the mean and variance of the estimate. Additionally, the two-parameter Weibull distribution has been extended by incorporating additional parameters to capture the uncertainty behaviour in the financial data.
Evaluating A New Adaptive Group Lasso Imputation Technique For Handling Missing Values In Compositional Data
(2024-08)
Tian, Ying
Pie chart is a widely used statistical chart to represent the proportions of various components in a certain entity. The shares of data in a pie chart, also known as compositional data, consist of non-negative values, containing only relative information. However, in many real-life domains, a substantial amount of missing values is often collected. The complexity of compositional data with missing values renders traditional estimation methods inadequate. In this thesis, a compositional data imputation method designed based on LASSO is proposed combining group LASSO and adaptive LASSO analysis methods. The estimation effects of highdimensional and low-dimensional compositional data with missing values are compared through simulation studies and case analyses under different missing rates, dimensions, and correlation coefficients. Considering the impact of outliers on the accuracy of estimation, both simulation and case analysis are conducted to compare the proposed algorithm against four existing methods. The experimental results demonstrate that the proposed adaptive group LASSO method produces a better imputation performance, MSE, MADE, RMSE and NRMSE increased by up to 26.6% at selected missing rates. Future work analyses the effect of imputation under continuous missing rates, MAR missing mechanism and more model evaluation criteria.

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