http://ir.bdu.edu.et/handle/123456789/1822 Sat, 13 Jan 2001 07:33:11 GMT 2001-01-13T07:33:11Z http://ir.bdu.edu.et/handle/123456789/16846 “Fuzzy Set in UP-Algebra” Birtukan, Yirga The aim of this project, we introduce a new algebraic structure, called UP-algebra (UP means the University of Phayao) and a concept of UP-ideals, UP-sub algebras and UP-filters of UP-algebra and then we introduce and study fuzzy UP-sub algebras, fuzzy UP-ideals and fuzzy UP-filters of UP-algebras and investigate some of its properties. The notions of upper t- level subsets and lower t- level subsets are introduced from some fuzzy sets, and its characterizations are given. Keywords: UP-algebra, UP-sub algebras, UP-ideals , UP-filters, Fuzzy UP-sub algebra, Fuzzy UP-ideal, Fuzzy UP-filter, Upper t- level subset, Lower t- level subset, prime subsets, prime fuzzy sets. Sat, 01 Jun 2024 00:00:00 GMT http://ir.bdu.edu.et/handle/123456789/16846 2024-06-01T00:00:00Z http://ir.bdu.edu.et/handle/123456789/16845 ”Mathematical modeling and analysis of cholera dynamics Gashaw, Mihiret In this project, we investigate an epidemic model for the dynamics of cholera infections. The model consists of four compartments; the susceptible population( ), infectious population ( ), the recovered population( ) and the environment that serves as a breeding ground for the bacteria ( ). We conducted an analysis on the existence of all the equilibrium points; the disease free equilibrium and endemic equilibrium. The reproduction number ( ) was computed by using Next generation matrix approach. Disease free equilibrium was found to be locally asymptotically stable if the reproduction number was less than one ( ). The most sensitive parameter to the basic reproduction number was determined by using sensitivity analysis. A numerical simulation of the system of differential equations of the epidemic model was carried out for interpretations and comparison to the qualitative solutions. The findings showed that as the number of infectious population increases, the number of susceptible human decreases in the system. Sun, 01 Sep 2024 00:00:00 GMT http://ir.bdu.edu.et/handle/123456789/16845 2024-09-01T00:00:00Z http://ir.bdu.edu.et/handle/123456789/16825 Hybrid Machine Learning Models in Banking and Peer-to-Peer Lending for Credit Card Fraud and Credit Risk Prediction: Addressing Data Imbalance with SMOTE Tamiru, Melese Advancements in technology and e-commerce have made credit cards a common payment method, reducing reliance on cash. However, this shift has also led to a rise in online fraud, causing significant financial losses. Detecting credit card fraud and predicting credit risk re mains a challenge for banks and emerging Peer-to-Peer (P2P) lending systems. The growing demand for credit and the rapid expansion of financial institutions highlight the need for ad vanced tools to detect fraud, manage risks, streamline operations, and enhance customer ser vice. In traditional banking, credit officers assess creditworthiness, but biased data and subjec tive evaluations make it difficult to distinguish defaulters from non-defaulters. Similarly, P2P lending faces challenges such as limited borrower information, trust issues, and poor risk as sessment. Information asymmetry often results in inaccurate default risk estimates. Moreover, the online nature and high volume of applications in both sectors complicate manual risk as sessments, leading to inefficiency and herding behavior. Efficient credit risk prediction is vital to mitigate both credit risk and fraud. While ma chine learning is widely used for these purposes, standalone models often struggle with large, complex datasets, non-linear effects, and preserving high-dimensional correlations. These limi tations hinder their predictive performance. In this thesis, we developed hybrid machine learning models for credit card fraud detection and credit risk prediction. The research focuses on three key areas: credit card fraud detection, credit risk in P2P lending, and credit risk in traditional banking. A Convolutional Neural Network (CNN) was utilized to extract features from various datasets, transforming them into one-dimensional arrays for integration with machine learning classifiers such as Support Vector Machine (SVM), Random Forest (RF), Decision Tree (DT), Gradient Boosting Decision Trees (GBDT), Logistic Regression (LR), and k-Nearest Neighbors (kNN). Datasets were sourced from Kaggle, a local Ethiopian bank, and P2P lending platforms. To address data imbalance, the Synthetic Minority Oversampling Technique (SMOTE) was em ployed to generate synthetic data points. Model performance was evaluated using metrics such as accuracy, precision, recall, F1-score, and Area Under the Curve (AUC). The hybrid CNN-SVM model achieved notable success in fraud detection, with an accuracy of 91.08%. For credit risk prediction in banks, the hybrid models outperformed traditional methods, with CNN-SVM achieved 98.60% accuracy. In P2P lending, the CNN-kNN model reached an accuracy of 97.60%. These findings demonstrate that hybrid models significantly improve credit risk assessment and fraud detection capabilities. Their integration into financial institutions’ processes can help mitigate losses, protect customers, and optimize resource allocation. We recommend that stakeholders in the financial sector adopt these models while ensuring ongoing evaluation for effectiveness and compliance with industry standards Sat, 01 Feb 2025 00:00:00 GMT http://ir.bdu.edu.et/handle/123456789/16825 2025-02-01T00:00:00Z http://ir.bdu.edu.et/handle/123456789/16798 Superposition Operator on Fock and Harmonic Fock Spaces Eshetu, Yonas The superposition operator is a nonlinear operator that arises in a wide range of mathematical contexts, particularly in functional analysis and operator theory. It plays a crucial role in several areas including nonlinear functional analysis, integral equations, differential equations, and harmonic analysis. The study of this operator has a long history especially in the context of real-valued func tion domains. In recent years, there has been increasing interest in exploring its properties within spaces of analytic functions. Much of this research fo cuses on identifying the various forms of the operator that map one space to another, as well as analyzing its boundedness, compactness, and continuity an alytic structures. However, its topological, dynamical, and spectral structures in these spaces remain less understood. This dissertation aims to address this gap by thoroughly investigating these aspects of the operator on Fock and harmonic Fock spaces. The dissertation is structured into six chapters with each chapter focusing on specific structural aspects of the operator. The first chapter provides historical context, introduces the operator, and presents the essential background results that lay the foundation for the subsequent analysis. Chapter two presents our findings on the various topological properties of weighted superposition operator on analytic Fock spaces. More specifically, we analyze key structures such as boundedness from below, strict singularity, or der boundedness, compact difference, Fréchet differentiability, Hilbert adjoint, self-adjointness, closed range, fixed point, and the invariant subspace problem. Additionally, we characterize the operator’s global homeomorphism property in terms of its ray invertibility conditions. The results in this chapter effectively illustrate how the weighted superposition operator serves as a prototypical ex amplefor highlighting the fundamental differences between linear and nonlinear operator theories. The dissertation then delves into Chapter three where the iterated structures of the operator are studied. We establish that the operator is power bounded if and only if it is mean ergodic. We further show the Fock spaces do not support cyclic weighted superposition operators, implying that no orbit of the operator forms a frame. We also identify conditions under which the operator preserves frames, tight frames, Riesz bases, and semigroup structures. In particular, the results show that the operator preserves frames if and only if it is linear. vi Chapter four focuses on the spectral properties of the operator on Fock spaces. We follow several approaches in nonlinear spectral theory and iden tify its various spectral sets. The results show that most of the spectral forms introduced so far coincide and contain singletons for this operator. The classi cal, asymptotic, and connected eigenvalues, and some numerical ranges of the operator are also identified. We further prove the operator is both linear and odd asymptotically with respect to the pointwise multiplication operator on the spaces. Expanding the scope of the underlying spaces, Chapter five reexamines the topological and spectral properties of the superposition operator on Harmonic Fock spaces Fp H . It is proven that these spaces do not support a nontrivial com pactness structure for the operator, and that a nontrivial order-bounded structure exists only when the operator acts on F∞ H . Furthermore, we show every su perposition operator in these spaces is a closed map and provide an explicit expression for its range. Unlike in the analytic Fock spaces setting, where no nontrivial bounded below superposition operator exists, we identify conditions under which the operator exhibits bounded-below behavior in harmonic Fock spaces. Additionally, we establish local invertibility conditions that imply global invertibility and observe that the operator’s spectral sets and numerical ranges are broader in harmonic Fock spaces compared to Fock spaces. Finally, Chapter six concludes the dissertation by summarizing the main f indings in tabular form and discussing potential directions for future research Thu, 01 May 2025 00:00:00 GMT http://ir.bdu.edu.et/handle/123456789/16798 2025-05-01T00:00:00Z