http://ir.bdu.edu.et/handle/123456789/1826 Mon, 13 Jul 2026 15:00:38 GMT 2026-07-13T15:00:38Z http://ir.bdu.edu.et/handle/123456789/16868 Hesitant Fuzzy Algebraic Structures on Pseudo-TM Algebra with Multicriteria Decision Making Girum, Alemayehu This dissertation presents an in-depth study of fuzzy algebraic structures, specifically focusing on TM-algebras and pseudo-TM algebras by using various extensions of fuzzy set theory such as hesitant fuzzy sets, and bipolar hesitant fuzzy soft sets. These theories help to deal with uncertainty, hesitation, and vagueness in mathematical modeling. In this study, we also define and investigate fuzzy subsets within pseudo-TM algebras. Important structures like fuzzy pseudo-TM subalgebras and fuzzy pseudo-TM ideals are introduced. Their properties are discussed using operations such as Cartesian product and homomorphism. It is shown that the intersection of two fuzzy pseudo- TM-subalgebras is also a fuzzy pseudo-TM subalgebra, but their union may not be. The study deals with the idea of fuzzy congruence relations more deeply. A fuzzy congruence relation is a fuzzy equivalence relation that respects the algebraic structure. It is shown how such relations can preserve the fuzzy structure under mappings and how they can be used to simplify the algebra into equivalent classes. The connection between fuzzy pseudo-ideals and fuzzy congruence relations is also discussed, providing a strong algebraic framework for fuzzy systems. The study moves from fuzzy sets to hesitant fuzzy sets. It introduces hesitant fuzzy TM-subalgebras, hesitant fuzzy Tideals, hesitant fuzzy pseudo-TM subalgebras, and hesitant fuzzy pseudo-ideals. These structures allow multiple degrees of membership for each element, capturing hesitation in decision-making. Various properties of these structures are analyzed. It is shown that Cartesian products and homomorphic images of hesitant fuzzy ideals preserve the structure, under certain conditions. This provides a useful tool for modeling uncertain systems in mathematics and applications. The notions of bipolar hesitant fuzzy soft sets in TM-algebras are introduced. The combination of bipolarity (positive and negative views), hesitation (multiple values), and soft sets (parameter-based uncertainty) creates a powerful structure. These structures are applied to decision-making problems, especially when both satisfaction and dissatisfaction need to be considered. A numerical example is provided on selecting the best alcoholic drink based on multiple criteria, such as taste, health impact, and cost. Each criterion is evaluated with both positive and negative opinions, along with hesitation. The bipolar hesitant fuzzy soft set model is used to combine these opinions and find the best option. This shows the practical usefulness of the theoretical framework developed in this work. This research not only advances the theoretical understanding of fuzzy and hesitant fuzzy structures in algebra but also offers practical tools for modeling complex decision-making problems. The findings have potential applications in artificial intelligence, computer science, medical diagnosis, and other fields where human hesitation, dual opinions, and uncertainty are common Sat, 01 Nov 2025 00:00:00 GMT http://ir.bdu.edu.et/handle/123456789/16868 2025-11-01T00:00:00Z http://ir.bdu.edu.et/handle/123456789/16867 Fuzzy Hyper and Pythagorean Fuzzy Composite Structures on BCL–Algebra and LiuB–Algebra Abebe, Asmamaw This dissertation presents det ailed and thorough research on the notions of hyper BCL–algebra, fuzzy substructures in hyper BCL–algebra, fuzzy substructures in BCL–algebra, Pythagorean fuzzy substructures in BCL–algebra, fuzzy substructures in LiuB–algebra and Pythagorean fuzzy substructures in LiuB–algebra. It provides new theoretical understanding, well refined definitions and rigorous characterizations that contribute to the development of algebraic knowledge about these structures. The research begins by introducing the hyper BCL–algebraic structures, supported by proven properties, under which (weak, strong) hyper subalgebras, (weak, strong) hyper deductive systems and (weak, strong) hyper ideals of hyper BCL–algebra are defined and several relevant properties are investigated. The relations among strong hyper subalgebras, weak hyper subalgebras and hyper subalgebras, as well as among strong hyper ideals, weak hyper ideals and hyper ideals of hyper BCL– algebra are clearly demonstrated in the context of hyper BCL–algebras. In hyper BCL–algebras, the relationship between hyper deductive systems and weak deductive systems is established. The intersection and union of corresponding (weak, strong) hyper substructures of hyper BCL–algebras are shown to be conserved. Following the introduction of hyper substructures, the notions of fuzzy hyper algebras are introduced, characterized as fuzzy (weak, strong) hyper subalgebras, fuzzy (weak, strong) hyper deductive systems and fuzzy (weak, strong) hyper ideals. The conservation of intersections of corresponding substructures is established; however, unions of such substructures are generally not conserved justified by examples. The relationships among fuzzy (weak, strong) hyper substructures are also explored. After investigating additional relevant properties, we introduce the notions of fuzzy subalgebra, fuzzy deductive system and fuzzy ideal of BCL–algebra. Moreover, we prove that the complements of fuzzy substructures of BCL–algebra and its characteristic functions correspond to fuzzy substructures of BCL–algebra. In the BCL–algebra, we also prove that intersections of fuzzy subalgebras, fuzzy deductive systems and fuzzy ideals are fuzzy subalgebra, fuzzy deductive system and fuzzy ideal of BCL–algebra, respectively; however, unions of such substructures are not conserved justified by counter examples. Several additional properties of fuzzy substructures of BCL–algebra are also demonstrated. Following the introduction and investigation of fuzzy subsets of BCL–algebra, we extend these notions to Pythagorean fuzzy substructures of BCL–algebra; viii namely, Pythagorean fuzzy subalgebra, Pythagorean fuzzy deductive system and Pythagorean fuzzy ideal of BCL–algebra along with an investigation of their relevant properties. After introducing the Pythagorean fuzzy substructures of BCL–algebra, we present new definitions of LiuB–algebra based on BCL–algebra combined with a semi–group. These definitions are illustrated with examples and their properties are explored. Following these investigations, we introduce fuzzy substructures of LiuB–algebras, including fuzzy subalgebras, fuzzy deductive systems and fuzzy ideals. In relation to substructures of LiuB–algebra, we extend these notions to Pythagorean fuzzy subalgebra, Pythagorean fuzzy deductive system and Pythagorean fuzzy ideal and relevant results are derived, with their properties explored in detail. Finally, the fuzzy subsets of BCL-algebra and LiuB–algebra and Pythagorean fuzzy sets of BCL-algebra and LiuB–algebra are described by making use of some basic tools. These include the Cartesian products of fuzzy subalgebras in BCL-algebra, the level sets in Pythagorean fuzzy deductive systems of BCL-algebra, and the homomorphisms of Pythagorean fuzzy deductive systems of LiuB–algebra. In addition, LiuB–algebra is also described through the Pythagorean ( , )–fuzzy ideal, and related properties arising from each of these descriptions are carefully examined. ix Sat, 01 Nov 2025 00:00:00 GMT http://ir.bdu.edu.et/handle/123456789/16867 2025-11-01T00:00:00Z 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