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