Fuzzy normed rings

This thesis consists of six chapters. The first part of the thesis is devoted to the introduction. In this section, the concept of uncertainty, the historical background and development of our subjects, past studies and the deficiencies we aim to eliminate, the purpose and motivation of our study and the flow of our thesis are included. In the second chapter, basic concepts and theorems about fuzzy logic, semigroup theory and normed rings are given. The third section consists of fuzzy semigroups. Here, some fuzzy transformation semigroups are defined and examined and a notation that will provide convenience is proposed. The fourth chapter is the most comprehensive part of our study. In this section, by using fuzzy sets, fuzzy normed rings are defined using continuous t-norms and s-norms, some related algebraic structures are examined, and examples are given. At the same time, some fuzzy subrings and ideals on normed rings are studied. Finally, fuzzy prime and fuzzy maximal ideals are defined, exemplified and various theorems are stated and proven in this section. The fifth chapter of our thesis consists of our studies on level ideals on fuzzy normed rings, fuzzy semiprime ideals and fuzzy normed cosets. In this section, auxiliary lemmas and theorems are proven and necessary definitions are put forward. The sixth chapter is devoted to the discussion of the results and the suggestion of possible future work and is the final part of our thesis. Key Words: Normed Ring, Fuzzy Set, Fuzzy Transformation Semigroup, Fuzzy Ideal, Fuzzy Normed Coset.