Fuzzy subcrossed module

In this study, the concept of crossed modules that forms a significant generalization of groups, as well as fuzzy sub-crossed modules, is introduced for the first time in a fuzzy environment. In this context, the relationship between crossed modules and fuzzy sub-crossed modules is examined, the normality criteria for these structures are explained, and the focus is placed on the objects related to the section. In the first chapter, a review of the literature and the history of sources is provided to ensure the clarity of the thesis topic. The second chapter presents some algebraic structures, theorems, and expressions related to the subject. The third chapter introduces the algebraic structure of fuzzy sub-crossed modules, along with relevant theorems. The fourth chapter constructs the normality of fuzzy sub-crossed modules and provides information on the subject, followed by the proof of several theorems. The fifth chapter defines the properties of normal fuzzy sub-crossed modules in the module context, explaining the characteristics of the structure. Some theorems are also proven in this section. In the sixth chapter, the properties of fuzzy sections within the normal fuzzy subcrossed module are examined, and the characteristics of the structure are explained. Several theorems are proven. Keywords: Fuzzy subgroup, crossed module, normality, quotient crossed module.