Abstract:

Suppose R is a commutative ring with unity. The main goal of this study is to expand on the idea of chained hesitant fuzzy R-modules by building upon the concept of chained fuzzy R-modules. By introducing this extension, we provide a more comprehensive framework for understanding the behavior of fuzzy modules over commutative rings. Moreover, we introduce hesitant fuzzy-level concept subsets within this new framework. This concept offers a unique perspective on the structure of fuzzy R-modules, allowing for a more nuanced analysis of their properties and interactions within the context of commutative rings. Overall, our exploration of chained hesitant fuzzy R-modules and hesitant fuzzy level subsets enrich the existing literature on fuzzy modules and contribute to the ongoing discussions within the field of algebra and commutative ring theory. First, some examples and properties of these concepts were provided. Uniform hesitant fuzzy R-module is a concept that delve into, showcasing its defining characteristics and applications. Furthermore, the connection between chained hesitant fuzzy R-modules and uniform hesitant fuzzy R-modules will be investigated.