Optimization of Z-fuzzy soft $\beta$-covering based fuzzy rough sets and their application to multiple attribute group decision making

Fuzzy sets play a crucial role in representing real-world complexities where precise binary logic falls short. Rough sets are closely related to fuzzy sets, and their combined use provides a powerful framework for handling uncertain and incomplete information.The combination of rough sets and fuzzy sets is an intriguing area of research that bridges the gap between crisp and uncertain information. In this paper, three different kinds of fuzzy serial relations are introduced. These relations form new fuzzy soft $\beta$ covering based fuzzy rough set models. The main objective of this research is to maximize the lower approximation and minimize the upper approximation of existing models. Eventually, we use the suggested rough set model to resolve MAGDM problems. The proposed MAGDM algorithm demonstrated superior performance when compared to other algorithms. Its effectiveness lies in its ability to find optimal solutions.