Abstract
Purpose of the present research is to detail the importance of using a fuzzy soft-β-open set and study its characteristics and applications. Also, we introduce more basic fuzzy-soft topological concepts, namely, fuzzy soft-β-interior, fuzzy soft-β-closure,
operators based on fuzzy soft-β-open set, and also present more of their properties. The connections between them as well as other concepts are listed. This notion is used to introduce a proposed approximation of fuzzy-soft space as per the fuzzy soft-β set as a generalization
for the fuzzy-soft approximation space. This research also attempted on revealing that this model presents higher accuracy calculation and is better as compared to all other models. The results are given using the MATLAB program. It occurs in many areas of science and technology.