Study on Z-soft Fuzzy Rough Sets in Hemirings

In recent years, the theory of soft sets including their applications has brought a great concern in all kinds of areas. In particular, some hybrid soft set theory models by means of soft set theory and other mathematical theory have been a great development. The paper puts forward the concept of Z-SFR-sets, which is an important extended notion of Z-soft rough fuzzy sets (briefly, Z-SRF-sets). As a novel theory model, we consider their applications in the corresponding decision making problems. It is noteworthy that our approach will involve less calculations when we apply our theory to algebraic structures. We show that there exists a corresponding relation between one set of all PFS-sets and another set consisting of all fuzzy relations. It is pointed out that we provide a novel way for its applications by means of this novel soft set models.