Study on Z-soft Fuzzy Rough Sets in Hemirings
Jianming Zhan, Kuanyun Zhu and Muhammad Irfan Ali
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 Zsoft 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.
Keywords: Hemiring; PFS-set; Z-SFR-set; decision-making method.
2000 Mathematics Subject Classification: 16Y60; 13E05; 03G25.