| Some theories on fuzzy sets, rough sets and soft sets about uncertainties of hemirings are studied in this paper. By means of fuzzy sets, rough sets and soft sets,we investigate some structures and properties of hemirings. At the same time, we deal with the uncertainties problems in real life by combining these theories. The paper is divided into three chapters.In the first chapter, we briefly introduce the development history and research status of hemirings, fuzzy sets, rough sets, soft sets, and the relevant knowledge which will be used in the paper.In the second chapter, by combining fuzzy sets, rough sets and soft sets, we characterize Z- soft rough fuzzy ideals. We mainly discuss the operations of Z- soft rough fuzzy sets and investigate Z- soft rough fuzzy ideals. Finally, we study the Z- soft rough fuzzy sets in the application of decision making. Moreover,we give an example about actual application.In the third chapter, based on Z- soft rough fuzzy sets, we propose the concept of Z- soft fuzzy rough sets. The operations of Z- soft fuzzy rough sets are investigated. Further, we characterize Z- soft fuzzy rough ideals. At last, as an application, we put forward an approach for decision making problems based on Z- soft fuzz rough sets and the corresponding example is also given. |
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