A Study On Hemirings Based On Fuzzy Sets, Soft Sets And Rough Sets

This paper mainly studies some theories of fuzzy sets, rough sets and soft sets based on hemirings. We study some structures and properties of hemirings by means of fuzzy parameterized fuzzy soft sets, intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets and rough soft sets. At the same time, we deal with real-life uncertain problems by using these theories. The paper is made up of five chapters.The first chapter introduces the backgrounds and status on hemirings, fuzzy sets, rough sets, soft sets, and the basic conceps which will be used in the paper.In the second chapter, we explore fuzzy parameterized fuzzy soft hemirings, and study some operations. At last, we give an aggregate fuzzy operator and study its characterizations.In the third chapter, based on the fuzzy parameterized fuzzy soft hemirings, we obtain intuitionistic fuzzy parameterized intuitionistic fuzzy soft hemirings. Also we investigate some properties and structures of various operations. Finally, we define aggregate intuitionistic fuzzy sets and establish decision-making methods through this kind of aggregation operators so as to deal with uncertainty problems in real-life world.In the fourth chapter, we apply rough soft sets to hemirings and obtain rough soft hemirings. We mainly discuss some characterizations of upper and lower rough approximations as well as some operations of rough soft hemirings. At last, the algebraic structures of upper and lower rough approximations over rough soft hemirings are studied.In the fifth chapter, based on the rough soft hemirings, we further get a novel rough soft hemirings with respect to strong h - ideals of hemirings. Then we discuss some properties of upper and lower rough approximation operators. Finally, we first provide two kinds of decision-making methods of rough soft hemirings and give examples to illustrate them.