A Study On Several Uncertain Models Of Groups And Their Applications In Decision Making

The paper focuses on the uncertainties of groups.By combining fuzzy sets,rough sets and soft sets into groups,we investigate the structures and properties of groups.At the same time,we put forward the corresponding decision method to tackle the uncertainty in our real life.The whole paper is divided into four chapters.The first chapter briefly introduces the development background and research status about fuzzy sets,rough sets and soft sets,and briefly introduces the main work and some preliminary knowledge of this paper.The second chapter combines fuzzy sets and soft sets with rough set,respectively.We discuss the operators of rough fuzzy sets and rough soft sets and study the properties of rough fuzzy groups(normal subgroups)and rough soft groups(normal subgroups).Finally,we apply rough soft groups to the decision problems,and give an example to explain it.The third chapter combines fuzzy sets and soft sets with rough set,respectively.We discuss the properties of the lower and upper soft rough approximation operators,and characterize the soft rough groups(normal subgroups).Finally,based on the soft rough groups,we propose a decision algorithm and give the corresponding algebraic example.The forth chapter explores the lower and upper P-soft rough fuzzy and P-soft fuzzy rough approximation operators,and discusses the properties of P-soft rough fuzzy groups(normal subgroups)and P-soft fuzzy rough groups(normal subgroups).Finally,we put forward the decision methods of P-soft rough fuzzy sets and P-soft fuzzy rough sets over groups,and examples are given to compare the two kinds of decision methods.