Three-way Decisions For Composed Set-valued Decision Tables

When the rough set theory was put forward,it was only used to deal with the complete data.Then,the rough set theory is extended to deal with incomplete data.When the information system is incomplete,we can transform the incomplete information system into set-valued information system.Scholars have done a lot of research work about it.While dealing with incomplete decision table,we can also transform the incomplete decision tables into set-valued decision tables.In this paper,composition of the set-valued decision tables is investigated based on the pre-order relation on set-valued information system.Object-composed set-valued decision tables and attribute-composed set-valued decision tables are discussed.Furthermore,the characteristic of object-composed and attributecomposed set-valued decision tables are investigated.The three-way decision theory is developed from the two-way decision theory,it has the characteristics of human cognition.It not only has a good explanation but also reduces the loss of two-way decisions to a certain extent.Three-way decision theory is increasingly applied in different field.It has high research value.In this paper,the three-way decision theory is introduced into set-valued decision tables,based on the theory of the threeway decisions,and decision method of the set-valued decision tables are discussed.This paper define the three-way decisions of object-composed set-valued decision tables and the three-way decisions of attribute-composed set-valued decision tables.The characteristic of three-way decisions of object-composed and attribute-composed set-valued decision tables are also studied.