Applications Of Three-Way Decisions And Rough Set In Semiconcepts And Preconcepts

Formal concept analysis is an information theory about a given formal context developed by introducing partial order relations and two kinds of operators through sets.It defines the“concepts” in philosophy mathematically through intent and extent.Three-way decisions,as a wider range of decision-making methods than two-way decisions,has played an important role in many fields.So far,three-way formal concepts has been an effective tool for solving knowledge extraction.However,in practice,satisfying both the intent and extent constraints is very harsh for the “knowledge” to be extracted.Semiconcepts and preconcepts,as extensions of formal concepts,constitute two new data analysis methods.Since there are many types of semiconcepts,we will focus on rough semiconcepts which are used widely.Therefore,based on the above analysis,this thesis hopes to apply three-way decisions to the study on rough semiconcepts and preconcepts.The main research contents of this thesis are as follows:(1)The definition of the existing rough semiconcepts is extended from two-way forms to three-way forms—three-way rough semiconcepts,under the guidance of three-way decisions.Then,its algebraic properties are obtained,and further,its double Boolean algebra structure is received.The upper and lower approximation operators which based on rough set will equivalently represent three-way rough semiconcepts.(2)The definition of preconcepts is extended from two-way decisions to three-way preconcepts under the guidance of three-way decisions.The algebraic properties of three-way preconcepts are studied,and further its generalized double Boolean algebra structure is obtained.Through rough set and the given equivalence relations,two pairs of upper and lower approximation operators based on the three-way preconcepts are obtained,respectively.Through these two approximation operators,three-way preconcepts are equivalently described.