Rules Acquisition Of Formal Decision Contexts Based On Three-way Concept Lattices

Formal concept analysis(FCA)was put forward in 1982 by German math-ematician Wille R,it is a useful tool for data analysis and rules acquisition.It has been one of the most important research fields in artificial intellegence,and widely used in machine learning,data mining and information retrieval.Rules acquisition is an important and useful research direction in FCA and the research about it mainly concentrate on classical concept lattices.In 2014,Qi et al.proposed 3-way concept analysis(3-WCA),whose foundation are object-induced(attribute-induced)three-way concepts and object-induced(attribute-induced)three-way concept lattices.In this paper,we study the method of rules acquisition in formal decision contexts from the view of 3-way concept lattices.The details are as follows:1.We first define object-induced(attribute-induced)three-way consistence of formal decision context,based on which,the method of rules acquisition is given.Then the irredundant rules and the relationship between these new rules and the rules from view of concept lattices are presented.2.The connection among strongly consistence and object-induced(attribute-induced)three-way consistence on the basis of formal decision contexts are dis-cussed.And it is proved that attribute-induced three-way consistence can deduce strongly consistence.3.By introducing the confidence into three-way concept lattices,the method of rules acquisition in inconsistent formal decision context are provided.Then the necessary and sufficient condition of irredundant three-way decision rules are discussed.