Attribute Reduction And Rules Acquisition Of Incomplete Formal Contexts Based On Partially-known Formal Concept Lattices

Formal concept analysis(FCA),proposed by Wille in 1982,is an efficicent tool for knowledge discovery and decision making.Its data foundation is formal contexts whose information is totally known by us.So far,FCA has became an important theory in artificial intelligence and been extensively applied in machine learning,da-ta mining,information retrieval,and so on.However,in practical application,the situations of information missing are omnipresent,so the study of knowledge discov-ery and decision making based on incomplete formal contexts has became one of the most meaningful study directions.Based on that,Yao generalized three-way concept analysis(3WCA),proposed by Qi et al.in 2014,and he proposed partially-known for-mal concept analysis,which lays the foundation of knowledge discovery and decision making for incomplete formal contexts.Attribute reduction and rules acquisition are two important and significant re-search directions of FCA and 3WCA,and recent studies are mainly based on formal concept lattices and three-way concept lattices,which are generated from formal con-texts.Different from the two concept lattices from formal contexts,partially-known formal concept lattices,including partially-known SE-ISI formal concept lattice and partially-known ISE-SI formal concept lattice,are generated from incomplete formal contexts.Therefore they have more uncertain information than the two kinds of con-cept lattices from formal contexts.In this paper,based on the two types of partially-known formal concept lattices,we studied attribute reduction and the method of rules acquisition for incomplete formal contexts.The main contents of this paper are organized as follows:1.Based on the partially-known SE-ISI formal concept lattices,we defined several types of SE-ISI attribute reduction from the perspectives of the structure and the construction of the lattices and granular computing,and studied their relationships.And based on the partially-known ISE-SI formal concept lattices,we defined ISE-SI attribute reduction only from the consideration of the structure and the construction of the lattices for the particularity of the granules in the lattices.2.By defining the SE-ISI discernibility matrices and the SE-ISI discernibility functions,and the ISE-SI discernibility matrices and the ISE-SI discernibility func-tions,we studied the judging theorems and calculating methods of SE-ISI attribute reduction and ISE-SI attribute reduction for incomplete formal contexts respectively.3.For incomplete decision formal contexts,based on the partially-known SE-ISI formal concept lattices,we defined SE-ISI consistency and gave the method of rules acquisition for the SE-ISI consistent contexts.Further,combing with inclusion theory,we also presented the method of rules acquisition for the SE-ISI non-consistent contexts.