| Crisp formal concept analysis is an effective tool for data analysis and rule extraction by constructing concept lattices based on crisp formal contexts,but in real life,information data is often vague and uncertain.Therefore,in order to solve the problem,it is necessary to promote crisp formal contexts into fuzzy formal contexts,and the study of fuzzy concept lattices theory and its application has become a hot issue.Single-sided fuzzy concept lattice is a type of fuzzy concept lattice,because the extension and connotation of the concept one is a crisp set,the other is a fuzzy set,so it is divided into crisp-fuzzy concept lattice and fuzzy-crisp concept lattice.This paper combines rough set theory with formal concept analysis,and proposes a crisp-fuzzy concept lattice model based on rough approximation to study the relevant problems in the fuzzy concept lattice,which can not only enrich the fuzzy concept lattice theory,but also promote the practical application of fuzzy concept lattice.This dissertation studies the problem of rule extraction and attribute reductions of crispfuzzy concept lattices based on generalized rough approximations.The main research contents are as follows:Firstly,the problem of attribute reduction that keeps the lattice structure unchanged under the crisp-fuzzy concept lattice is studied.Gives the concept of a consistent set of attributes,some judgement theorems for consistent sets are proposed;Then,according to all reductions,the attributes are divided into three classes,and the characteristics of different attributes are given;Combined with the rough set theory,the concepts of discernible matrix and discernible function are given in fuzzy formal contexts,according to which a method based on attribute reduction of discernible function is obtained,and the feasibility of the reduction method is verified by examples.Secondly,the study of crisp-fuzzy concept lattice is based on the attribute reduction problem of three-way decisions.For a determined target set,all crisp-fuzzy concepts are divided into three parts,thereby deriving two sets of deterministic decision rules and one set of possibility decision rules;The concept of attribute reduction that keeps the performance of decision rules unchanged is proposed,and the corresponding consistent sets judgement theorems are given,which not only keeps the performance of decision rules unchanged,but also simplifies the rule representation.Define the discernible matrix and discernible function,and gives a calculation method for attribute reduction.Finally,the problem of attribute reductions based on decision rules in fuzzy formal decision contexts is studied.The definition of decision rules under fuzzy formal decision contexts is given,the concept of non-redundant decision rules is proposed,the condition reduction that keeps the extension corresponding to the antecedent of the non-redundant rule unchanged is given,and the decision reduction that keeps the extension corresponding to the afterpart of the non-redundant rule unchanged,the consistent set judgement theorems are proved,the corresponding discernible attribute set and discernible function are defined,and the method of finding all reductions through the discernible function is obtained. |
