Attribute Reduction Of Variable Threshold Concept Lattices In Formal Fuzzy Contexts

Formal concept analysis is an effective method to process data.Knowledge reduction of concept lattice is one of the main problems in formal concept analysis.Among all knowledge reduction,attribute reduction is the most important.Classical formal contexts is the basic data frame of classical formal concept analysis.However,fuzzy formal contexts is often encountered in many practical problems,so there are more and more studies on formal concept analysis in fuzzy formal contexts.Variable threshold concept lattice is an important fuzzy concept model in fuzzy formal contexts,which mainly includes: crisp-crisp variable threshold concept lattice,crisp-fuzzy variable threshold concept lattice,fuzzy-crisp variable threshold concept lattice,fuzzy-fuzzy variable threshold concept lattice.There are few researches on these four kinds of variable threshold concept lattice.This dissertation focuses on rule extraction and attribute reduction for crisp-crisp variable threshold concept lattices and crisp-fuzzy variable threshold concept lattices.The main contents are as follows:Firstly,we study the crisp-crisp variable threshold concept lattice attribute reduction based on prediction rules.This paper discusses the extraction of prediction rules based on the crisp-crisp variable threshold concept lattice from the fuzzy formal contexts,proposes the attribute reduction of simplified prediction rules,and gives the decision theorem of attribute prediction coordination set and the characterization of core attributes.The method of attribute reduction based on prediction identification matrix is explored.Secondly,according to the three-way decision theory,a three-way decision rule extraction method based on crisp-crisp variable threshold concept lattice and crispfuzzy variable threshold concept lattice is proposed respectively.For a given target set and a threshold sequence,all variable precision concepts are divided into three parts,namely,positive concept class,negative concept class and boundary concept class.Based on this,two types of deterministic decision rules and one type of possibility decision rules are given.The concept of fuzzy formal background attribute reduction which keeps the performance of non-redundant decision rules unchanged and simplifies the representation of decision rules is proposed.The corresponding attribute coordination set decision and attribute reduction calculation methods are studied.