Attribute Reduction Based On Extensions Of Concepts In Formal Contexts

The important data structure of formal concept analysis which is proposed by Wille isconcept lattice model. Based on this model, many scholars presented the definition of conceptlattice-based reduct, which is the minimal attribute subset that maintains the extensions of allconcepts. A new kind of attribute reduction called meet-reduct is introduced in this thesis, whichis not only equivalent to the concept lattice-based reduct, but also simple to be computed. Inaddition, since one concept can be expressed as the meet or union of some basic concepts, andthese basic concepts are object concepts and attribute concepts, we can remove the redundantconcepts from all the basic concepts, and all the concepts can also be obtained. Based on thefact above, we propose some new concepts of lower,upper-approximation reduct, (relative)belief reduct and (relative) plausibility reduct, and approaches to research for these reducts areconstructed. A summary of the main results in this thesis are as follows:1. Attribute reduction in formal contexts is considered in terms of topology. First, anew definition of meet-reduct is proposed, which preserves the meet of extensions of attributeconcepts, and an approach to research for such an attribute reduction is constructed. The equiv-alence of meet consistent set and concept lattice-based consistent set is proved. Furthermore,attribute reduction in consistent decision formal contexts is discussed similarly.2. From the Dempster-Shafer theory of evidence point, the problem of attribute reductionis discussed. (Relative) belief reduct and (relative) plausibility reduct are introduced in (deci-sion) formal contexts. In addition, the relationships among the (relative) belief reduct, (relative)plausibility reduct, (relative) granular reduct are discussed. The equivalence of (relative) gran-ular consistent set and (relative) belief consistent set is proved, and the methods of determininggranular reducts and relative granular reducts are obtained.3. The approaches of attribute reduction in inconsistent decision formal contexts arediscussed. Employing object concepts, the definitions of lower and upper operator are pro-posed , and two new kinds of attribute reducts called upper-approximation reduct and lower-approximation reduct are presented. The judgment theorems using discernibility matrices ofthe two reducts were examined, base on which we can obtain all the upper and lower approxi-mation reducts in inconsistent decision formal contexts. Furthermore, by employing the theoryof dependence space, we develop a novel approach to calculate the two reducts.