Variable Precision Approximations In Formal Concept Analysis

Formal Concept Analysis(FCA)and Rough Set Theory(RST),two math-ematical tools for data analysis and knowledge discovery,have played vital roles in artificial intelligenceFor the purpose of increasing the accuracy in modeling classification prob-lems,Variable Precision Rough Set Model(VPRS)introduced conditional prob-ability to classic rough set model,and then improve the classification results through quantitatively analysing uncertain and unprecise information of systems As an important direction to acquire unprecise information in formal contexts,the approximations of knowledge in FCA,use the approximation method of RST.The basic idea of RST approach processes approximation representations of objectives through upper and lower approximation operators.This method.however,doesn't consider precision,and can't measure the degree of accuracy of acquired informationInspired by VPRS,we propose the variable precision approximations in formal concept analysis to give approximate representations of objectives quan-titatively.The main contents of this paper are as follows(1)?-approximations and ?-approximation descriptions of the objec-t subsets based on extents are defined,as well as ?-approximations and?-approximation interpretations of the attribute subsets based on intents(2)For the sets of objects(attributes),the relationships among?-approximation description(substance),common description(substance),possibility description(substance)and necessity description(substance)are dis-cussed.The relationships show that the variable precision approximations in formal concept analysis proposed in this paper are able to analyze information.