In order to improve the efficiency and quality of rule extraction in LEM2 series algorithms,an improvedLEM2 algorithm on the basis of generalized decision function,namely GDF- LEM2,is proposed.In this algorithm,candidate attribute- value pair set T(G) is calculated according to generalized decision function and is downsized bydeleting newly- defined redundancy attribute- value pair sets,and thus the efficiency of rule extraction is improved.Moreover,the choice of attribute- value pair sets is guided with the minimum intersection of generalized decisionfunction strategy,which makes the extracted rule more laconic and thus improves the quality of rule extraction.Ex-perimental results show that GDF- LEM2 algorithm effectively improves the efficiency and quality of rule extractionfrom complete or incomplete decision systems.