Analysis And Proof About Attribute Reduction Of Discernibility Function Based On Granular Computing

Information System is one of the important research objects in many fields of computer science. It occupies a very important position in data reasoning, data mining, data analysis and database system, etc. And reduction of information system is the main research contents of information system. Therefore, many scholars do a lot of research and produce many theoretical methods on reduction of information system. Skowron, the founder of rough set theory Pawlak's students, established a method named attribute reduction by discernibility function in 1991. The reduction method suffered from since the advent. Many scholars' attention to the discussion and debate has not stopped, because the reduction method has not been proved. Until 2009, YanLin and LiuQing gave a proof method based on granular computing. This proof is on deformation of discernibility function. But it is one and only one completely right proof at present.Granular computing includes the relevant granularity theory, technology and method. It is a new method of solving complex problems in artificial intelligence fields. Therefore, it is a new tool used by solving complex problem and processing fuzzy data.The proof given by YanLin and LiuQing is only for complete information system. Is it right on incomplete information system? This article gives the answer. Because of incomplete information system is omnipresent in reality, so researches on incomplete information systems is very meaningful. The main research work of this paper is as follows:(1) Establishing a granular space by the way of logical reasoning and granular computing theory on incomplete information system , constructing corresponding granular of discernibility function and proving the method of attribute reduction by discernibility function.(2) Extending the proof given by YanLin and LiuQing, Proving attribute reduction on discernibility function right in generalized information system. It not only makes it clear on the reduction, but also adds new contents and approaches on granular computing research.