The Research Of Attribute Reduction In The Decision System

In varying degrees,the handling of uncertainty is involved in many fields ofnatural science,social science and engineering technology.There have been manytools that dealt with the uncertainty,such as rough set,fuzzy set and probability theory.As a relatively new soft computing method among them,rough set is becoming moreand more concerned in academic circles.However, Palwak rough set is based on equivalence relation and its stringencylimits the application of classic rough set in many practical fields.In order to solve thisproblem,the scholars came up with varieties of extended mathematical models one byone.For example, starting from the practical application,Zakowski raised coveringrough set and discussed relative properties;In1999, an Russian scholar namedMolodtsov proposed the definition of soft set and relevant operations.For the sake ofsolving practical problems better,Gong K and so on also gave the definition of softtheory and its operations on the basis of soft theory.Attribute reduction is a kind of technology of eliminating redundant data ininformation system and data mining.Based on covering rough set,people have givenmany attribute reduction methods in recent years and the commonality of them isoperating on a given covering information system directly.Under the circumstance ofhuge data volume,the operation is complex.This article considers utilizing amathematical tool named homomorphic function to do data compression on acovering decision system first, then do attribute compression on the relatively smallerand equivalent decision system to solve some practical problems better.Attribute reduction not only is the elementary problem in rough set research,butalso is the most critical and tricky problem in soft set theory.Many attribute reductionmethods about soft information system have appeared so far.After giving thedefinition of bijective soft set along with relative operations by Gong K and so on,they advanced the definition of bijective soft decision system and discussed thereduction method.Yet the method of utilizing the principle of unvariant depengency todo attribute reduction on bijective soft decision system is complex and can’t get allthe reductions at one time.This article considers applying the reduction method of basing on discernibility matrix in rough set theory to the bijective soft decision systemto give a more simple and convenient reduction method.Finally,this article does some analyses and discussions on the attribute reductionmethods of covering decision system and bijective soft decision system.