Sorting And Attribute Reduction In Numerical Decision Systems

Numerical data widely exists in real life. It is important that how can we analysis,extract and handle of information precisely.This paper is divided into four parts. The introduction of this article is the first part.The second part is numerical decision systems. In this part, some concepts andproperties were presented in numerical decision systems. The third part is sorting innumerical decision systems. Order relation widely exists in numerical decision systems.In this part, author extends the concept of classical dominance relation and dominanceset, and new ways and algorithms were presented for establishing dominance relation.Sorting algorithm based on dominance relation was presented and its effectiveness hasbeen tested by experiments. The last part is that attribute reduction in numericaldecision systems. For numerical data, using the classical rough set approach to attributereduction must discrimination, which lead to some of the available information lost.Firstly, author presented the concept and some important properties of assignment setbased on numerical data sets. Then, author defined discernibility matrix based onassignment set and proposed a new method, which aims at attribute reduction, based ondiscernibility matrix in numerical data sets. Finally, an algorithm for computingdiscernibility matrix was presented. Example analysis show that this method caneffectively handle attribute reduction in numerical decision systems.