Multi-granulation Rough Sets And Granular Reductions Based On Similarity Measure

Rough sets theory is a theoretical method for the study of soft computing proposed by Pawlak,a mathematician of Poland in 1980 s.Rough sets is an effective tool for analyzing and dealing with incomplete,imprecise and uncertain knowledge.And the problems of attribute reductions and the construction and reductions of the information granules with multi-granulation rough sets are the hot research contents of rough sets.The similarity measure is a degree of the difference between individuals,which can be used as a powerful tool to measure the similarity between two objects.Based on the cosine similarity,a new method of definition for similarity measure of rough sets is given in this paper.And the influence of the vector modulus formed by the object attribute value on the similarity degree is considered.It overcomes the disadvantage that the original cosine similarity only considers object similarity from vector direction.The new similarity measure takes into account both the direction of vector and the difference between vector modes.At the same time,some properties of the similarity measure are also discussed.Attribute reductions is one of the most important contents in the application of rough sets theory,and it is a process of deleting redundant attributes.Firstly,this paper constructs the information granule by using the method of cluster analysis.Then it constructs the mass function of the information granule by using the obtained information granule and obtains the object weight by using the mass function of the information granule,thus eliminating the subjective factor's influence on the object weight.Finally,a new attribute reductions algorithm based on weighted conditional entropy is presented with the weight of the object and information entropy theory.Granulation of information system and reduction of information granules are important research contents of multi-granulation rough sets.By granulation,the structure of the problem space can be considered,and by using reduction of information granules,more concise decision rules can be get.In this paper,the information system is granulated by the granulation criterion based on principal component analysis,and then the approximate space of the rough sets with multi-granulation is constructed.And the corresponding method to determine the weight of information granules is given.At the same time,the definition of the inner importance measure and outer importance measure of information granules is given based on information entropy theory.Finally,a reduction algorithm for information granules is given based on the definition of importance degree.