Issues On Two Types Of Matroidal Structures Based On Rough Sets

Rough set theory and matroid theory have broad application prospects. Moreover, there are many similarities between rough set theory and matroid theory, thus many researchers explore the cross study of them recently. In this paper, we also study some problems about the connections between them, the main work are as follows:(1) Based on the study of literature [46]. we propose a series of matroidal structures M^(R) induced by upper approximation number based on equivalence relations (Where R is an equiva-lence relation on U. and k is an positive integer). Then we study the relationships between the classical degree rough sets which are based on R and k and matroids Mk(R). and characterize the circuit, independent set. rank function, base and closure of these matroids by degree ap-proximation operators. In order to discuss the general condition. we also study the connections between generalized degree rough sets and matroids. Moreover, conditions of the same matroid induced by different binary relations are studied.(2) Another series of matroidal structures were induced by upper approximation number which are based on equivalence relations similarly. Then we study the connections between these matroids and classical rough sets. Finally, we discuss the relationships between these matroids and the matroids in literature [47].