On singleton 1-rounded sets of matroids

Rough Sets and Matroids

We prove the recent result of Liu and Zhu [2] and discuss some consequences of that and related facts for the development of rough set theory.

Connectivity for matroids based on rough sets

In mathematics and computer science, connectivity is one of the basic concepts of matroid theory: it asks for the minimum number of elements which need to be removed to disconnect the remaining nodes from each other. It is closely related to the theory of network flow problems. The connectivity of a matroid is an important measure of its robustness as a network. Therefore, it is very necessary ...

Algebraic characteristic sets of matroids

For a matroid M, define the algebraic characteristic set x4(M) to be the set of field characteristics over which M can be algebraically represented. We construct many examples of rank three matroids with finite, non-singleton algebraic characteristic sets. We also determine x,,(PG(Z, p)) and xa(AG(2, p)). An infinite family of rank three matroids with empty algebraic characteristic set is const...

Some characteristics of matroids through rough sets

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid, as a branch of mathematics, is a structure that generalizes linear independence in vector spaces. Further, matroid theory borrows extensively from the termin...

Learning Families of Closed Sets in Matroids