Characteristic matrix of covering and its application to boolean matrix
  decomposition and axiomatization
  Covering is an important type of data structure while covering-based rough
sets provide an efficient and systematic theory to deal with covering data. In
this paper, we use boolean matrices to represent and axiomatize three types of
covering approximation operators. First, we define two types of characteristic
matrices of a covering which are essentially square boolean ones, and their
properties are studied. Through the characteristic matrices, three important
types of covering approximation operators are concisely equivalently
represented. Second, matrix representations of covering approximation operators
are used in boolean matrix decomposition. We provide a sufficient and necessary
condition for a square boolean matrix to decompose into the boolean product of
another one and its transpose. And we develop an algorithm for this boolean
matrix decomposition. Finally, based on the above results, these three types of
covering approximation operators are axiomatized using boolean matrices. In a
word, this work borrows extensively from boolean matrices and present a new
view to study covering-based rough sets.
