  The application of rough set theory in incomplete information systems is a
key problem in practice since missing values almost always occur in knowledge
acquisition due to the error of data measuring, the limitation of data
collection, or the limitation of data comprehension, etc. An incomplete
information system is mainly processed by compressing the indiscernibility
relation. The existing rough set extension models based on tolerance or
symmetric similarity relations typically discard one relation among the
reflexive, symmetric and transitive relations, especially the transitive
relation. In order to overcome the limitations of the current rough set
extension models, we define a new relation called the positive transitive
relation and then propose a novel rough set extension model built upon which.
The new model holds the merit of the existing rough set extension models while
avoids their limitations of discarding transitivity or symmetry. In comparison
to the existing extension models, the proposed model has a better performance
in processing the incomplete information systems while substantially reducing
the computational complexity, taking into account the relation of tolerance and
similarity of positive transitivity, and supplementing the related theories in
accordance to the intuitive classification of incomplete information. In
summary, the positive transitive relation can improve current theoretical
analysis of incomplete information systems and the newly proposed extension
model is more suitable for processing incomplete information systems and has a
broad application prospect.
