Approaches to attribute reductions based on rough set and matrix computation in inconsistent ordered information systems

In order to conduct classification analysis in inconsistent ordered information systems, notions on possible and compatible distribution reductions are proposed in this paper. The judgement theorems and discernibility matrices associated with the two reductions are examined, from which we can obtain an approach to the two reductions in rough set theory. Furthermore, the dominance matrix, possible and compatible decision distribution matrices are also considered for approach to these two forms of reductions in inconsistent ordered information systems. Algorithms of matrix computation for possible and compatible distribution reductions are constructed, by which we can provide another efficient approach to these two forms of distribution reductions. To interpret and help understand the algorithm, an experimental computing program is designed and two cases are employed as case study. Results of the small-scale case are calculated and compared by the discernibility matrix and the matrix computation to verify the new method we study in this paper. The large-scale case are calculated by the experimental computing program and validated by the definition of the reductions.