International Journal of Mathematical Sciences and Computing (IJMSC)
IJMSC Vol. 11, No. 1, 8 Apr. 2025
Cover page and Table of Contents: PDF (size: 388KB)
Matrix Approach to Rough Sets Based on Tolerance Relation
PDF (388KB), PP.31-36
Views: 0 Downloads: 0
Author(s)
Index Terms
Rough Matrix (RM), Maximal Compatibility Block (MCB), Matrix approach of MCB Covering
Abstract
There are many complex issues with incomplete data to make decisions in the field of computer science. These issues can be resolved with the aid of mathematical instruments. When dealing with incomplete data, rough set theory is a useful technique. In the classical rough set theory the information granules are equivalence classes. However, in real life scenario tolerance relations play a major role. By employing rough sets with Maximal Compatibility Blocks (MCBs) rather than equivalence classes, we were able to handle the challenges in this research with ease. A novel approach to define matrices on MCBs and operations on them is proposed. Additionally, applied the rough matrix approach to locate a consistent block related to any set in the universal set.
Cite This Paper
N. Kishore Kumar, M. P. K. Kishore, S. K. Vali, "Matrix Approach to Rough Sets Based on Tolerance Relation", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.11, No.1, pp. 31-36, 2025. DOI: 10.5815/ijmsc.2025.01.02
Reference
[1]Z.Pawalk, Rough Sets, International Journal of Computer and Information Science, 11(1982),341-356.
[2]J. Mahanta and P.K. Das, A New Type of Covering Based Rough Set, IFRSA International Journal of Data Warehousing and Mining, 1(1), Aug 2011, 16-19.
[3]Kishore Kumar.N, M. P. K. Kishore, and S. K. Vali. "Tolerance Based Rough Algebras Induced by Blocks." i- Manager's Journal on Mathematics 12.2 (2023): 12.
[4]Kishore kumar N., M.P.K. Kishore., S.K.Vali., A NEW TYPE OF COVERING BASED ROUGH SETS USING MAXIMAL COMPATIBILITY BLOCKS,Advances in Mathematics: Scientific Journal 9 (2020), no.9, 6537–6546.
[5]S.Vijaybalaji, P Balaji, Rough matrix theory and its Decision Makin, International Journal of Pure applied Mathematics Proc. vol. 87 No.6 2013, 845-853.
[6]Wu, Q., Wang, T., Huang, Y., Li, J., Topological Theory on Rough Sets,IEEE Transaction on systems, Man and Cybernetics-Part B, Cybernetics, 38(1),(2008), 68-77.
[7]Zhu, W., Properties of the second type of covering based rough sets, In: Proc.International Conference on Web Intelligence and Intelligent Agent Technology-Workshops, Hong Kong, China, (2006), 18-22.
[8]Zhu, W., Wang, F.Y., Properties of the third type of covering based rough sets,In: Proc. Sixth International Conference on Machine Learning and Cybernetics, Hong Kong, China, (2007), 3746-3751.