Topological Characterization, Measures of Uncertainty and Rough Equality of Sets on Two Universal Sets

Автор: D. P. Acharjya, B. K. Tripathy

Журнал: International Journal of Intelligent Systems and Applications(IJISA) @ijisa

Статья в выпуске: 2 vol.5, 2013 года.

Бесплатный доступ

The notion of rough set captures indiscernibility of elements in a set. But, in many real life situations, an information system establishes the relation between different universes. This gave the extension of rough set on single universal set to rough set on two universal sets. In this paper, we introduce rough equality of sets on two universal sets and rough inclusion of sets employing the notion of the lower and upper approximation. Also, we establish some basic properties that refer to our knowledge about the universes.

Rough Set, Solitary Set, Boolean Matrix, Rough Equality, Rough Inclusion

Короткий адрес: https://readera.org/15010361

IDR: 15010361

Список литературы Topological Characterization, Measures of Uncertainty and Rough Equality of Sets on Two Universal Sets

  • Zadeh L A. Fuzzy sets. Information and Control, 1965, 8: 338-353.
  • Pawlak Z. Rough sets. International Journal of Computer and Information Sciences, 1982, 11: 341-356.
  • Pawlak, Z. Rough Sets Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991.
  • Molodtsov, D. Soft set theory-First results, Computers and Mathematics with Applications, 1999, 37: 19-31.
  • Kryszkiewlcz, M. Rough set approach to incomplete information systems, Information Sciences, 1998, 112: 39-49.
  • Lin, T. Y. Granular computing on binary relations I: Data mining and neighborhood systems, in: Rough sets in Knowledge Discovery (Skoworn, A. and Polkowski, L. Eds.), Springer-Verlag, London, 1998, 107-121.
  • Lin, T. Y. Granular computing: Examples, intuitions and Modeling, Proceeding of the IEEE International Conference on Granular Computing, Beijing, China, 2005, 40-44.
  • Maji, P. K., and Roy, A. R. An application of soft sets in a decision making problem, Computers and Mathematics with Applications, 2002, 44: 1077-1083.
  • Pawlak, Z. Decision rules and flow networks', European Journal of Operational Research, 2004, 154 (1): 184-190.
  • Zhong, N., and Skowron, A. A rough set based knowledge discovery process, International Journal of Applied Mathematics Computer Science, 2001, 11 (3): 603-619.
  • Bonikowski, Z. Algebraic structure of rough sets, in: Rough sets, Fuzzy sets and Knowledge Discovery, (Ziarko, W. P. Ed.), Springer-Verlag, London, 1994, 242-247.
  • Kondo, M. Algebraic approach to generalized rough sets, Lecturer Notes in Artificial Intelligence, 2005, 3641: 132-140.
  • Kondo, M. On the structure of generalized rough sets, Information Sciences, 2006, 176: 589-600.
  • Pawlak Z, Skowron A. Rough sets: some extensions. Information Sciences, Elsevier, 2007, 177 (1): 28-40.
  • Yao, Y. Y. Constructive and algebraic methods of the theory of rough sets, Information Sciences, 1998, 109: 21-47.
  • Zhu, W. Generalized rough sets based on relations, Information Sciences, 2007, 177 (22): 4997-5011.
  • Lin, T. Y. Neighborhood systems and approximation in database and knowledge based systems, Proceeding of the fourth International Symposium on Methodologies of Intelligent Systems, 1989, 75-86.
  • Zhu, W., and Wang, F. Y. On three types of covering rough sets, IEEE transactions on Knowledge and Data Engineering, 2007, 19 (8): 1131-1144.
  • Liu, G. L. Rough sets over the Boolean algebras, Lecture Notes in Artificial Intelligence, 2005, 3641: 24-131.
  • Pawlak, Z., and Skowron, A. Rough sets and Boolean reasoning, Information Sciences, Elsevier, 2007, 177 (1): 41-73.
  • Liu, G. L. Generalized rough sets over fuzzy lattices, Information Sciences, 2008, 178: 1651-1662.
  • Chen, D., Zhang, W., Yeung, D. and Tsang, E. C. C. Rough approximations on a complete completely distributive lattice with applications to generalized rough sets, Information Sciences, 2006, 176: 1829-1848.
  • Dubois, D., and Prade, H. Rough fuzzy sets and fuzzy rough sets, International Journal of General System, 1990, 17: 191-208.
  • Yao, Y. Y. Two views of the theory of rough sets in finite universes, International Journal of Approximation Reasoning, 1996, 15: 291-317.
  • Acharjya D P, Tripathy B K. Rough sets on fuzzy approximation spaces and applications to distributed knowledge systems. International Journal of Artificial Intelligence and Soft Computing, 2008, 1 (1): 1-14.
  • Tripathy, B. K., and Acharjya, D. P. Knowledge mining using ordering rules and rough sets on
  • fuzzy approximation spaces, International Journal of Advances in Science and Technology, 2010, 1 (3): 41-50.
  • Tripathy, B. K. Rough sets on intuitionistic fuzzy approximation spaces, Proceedings of 3rd International IEEE Conference on Intelligent Systems, London, 2006, 776-779.
  • Acharjya D P, Ezhilarsi L. A knowledge mining model for ranking institutions using rough computing with ordering rules and formal concept analysis. International Journal of Computer Science Issues, 2011, 8 (2): 417-425.
  • Acharjya D P, Tripathy B K. Rough sets on intuitionistic fuzzy approximation spaces and knowledge representation. International Journal of Artificial Intelligence and Computational Research, 2009, 1 (1): 29-36.
  • Tripathy, B. K., and Acharjya, D. P. Association rule granulation using rough sets on intuitionistic fuzzy approximation spaces and granular computing, Annals. Computer Science Series, 2011, 9 (1): 125-144.
  • Wong, S. K. M., Wang, L. S., and Yao, Y. Y. Interval structure: a framework for representing uncertain information, Proceedings of the 8th Conference on Uncertainty in Artificial Intelligence, 1993, 336-343.
  • Liu, G. L. Rough set theory based on two universal sets and its applications, Knowledge Based Systems, 2010, 23: 110-115.
  • Tripathy, B. K., Acharjya, D. P., and Ezhilarasi, L. Topological characterization of rough set on two universal sets and knowledge representation, Global Trends in Information Systems and Software Applications, CCIS, 2012, 270: 68-81.
  • Tripathy, B. K., and Acharjya, D. P. Approximation of classification and measures of uncertainty in rough set on two universal sets, International Journal of Advanced Science and Technology, 2012, 40: 77 – 90.
  • Novotny, M., and Pawlak, Z. Characterization of rough top equalities and rough bottom equalities, Bulletin Polish Academy of Science and Mathematics, 1985, 33: 91-97.
Еще
Статья научная