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The Bipolar Complemented de Morgan Brouwer-Zadeh Distributive Lattice as an Algebraic Structure for the Dominance-based Rough Set Approach

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EN
We introduce the bipolar complemented de Morgan Brouwer-Zadeh distributive lattice in order to give an algebraic model the to Dominance-based Rough Set Approach. We present also the concept of bipolar approximation space and we show how it can be induced from a bipolar quasi Brouwer-Zadeh lattice.
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Rocznik
Strony
25--56
Opis fizyczny
Bibliogr. 22 poz.
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autor
autor
  • Department of Economics and Business University of Catania Corso Italia 55, 95129 Catania, Italy, salgreco@unict.it
Bibliografia
  • [1] Bezhanishvili, G., Bezhanishvili, N. , Gabelaia, D. , Kurz, A., Bitopological Duality for Distributive Lattices and Heyting Algebras, Mathematical Structures in Computer Science, 20, (2010) 359-393.
  • [2] Cattaneo, G., Generalized Rough Sets (Preclusivity Fuzzy-Intuitionistic (BZ) Lattices), Studia Logica, 58 (1997) 47-77.
  • [3] Cattaneo, G., Nisticó, G., Brouwer-Zadeh Posets and three valued Łukasiewicz posets, Fuzzy Sets and Systems, 33 (1989) 165-190.
  • [4] Dubois, D., Prade, H., Foreword, in: Pawlak, Z., Rough Sets, Kluwer, Dordrecht, 1991.
  • [5] Greco, S., Matarazzo, B., Słowiński, R., Rough set theory for multicriteria decision analysis, European Journal of Operational Research, 129 (2001) 1-47.
  • [6] Greco, S.,Matarazzo, B., Słowiński, R., Rough approximation by dominance relations, International Journal of Intelligent Systems, 17 (2002) 153-171.
  • [7] Greco, S., Matarazzo, B., Słowiński R., Decision rule approach, in: J. Figueira, S. Greco and M. Ehrgott (eds.) Multiple Criteria Decision Analysis: State of the Art Surveys, Springer, Berlin, 2005, pp. 507-563.
  • [8] Greco, S., Matarazzo, B., Słowiński, R., Dominance-based Rough Set Approach as a proper way of handling graduality in rough set theory, Transaction on Rough Sets II, LNCS 4400 (2007) 36-52.
  • [9] Greco, S., Matarazzo, B., Słowiński, R., Algebraic structures for Dominance-based Rough Set Approach, In: G. Wang et al. (eds.) Rough Sets and Knowledge Technology, LNAI 5009, Springer, Berlin, 2008, pp. 252-259.
  • [10] Greco, S., Matarazzo, B., Słowiński, R., Dominance-based Rough Set Approach and Bipolar Abstract Approximation Spaces, In: C-C. Chan et al. (eds.) Rough Sets and Current Trends in Computing, LNAI 5306, Springer, Berlin, 2008, pp. 31-40.
  • [11] Greco, S., Matarazzo, B., Słowiński, R., Granular Computing and Data Mining for Ordered Data - the Dominance-based Rough Set Approach, in: R. A. Meyers, (ed.): Encyclopedia of Complexity and Systems Science, Springer, New York, 2009, pp. 4283-4305.
  • [12] Greco, S., Matarazzo, B., Słowiński, R., Dominance-based Rough Set Approach to Granular Computing, Chapter 19 in: J.T. Yao (ed.), Novel Developments in Granula Computing, IGI Global, Hershey, 2010, pp. 439-496.
  • [13] Greco, S., Matarazzo, B., Słowiński, R., On Topological Dominance-based Rough Set Approach, Transactions on Rough Sets XII, Lecture Notes in Computer Science, 2010, Volume 6190/2010, 21-45.
  • [14] Kelly, J. C., Bitopological spaces, Proc. London Math. Soc., 13 (1963) 71-89.
  • [15] Pagliani, P., "Rough Sets and Nelson Algebras", Fundamenta Informaticae, 27 (2-3), 1996, pp. 205-219.
  • [16] Pagliani, P., Chakraborty, M. K., Information Quanta and Approximation Spaces. I: Non-classical approximation operators, in: Hu, X., Liu, Q., Skowron, A., Lin, T. S., Yager, R., Zhang, E. B. (eds.) Proceedings of the IEEE International Conference on Granular Computing, Vol. 2, IEEE, 2005, 605-610.
  • [17] Pagliani, P., Chakraborty, M. K., Information Quanta and Approximation Spaces. II: Generalised Approximation Spaces, in: Hu, X., Liu, Q., Skowron, A., Lin, T. S., Yager, R., Zhang, E. B. (eds.) Proceedings of the IEEE International Conference on Granular Computing, Vol. 2, IEEE, 2005, 611-616.
  • [18] Pawlak, Z., Rough Sets, International Journal of Computer and Information Sciences, 11 (1982) 341-356.
  • [19] Pawlak, Z., Rough Sets, Kluwer, Dordrecht, 1991.
  • [20] Priestley, H. A., Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc., 2 (1970) 186-190.
  • [21] Słowiński, R., Greco, S., Matarazzo, B. Rough Sets in Decision Making. In: R. A. Meyers, (ed.): Encyclopedia of Complexity and Systems Science, Springer, New York, 2009, pp. 7753-7786
  • [22] Vakarelov, D., Information systems, similarity and modal logics, in: E. Orłowska (ed.) Incomplete Information: Rough Set Analysis, Physica, Heidelberg, 1998, pp. 492-550
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0023-0036
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