Abstract
Another formulation of the notion of rough relations is presented. Instead of using two equivalence relations on two universes, or a joint equivalence relation on their Cartesian product, we start from specific classes of binary relations obeying certain properties. The chosen class of relations is a subsystem of all binary relations and represents relations we are interested. An arbitrary relation is approximated by a pair of relations in the chosen class.
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References
Cattaneo, G.: Abstract approximation spaces for rough theories. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery, pp. 59–98. Physica-Verlag, Heidelberg (1998)
Cohn, P.M.: Universal Algebra. Harper and Row Publishers, New York (1965)
Düntsch, I.: Rough sets and algebras of relations. In: Orlowska, E. (ed.) Incomplete Information: Rough Set Analysis, pp. 95–108. Physica-Verlag, Heidelberg (1998)
Greco, S., Matarazzo, B., Slowinski, R.: Rough approximation of preferential information by dominance relations. In: Proceedings of Fourth International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery, pp. 125–130 (1996)
Greco, S., Matarazzo, B., Slowinski, R.: A new rough set approach to multicriteria and multiattribute classification. In: Polkowski, L., Skowron, A. (eds.) Rough Sets and Current Trends in Computing, pp. 60–67. Springer, Berlin (1998)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Rough relations. Bulletin of Polish Academy of Sciences, Technical Sciences 34, 557–590 (1986)
Pawlak, Z.: Rough functions. Bulletin of Polish Academy of Sciences, Technical Sciences 35, 249–251 (1987)
Pawlak, Z.: Rough sets, rough relations and rough functions. Fundamenta Informaticae 27, 103–108 (1996)
Skowron, A., Stepaniuk, J.: Approximation of relations. In: Ziarko, W.P. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, pp. 161–166. Springer, London (1994)
Stepaniuk, J.: Properties and applications on rough relations. In: Proceedings of the Fifth International Workshop on Intelligent Information Systems, pp. 136–141 (1996)
Stepaniuk, J.: Approximation spaces in extensions of rough set theory. In: Polkowski, L., Skowron, A. (eds.) Rough Sets and Current Trends in Computing, pp. 290–297. Springer, Berlin (1998)
Stepaniuk, J.: Rough relations and logics. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery, pp. 248–260. Physica-Verlag, Heidelberg (1998)
Yao, Y.Y.: Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning 15, 291–317 (1996)
Yao, Y.Y.: On generalizing Pawlak approximation operators. In: Polkowski, L., Skowron, A. (eds.) Rough Sets and Current Trends in Computing, pp. 298–307. Springer, Berlin (1998)
Yao, Y.Y.: A comparative study of fuzzy sets and rough sets. Information Sciences 109, 227–242 (1998)
Yao, Y.Y., Lin, T.Y.: Generalization of rough sets using modal logic. Intelligent Automation and Soft Computing, an International Journal 2, 103–120 (1996)
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Yao, Y.Y., Wang, T. (1999). On Rough Relations: An Alternative Formulation. In: Zhong, N., Skowron, A., Ohsuga, S. (eds) New Directions in Rough Sets, Data Mining, and Granular-Soft Computing. RSFDGrC 1999. Lecture Notes in Computer Science(), vol 1711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48061-7_12
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DOI: https://doi.org/10.1007/978-3-540-48061-7_12
Publisher Name: Springer, Berlin, Heidelberg
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