Abstract
In this paper, we focus on the extension of the theory of rough set in lattice-theoretic setting. First we introduce the definition for generalized lower and upper approximation operators determined by mappings between two complete atomic Boolean algebras. Then we find the conditions which permit a given lattice-theoretic operator to represent a upper (or lower) approximation derived from a special mapping. Different sets of axioms of lattice-theoretic operator guarantee the existence of different types of mappings which produce the same operator.
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References
Pawlak, Z.: Rough sets. International Journal of Computer and Information Science 11, 341–356 (1982)
Yao, Y.Y.: Two views of the theory of rough sets in finite universe. International Journal of Approximate Reasoning 15, 291–317 (1996)
Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. Information Sciences 109, 21–47 (1998)
Iwinski, T.B.: Algebraic approach to rough sets. Bulletin of the Polish Academy of Sciences, Mathematics 35, 673–683 (1987)
Järvinen, J.: On the structure of rough approximations. Fundamenta Informaticae 53, 135–153 (2002)
Lin, T.Y.: A rough logic formalism for fuzzy controllers: a hard and soft computing view. International Journal of Approximate Reasoning 15, 395–414 (1996)
Qi, G., Liu, W.: Rough operations on Boolean algebras. Information Sciences 173, 49–63 (2005)
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)
Mi, J.S., Zhang, W.X.: An axiomatic characterization of a fuzzy generalization of rough sets. Information Science 160, 235–249 (2004)
Wu, W.Z., Mi, J.S., Zhang, W.X.: Generalized fuzzy rough sets. Information Sciences 151, 263–282 (2003)
Thiele, H.: On axiomatic characterization of fuzzy Approximation operators I, the fuzzy rough set based case. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 239–247. Springer, Heidelberg (2001)
Thiele, H.: On axiomatic characterization of fuzzy approximation operators II, the rough fuzzy set based case. In: Proceeding of the 31st IEEE Internatioanl Symposium on Multiple-Valued Logic, pp. 230–335 (2000)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)
Skowron, A., Stepaniuk, J.: Generalized approximation spaces. In: Lin, T.Y., Wildberger, A.M. (eds.) Soft Computing, Simulation Councils, San Diego, pp. 18–21 (1995)
Skowron, A., Stepaniuk, J., Peters, J.F., Swiniarski, R.: Calculi of approximation spaces. Fundamenta Informaticae LXXII, 1001–1016 (2006)
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Li, T. (2006). On Axiomatic Characterization of Approximation Operators Based on Atomic Boolean Algebras. In: Wang, GY., Peters, J.F., Skowron, A., Yao, Y. (eds) Rough Sets and Knowledge Technology. RSKT 2006. Lecture Notes in Computer Science(), vol 4062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11795131_19
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DOI: https://doi.org/10.1007/11795131_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36297-5
Online ISBN: 978-3-540-36299-9
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