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2015 | OriginalPaper | Buchkapitel

Interface of Rough Set Systems and Modal Logics: A Survey

verfasst von : Pulak Samanta, Mihir Kumar Chakraborty

Erschienen in: Transactions on Rough Sets XIX

Verlag: Springer Berlin Heidelberg

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Abstract

In this paper the relationship between rough set theory and modal logic has been discussed. Pawlakian rough set theory has obvious connection with modal logic system \(S_5\). With the introduction of various other lower and upper approximation operators, other modal systems come into picture. Besides, the possibility of new modal systems also crop up. Some of these issues are focused here.

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Literatur
1.
2.
Zurück zum Zitat Banerjee, M., Chakraborty, M.K.: Rough algebra. Bull. Polish Acad. Sc. (Math.) 41(4), 293–297 (1993)MathSciNetMATH Banerjee, M., Chakraborty, M.K.: Rough algebra. Bull. Polish Acad. Sc. (Math.) 41(4), 293–297 (1993)MathSciNetMATH
3.
Zurück zum Zitat Banerjee, M., Chakraborty, M.K.: Rough sets through algebraic logic. Fundamenta Informatica 28(3–4), 211–221 (1996)MathSciNetMATH Banerjee, M., Chakraborty, M.K.: Rough sets through algebraic logic. Fundamenta Informatica 28(3–4), 211–221 (1996)MathSciNetMATH
4.
Zurück zum Zitat Banerjee, M., Chakraborty, M.K.: Rough logics : a survey with further directions. In: Orloska, E. (ed.) Incomplete Information: Rough Set Analysis Studies in Fuzziness and Soft Computing, vol. 13, pp. 578–600. Physica-Verlag, Heidelberg (1998) Banerjee, M., Chakraborty, M.K.: Rough logics : a survey with further directions. In: Orloska, E. (ed.) Incomplete Information: Rough Set Analysis Studies in Fuzziness and Soft Computing, vol. 13, pp. 578–600. Physica-Verlag, Heidelberg (1998)
5.
Zurück zum Zitat Banerjee, M., Chakraborty, M.K.: Algebras from rough sets. In: Pal, S., Polkowski, L., Skowron, A. (eds.) Rough-Neural Computing. Cognitive Technologies, pp. 157–184. Springer, Heidelberg (2004)CrossRef Banerjee, M., Chakraborty, M.K.: Algebras from rough sets. In: Pal, S., Polkowski, L., Skowron, A. (eds.) Rough-Neural Computing. Cognitive Technologies, pp. 157–184. Springer, Heidelberg (2004)CrossRef
6.
Zurück zum Zitat Banerjee, M., Yao, Y.: A categorial basis for granular computing. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 427–434. Springer, Heidelberg (2007) CrossRef Banerjee, M., Yao, Y.: A categorial basis for granular computing. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 427–434. Springer, Heidelberg (2007) CrossRef
8.
Zurück zum Zitat Bonikowski, Z., Bryniarski, E., Urszula, W.S.: Extensions and intentions in the rough set theory. J. Inf. Sci. 107, 149–167 (1998)CrossRefMATH Bonikowski, Z., Bryniarski, E., Urszula, W.S.: Extensions and intentions in the rough set theory. J. Inf. Sci. 107, 149–167 (1998)CrossRefMATH
9.
Zurück zum Zitat Bunder, M.W.: Rough consequence and Jaskowskis D2 logics. Technical report 2/04, School of Mathematics and Applied Statistics, University of Wollongong, Australia (2004) Bunder, M.W.: Rough consequence and Jaskowskis D2 logics. Technical report 2/04, School of Mathematics and Applied Statistics, University of Wollongong, Australia (2004)
10.
Zurück zum Zitat Bunder, M.W., Banerjee, M., Chakraborty, M.K.: Some rough consequence logics and their interrelations. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets VIII. LNCS, vol. 5084, pp. 1–20. Springer, Heidelberg (2008) CrossRef Bunder, M.W., Banerjee, M., Chakraborty, M.K.: Some rough consequence logics and their interrelations. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets VIII. LNCS, vol. 5084, pp. 1–20. Springer, Heidelberg (2008) CrossRef
11.
Zurück zum Zitat Chakraborty, M.K., Banerjee, M.: Rough consequence. Bull. Polish Acad. Sc(Math.) 41(4), 299–304 (1993)MathSciNetMATH Chakraborty, M.K., Banerjee, M.: Rough consequence. Bull. Polish Acad. Sc(Math.) 41(4), 299–304 (1993)MathSciNetMATH
12.
Zurück zum Zitat Hughes, G.E., Cresswell, M.J.: A New Introduction to Modal Logic. Routledge, London (1996) CrossRefMATH Hughes, G.E., Cresswell, M.J.: A New Introduction to Modal Logic. Routledge, London (1996) CrossRefMATH
13.
Zurück zum Zitat Kumar, A., Banerjee, M.: Definable and rough sets in covering-based approximation spaces. In: Li, T., Nguyen, H.S., Wang, G., Grzymala-Busse, J., Janicki, R., Hassanien, A.E., Yu, H. (eds.) RSKT 2012. LNCS, vol. 7414, pp. 488–495. Springer, Heidelberg (2012) CrossRef Kumar, A., Banerjee, M.: Definable and rough sets in covering-based approximation spaces. In: Li, T., Nguyen, H.S., Wang, G., Grzymala-Busse, J., Janicki, R., Hassanien, A.E., Yu, H. (eds.) RSKT 2012. LNCS, vol. 7414, pp. 488–495. Springer, Heidelberg (2012) CrossRef
14.
Zurück zum Zitat Li, T.-J.: Rough approximation operators in covering approximation spaces. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 174–182. Springer, Heidelberg (2006) CrossRef Li, T.-J.: Rough approximation operators in covering approximation spaces. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 174–182. Springer, Heidelberg (2006) CrossRef
15.
Zurück zum Zitat Liu, J., Liao, Z.: The sixth type of covering-based rough sets. In: Granular Computing - GrC, Hangzhou 26–28 August 2008. Published in IEEE International Conference on Granular Computing 2008, pp. 438–441 (2008) Liu, J., Liao, Z.: The sixth type of covering-based rough sets. In: Granular Computing - GrC, Hangzhou 26–28 August 2008. Published in IEEE International Conference on Granular Computing 2008, pp. 438–441 (2008)
16.
Zurück zum Zitat Orlowska, E.: A Logic of indiscernibility relations. In: Skowron, A. (ed.) Computation Theory. LNCS, vol. 208, pp. 177–186. Springer, Heidelberg (1985)CrossRef Orlowska, E.: A Logic of indiscernibility relations. In: Skowron, A. (ed.) Computation Theory. LNCS, vol. 208, pp. 177–186. Springer, Heidelberg (1985)CrossRef
17.
Zurück zum Zitat Orlowska, E.: Logic for nondeterministic information. Stud. Logica XLIV, 93–102 (1985)MathSciNet Orlowska, E.: Logic for nondeterministic information. Stud. Logica XLIV, 93–102 (1985)MathSciNet
18.
19.
Zurück zum Zitat Pawlak, Z.: Rough Sets - Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)MATH Pawlak, Z.: Rough Sets - Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)MATH
20.
Zurück zum Zitat Pagliani, P., Chakraborty, M.K.: A geometry of Approximation - Rough Set theory: Logic Algebra and Topology of Conceptual Patterns. Springer, Netherlands (2008)CrossRef Pagliani, P., Chakraborty, M.K.: A geometry of Approximation - Rough Set theory: Logic Algebra and Topology of Conceptual Patterns. Springer, Netherlands (2008)CrossRef
21.
Zurück zum Zitat Pomykala, J.A.: Approximation operations in approximation space. Bull. Pol. Acad. Sci. Math. 35, 653–662 (1987)MathSciNetMATH Pomykala, J.A.: Approximation operations in approximation space. Bull. Pol. Acad. Sci. Math. 35, 653–662 (1987)MathSciNetMATH
22.
Zurück zum Zitat Pomykala, J.A.: Approximation, Similarity and Rough Constructions. ILLC Prepublication Series for Computation and Complexity Theory CT-93-07, University of Amsterdam (1993) Pomykala, J.A.: Approximation, Similarity and Rough Constructions. ILLC Prepublication Series for Computation and Complexity Theory CT-93-07, University of Amsterdam (1993)
23.
Zurück zum Zitat Qin, K., Gao, Y., Pei, Z.: On covering rough sets. In: Yao, J.T., Lingras, P., Wu, W.-Z., Szczuka, M.S., Cercone, N.J., Ślȩzak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 34–41. Springer, Heidelberg (2007) CrossRef Qin, K., Gao, Y., Pei, Z.: On covering rough sets. In: Yao, J.T., Lingras, P., Wu, W.-Z., Szczuka, M.S., Cercone, N.J., Ślȩzak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 34–41. Springer, Heidelberg (2007) CrossRef
24.
Zurück zum Zitat Samanta, P., Chakraborty, M.K.: Covering based approaches to rough sets and implication lattices. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Slezak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS, vol. 5908, pp. 127–134. Springer, Heidelberg (2009) CrossRef Samanta, P., Chakraborty, M.K.: Covering based approaches to rough sets and implication lattices. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Slezak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS, vol. 5908, pp. 127–134. Springer, Heidelberg (2009) CrossRef
25.
Zurück zum Zitat Samanta, P., Chakraborty, M.K.: Generalized rough sets and implication lattices. In: Peters, J.F., Skowron, A., Sakai, H., Chakraborty, M.K., Slezak, D., Hassanien, A.E., Zhu, W. (eds.) Transactions on Rough Sets XIV. LNCS, vol. 6600, pp. 183–201. Springer, Heidelberg (2011) CrossRef Samanta, P., Chakraborty, M.K.: Generalized rough sets and implication lattices. In: Peters, J.F., Skowron, A., Sakai, H., Chakraborty, M.K., Slezak, D., Hassanien, A.E., Zhu, W. (eds.) Transactions on Rough Sets XIV. LNCS, vol. 6600, pp. 183–201. Springer, Heidelberg (2011) CrossRef
26.
Zurück zum Zitat Ślȩzak, D., Wasilewski, P.: Granular sets – foundations and case study of tolerance spaces. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 435–442. Springer, Heidelberg (2007) CrossRef Ślȩzak, D., Wasilewski, P.: Granular sets – foundations and case study of tolerance spaces. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 435–442. Springer, Heidelberg (2007) CrossRef
27.
Zurück zum Zitat Vakarelov, D.: A modal logic for similarity relations in Pawlak knowledge representation systems. Fundamenta Informaticae XV, 61–79 (1991)MathSciNet Vakarelov, D.: A modal logic for similarity relations in Pawlak knowledge representation systems. Fundamenta Informaticae XV, 61–79 (1991)MathSciNet
28.
Zurück zum Zitat Vakarelov, D.: Similarity relations and modal logics. In: Orlowska, E. (ed.) Incomplete Information : Rough Set Analysis Studies in Fuzziness and Soft Computing, vol. 13, pp. 492–550. Physica-Verlag, Heidelberg (1998) CrossRef Vakarelov, D.: Similarity relations and modal logics. In: Orlowska, E. (ed.) Incomplete Information : Rough Set Analysis Studies in Fuzziness and Soft Computing, vol. 13, pp. 492–550. Physica-Verlag, Heidelberg (1998) CrossRef
29.
Zurück zum Zitat Yao, Y.Y., Lin, T.Y.: Generalization of rough sets using model logic. Intell. Automaton Soft Comput. 2(2), 103–120 (1996)MathSciNetCrossRef Yao, Y.Y., Lin, T.Y.: Generalization of rough sets using model logic. Intell. Automaton Soft Comput. 2(2), 103–120 (1996)MathSciNetCrossRef
30.
Zurück zum Zitat Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. J. Inf. Sci. 109, 21–47 (1998)CrossRefMATH Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. J. Inf. Sci. 109, 21–47 (1998)CrossRefMATH
31.
Zurück zum Zitat Yao, Y.Y.: On generalizing rough set theory. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) Rough set, Fuzzy sets, Data Mining and Granular Computing. Lecture Notes in Computer Science, vol. 2639, pp. 44–51. Springer, Heidelberg (2003)CrossRef Yao, Y.Y.: On generalizing rough set theory. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) Rough set, Fuzzy sets, Data Mining and Granular Computing. Lecture Notes in Computer Science, vol. 2639, pp. 44–51. Springer, Heidelberg (2003)CrossRef
32.
Zurück zum Zitat Yao, Y., Yao, B.: Covering based rough set approximations. Inf. Sci. 200, 91–107 (2012)CrossRefMATH Yao, Y., Yao, B.: Covering based rough set approximations. Inf. Sci. 200, 91–107 (2012)CrossRefMATH
33.
Zurück zum Zitat Zhu, W.: Topological approaches to covering rough sets. Sci. Direct Inf. Sci. 177, 1499–1508 (2007)MATH Zhu, W.: Topological approaches to covering rough sets. Sci. Direct Inf. Sci. 177, 1499–1508 (2007)MATH
34.
Zurück zum Zitat Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Inf. Sci. 179, 210–225 (2009)CrossRefMATH Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Inf. Sci. 179, 210–225 (2009)CrossRefMATH
35.
Zurück zum Zitat Zhu, W.: Properties of the second type of covering-based rough sets. In: Butz, C.J., Nguyen, N.T., Takama, Y., Cheung, W., Cheung, Y.M. (eds.) IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology Hong Kong, China 18–22 December 2006 Proceedings of the - WI-IAT 2006 Workshops, pp. 494–497. IEEE (2006) Zhu, W.: Properties of the second type of covering-based rough sets. In: Butz, C.J., Nguyen, N.T., Takama, Y., Cheung, W., Cheung, Y.M. (eds.) IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology Hong Kong, China 18–22 December 2006 Proceedings of the - WI-IAT 2006 Workshops, pp. 494–497. IEEE (2006)
36.
Zurück zum Zitat Zhu, W., Wang, F.Y.: Relationship among three types of covering rough sets. In: Proceedings of the IEEE International Conference on Grannular Computing-GrC, pp. 43–48 (2006) Zhu, W., Wang, F.Y.: Relationship among three types of covering rough sets. In: Proceedings of the IEEE International Conference on Grannular Computing-GrC, pp. 43–48 (2006)
37.
Zurück zum Zitat Zhu, W., Wang, F.Y.: Properties of the first type of covering-based rough sets. In: Tsumoto, S., Clifton, C.W., Zhong, N., Xindong Wu, Liu, J., Wah, B.W., Cheung, Y.M. (eds.) Proceedings of the Sixth IEEE International Conference on Data Mining - Workshops, ICDMW Hong Kong, China December 2006, pp. 407–411. IEEE Computer Society (2006) Zhu, W., Wang, F.Y.: Properties of the first type of covering-based rough sets. In: Tsumoto, S., Clifton, C.W., Zhong, N., Xindong Wu, Liu, J., Wah, B.W., Cheung, Y.M. (eds.) Proceedings of the Sixth IEEE International Conference on Data Mining - Workshops, ICDMW Hong Kong, China December 2006, pp. 407–411. IEEE Computer Society (2006)
38.
Zurück zum Zitat Zhu, W., Wang, F.-Y.: Binary relation based rough sets. In: Wang, L., Jiao, L., Shi, G., Li, X., Liu, J. (eds.) FSKD 2006. LNCS (LNAI), vol. 4223, pp. 276–285. Springer, Heidelberg (2006) CrossRef Zhu, W., Wang, F.-Y.: Binary relation based rough sets. In: Wang, L., Jiao, L., Shi, G., Li, X., Liu, J. (eds.) FSKD 2006. LNCS (LNAI), vol. 4223, pp. 276–285. Springer, Heidelberg (2006) CrossRef
Metadaten
Titel
Interface of Rough Set Systems and Modal Logics: A Survey
verfasst von
Pulak Samanta
Mihir Kumar Chakraborty
Copyright-Jahr
2015
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-47815-8_8