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2018 | OriginalPaper | Buchkapitel

1. Introduction

verfasst von : Seiki Akama, Tetsuya Murai, Yasuo Kudo

Erschienen in: Reasoning with Rough Sets

Verlag: Springer International Publishing

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Abstract

This gives an introductory presentation to motivate our work on rough set theory. Rough set theory is interesting theoretically as well as practically, and a quick survey on the subject, including overview, history and applications, is helpful to the readers.

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Literatur
2.
Zurück zum Zitat Pawlak, P.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)CrossRefMATH Pawlak, P.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)CrossRefMATH
3.
Zurück zum Zitat Orlowska, E.: Kripke models with relative accessibility relations and their applications to inferences from incomplete information. In: Mirkowska, G., Rasiowa, H. (eds.) Mathematical Problems in Computation Theory. pp. 327–337. Polish Scientific Publishers, Warsaw (1987) Orlowska, E.: Kripke models with relative accessibility relations and their applications to inferences from incomplete information. In: Mirkowska, G., Rasiowa, H. (eds.) Mathematical Problems in Computation Theory. pp. 327–337. Polish Scientific Publishers, Warsaw (1987)
4.
Zurück zum Zitat Yao, Y., Lin, T.: Generalization of rough sets using modal logics. Intell. Autom. Soft Comput. 2, 103–120 (1996)CrossRef Yao, Y., Lin, T.: Generalization of rough sets using modal logics. Intell. Autom. Soft Comput. 2, 103–120 (1996)CrossRef
5.
Zurück zum Zitat Kudo, Y., Murai, T., Akama, S.: A granularity-based framework of deduction, induction, and abduction. Int. J. Approx. Reason. 50, 1215–1226 (2009)MathSciNetCrossRefMATH Kudo, Y., Murai, T., Akama, S.: A granularity-based framework of deduction, induction, and abduction. Int. J. Approx. Reason. 50, 1215–1226 (2009)MathSciNetCrossRefMATH
6.
Zurück zum Zitat Pawlak, P.: Information systems: theoretical foundations. Inf. Syst. 6, 205–218 (1981)CrossRefMATH Pawlak, P.: Information systems: theoretical foundations. Inf. Syst. 6, 205–218 (1981)CrossRefMATH
7.
Zurück zum Zitat Orlowska, E.: Logical aspects of learning concepts. Int. J. Approx. Reason. 2, 349–364 (1988)CrossRefMATH Orlowska, E.: Logical aspects of learning concepts. Int. J. Approx. Reason. 2, 349–364 (1988)CrossRefMATH
8.
Zurück zum Zitat Orlowska, E.: Logic for reasoning about knowledge. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 35, 559–572 (1989)MathSciNetCrossRefMATH Orlowska, E.: Logic for reasoning about knowledge. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 35, 559–572 (1989)MathSciNetCrossRefMATH
9.
Zurück zum Zitat Fariñas del Cerro, L., Orlowska, E.: DAL-a logic for data analysis. Theor. Comput. Sci. 36, 251–264 (1985) Fariñas del Cerro, L., Orlowska, E.: DAL-a logic for data analysis. Theor. Comput. Sci. 36, 251–264 (1985)
10.
Zurück zum Zitat Ziarko, W.: Variable precision rough set model. J. Comput. Syst. Sci. 46, 39–59 (1993) Ziarko, W.: Variable precision rough set model. J. Comput. Syst. Sci. 46, 39–59 (1993)
11.
Zurück zum Zitat Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17, 191–209 (1989)CrossRefMATH Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17, 191–209 (1989)CrossRefMATH
14.
Zurück zum Zitat Pagliani, P., Intrinsic co-Heyting boundaries and information incompleteness in rough set analysis. In: Polkowski, L., Skowron, A. (eds.) Rough Sets and Current Trends in Computing. PP. 123–130. Springer, Berlin (1998) Pagliani, P., Intrinsic co-Heyting boundaries and information incompleteness in rough set analysis. In: Polkowski, L., Skowron, A. (eds.) Rough Sets and Current Trends in Computing. PP. 123–130. Springer, Berlin (1998)
16.
Zurück zum Zitat Pomykala, J., Pomykala, J.A.: The stone algebra of rough sets. Bull. Pol. Acad. Sci. Math. 36, 495–508 (1988)MathSciNetMATH Pomykala, J., Pomykala, J.A.: The stone algebra of rough sets. Bull. Pol. Acad. Sci. Math. 36, 495–508 (1988)MathSciNetMATH
17.
Zurück zum Zitat Akama, S., Murai, T.: Rough set semantics for three-valued logics. In: Nakamatsu, K., Abe, J.M. (eds.) Advances in Logic Based Intelligent Systems. pp. 242–247. IOS Press, Amsterdam (2005) Akama, S., Murai, T.: Rough set semantics for three-valued logics. In: Nakamatsu, K., Abe, J.M. (eds.) Advances in Logic Based Intelligent Systems. pp. 242–247. IOS Press, Amsterdam (2005)
18.
Zurück zum Zitat Miyamoto, S., Murai, T., Kudo, Y.: A family of polymodal systems and its application to generalized possibility measure and multi-rough sets. JACIII 10, 625–632 (2006)CrossRef Miyamoto, S., Murai, T., Kudo, Y.: A family of polymodal systems and its application to generalized possibility measure and multi-rough sets. JACIII 10, 625–632 (2006)CrossRef
19.
Zurück zum Zitat Murai, T., Miyakoshi, M., Shinmbo, M.: Measure-based semantics for modal logic. In: Lowen, R., Roubens, M. (eds.) Fuzzy Logic: State of the Arts. pp. 395–405. Kluwer, Dordrecht (1993) Murai, T., Miyakoshi, M., Shinmbo, M.: Measure-based semantics for modal logic. In: Lowen, R., Roubens, M. (eds.) Fuzzy Logic: State of the Arts. pp. 395–405. Kluwer, Dordrecht (1993)
20.
Zurück zum Zitat Murai, T., Miyakoshi, M., Shimbo, M.: Soundness and completeness theorems between the Dempster-Shafer theory and logic of belief. In: Proceedings of the 3rd FUZZ-IEEE on World Congress on Computational Intelligence (WCCI). pp. 855–858. (1994) Murai, T., Miyakoshi, M., Shimbo, M.: Soundness and completeness theorems between the Dempster-Shafer theory and logic of belief. In: Proceedings of the 3rd FUZZ-IEEE on World Congress on Computational Intelligence (WCCI). pp. 855–858. (1994)
21.
Zurück zum Zitat Murai, T., Miyakoshi, M. and Shinmbo, M.: A logical foundation of graded modal operators defined by fuzzy measures. In: Proceedings of the 4th FUZZ-IEEE, pp. 151–156. (Semantics for modal logic, Fuzzy Logic: State of the Arts, pp. 395–405, 1993) Kluwer, Dordrecht (1995) Murai, T., Miyakoshi, M. and Shinmbo, M.: A logical foundation of graded modal operators defined by fuzzy measures. In: Proceedings of the 4th FUZZ-IEEE, pp. 151–156. (Semantics for modal logic, Fuzzy Logic: State of the Arts, pp. 395–405, 1993) Kluwer, Dordrecht (1995)
22.
Zurück zum Zitat Akama, S., Murai, T. and Kudo, Y.: Heyting-Brouwer Rough Set Logic. In: Proceedings of the KSE2013, Hanoi, pp. 135–145. Springer, Heidelberg (2013) Akama, S., Murai, T. and Kudo, Y.: Heyting-Brouwer Rough Set Logic. In: Proceedings of the KSE2013, Hanoi, pp. 135–145. Springer, Heidelberg (2013)
23.
Zurück zum Zitat Akama, S., Murai, T., Kudo, Y.: Da Costa logics and vagueness. In: Proceedings of the GrC2014, Noboribetsu, Japan. (2014) Akama, S., Murai, T., Kudo, Y.: Da Costa logics and vagueness. In: Proceedings of the GrC2014, Noboribetsu, Japan. (2014)
24.
25.
Zurück zum Zitat Adsiaans, P., Zantinge, D.: Data Mining, Addison-Wesley, Reading, Mass (1996) Adsiaans, P., Zantinge, D.: Data Mining, Addison-Wesley, Reading, Mass (1996)
26.
Zurück zum Zitat Lin, T., Cercone, N. (eds.): Rough Sets and Data Mining. Springer, Berlin (1997) Lin, T., Cercone, N. (eds.): Rough Sets and Data Mining. Springer, Berlin (1997)
27.
Zurück zum Zitat Slowinski, R., Greco, S., Matarazzo, B.: Rough sets and decision making. In: Meyers, R. (ed.) Encyclopedia of Complexity and Systems Science. pp. 7753–7787. Springer, Heidelberg (2009) Slowinski, R., Greco, S., Matarazzo, B.: Rough sets and decision making. In: Meyers, R. (ed.) Encyclopedia of Complexity and Systems Science. pp. 7753–7787. Springer, Heidelberg (2009)
28.
Zurück zum Zitat Pal, K., Shanker, B., Mitra, P.: Granular computing, rough entropy and object extraction. Pattern Recognit. Lett. 26, 2509–2517 (2005)CrossRef Pal, K., Shanker, B., Mitra, P.: Granular computing, rough entropy and object extraction. Pattern Recognit. Lett. 26, 2509–2517 (2005)CrossRef
29.
Zurück zum Zitat Bit, M., Beaubouef, T.: Rough set uncertainty for robotic systems. J. Comput. Syst. Coll. 23, 126–132 (2008) Bit, M., Beaubouef, T.: Rough set uncertainty for robotic systems. J. Comput. Syst. Coll. 23, 126–132 (2008)
30.
Zurück zum Zitat Tsumoto, S.: Modelling medical diagnostic rules based on rough sets. In: Rough Sets and Current Trends in Computing. pp. 475–482. (1998) Tsumoto, S.: Modelling medical diagnostic rules based on rough sets. In: Rough Sets and Current Trends in Computing. pp. 475–482. (1998)
31.
Zurück zum Zitat Hirano, S., Tsumoto, S.: Rough representation of a region of interest in medical images. Int. J. Approx. Reason. 40, 23–34 (2005)CrossRef Hirano, S., Tsumoto, S.: Rough representation of a region of interest in medical images. Int. J. Approx. Reason. 40, 23–34 (2005)CrossRef
Metadaten
Titel
Introduction
verfasst von
Seiki Akama
Tetsuya Murai
Yasuo Kudo
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-72691-5_1