Abstract
Rough set theory, proposed by Professor Zdzisław Pawlak in 1982 [163, 165, 166, 169], can be seen as a new mathematical approach to dealing with imperfect knowledge, in particular with vague concepts. The rough set philosophy is founded on the assumption that with every object of the universe of discourse we associate some information (data, knowledge). For example, if objects are patients suffering from a certain disease, symptoms of the disease form information about patients. Objects characterized by the same information are indiscernible (similar) in view of the available information about them. The indiscernibility relation generated in this way is the mathematical basis of rough set theory. This understanding of indiscernibility is related to the idea of Gottfried Wilhelm Leibniz that objects are indiscernible if and only if all available functionals take on identical values (Leibniz’s Law of Indiscernibility: The Identity of Indiscernibles) [4, 97]. However, in the rough set approach, indiscernibility is defined relative to a given set of functionals (attributes).
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References
Aggarwal, C.: Data Streams: Models and Algorithms. Springer, Berlin (2007)
Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.): RSCTC 2002. LNCS (LNAI), vol. 2475. Springer, Heidelberg (2002)
An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.): RSFDGrC 2007. LNCS (LNAI), vol. 4482. Springer, Heidelberg (2007)
Ariew, R., Garber, D. (eds.): Philosophical Essay, Leibniz, G. W. Hackett Publishing Company, Indianapolis (1989)
Balbiani, P., Vakarelov, D.: A modal logic for indiscernibility and complementarity in information systems. Fundamenta Informaticae 50(3-4), 243–263 (2002)
Banerjee, M., Chakraborty, M.: Logic for rough truth. Fundamenta Informaticae 71(2-3), 139–151 (2006)
Bargiela, A., Pedrycz, W. (eds.): Granular Computing: An Introduction. Kluwer Academic Publishers (2003)
Barr, B.: *-Autonomous categories. Lecture Notes in Mathematics, vol. 752. Springer (1979)
Barsalou, L.W.: Perceptual symbol systems. Behavioral and Brain Sciences 22, 577–660 (1999)
Barwise, J., Seligman, J.: Information Flow: The Logic of Distributed Systems. Cambridge University Press (1997)
Bazan, J.: Hierarchical classifiers for complex spatio-temporal concepts. In: Peters, et al. [188], pp. 474–750
Bazan, J.: Rough sets and granular computing in behavioral pattern identification and planning. In: Pedrycz, et al. [176], pp. 777–822
Bazan, J., Nguyen, H.S., Nguyen, S.H., Synak, P., Wróblewski, J.: Rough set algorithms in classification problems. In: Polkowski, et al. [200], pp. 49–88
Bazan, J., Skowron, A.: On-line elimination of non-relevant parts of complex objects in behavioral pattern identification. In: Pal, et al. [149], pp. 720–725
Bazan, J.G.: A comparison of dynamic and non-dynamic rough set methods for extracting laws from decision tables. In: Polkowski, Skowron [203], pp. 321–365
Bazan, J.G., Nguyen, H.S., Peters, J.F., Skowron, A., Szczuka, M., Szczuka: Rough set approach to pattern extraction from classifiers. In: Skowron, Szczuka [253], pp. 20–29, www.elsevier.nl/locate/entcs/volume82.html
Bazan, J.G., Nguyen, H.S., Skowron, A., Szczuka, M.: A view on rough set concept approximation. In: Wang, et al. [303], pp. 181–188
Bazan, J.G., Nguyen, H.S., Szczuka, M.S.: A view on rough set concept approximations. Fundamenta Informaticae 59, 107–118 (2004)
Bazan, J.G., Peters, J.F., Skowron, A.: Behavioral pattern identification through rough set modelling. In: Ślęzak, et al. [263], pp. 688–697
Bazan, J.G., Skowron, A.: Classifiers based on approximate reasoning schemes. In: Dunin-Kęplicz, et al. [41], pp. 191–202
Bazan, J.G., Skowron, A., Swiniarski, R.: Rough sets and vague concept approximation: From sample approximation to adaptive learning. In: Peters, Skowron [180], pp. 39–62
Behnke, S.: Hierarchical Neural Networks for Image Interpretation. LNCS, vol. 2766. Springer, Heidelberg (2003)
Bello, R., Falcón, R., Pedrycz, W.: Granular Computing: At the Junction of Rough Sets and Fuzzy Sets. STUDFUZZ, vol. 234. Springer, Heidelberg (2010)
Blake, A.: Canonical expressions in Boolean algebra. Dissertation, Dept. of Mathematics, University of Chicago, 1937. University of Chicago Libraries (1938)
Boole, G.: The Mathematical Analysis of Logic. G. Bell, London (1847); reprinted by Philosophical Library, New York (1948)
Boole, G.: An Investigation of the Laws of Thought. Walton, London (1854); reprinted by Dover Books, New York (1954)
Borrett, S.R., Bridewell, W., Langely, P., Arrigo, K.R.: A method for representing and developing process models. Ecological Complexity 4, 1–12 (2007)
Bower, J.M., Bolouri, H. (eds.): Computational Modeling of Genetic and Biochemical Networks. MIT Press (2001)
Breiman, L.: Statistical modeling: The two cultures. Statistical Science 16(3), 199–231 (2001)
Brown, F.: Boolean Reasoning. Kluwer Academic Publishers, Dordrecht (1990)
Cercone, N., Skowron, A., Zhong, N.: Computational Intelligence: An International Journal (Special issue) 17(3) (2001)
Chakraborty, M., Pagliani, P.: A Geometry of Approximation: Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns. Springer, Heidelberg (2008)
Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.): RSCTC 2008. LNCS (LNAI), vol. 5306. Springer, Heidelberg (2008)
Cios, K., Pedrycz, W., Swiniarski, R.: Data Mining Methods for Knowledge Discovery. Kluwer, Norwell (1998)
Ciucci, D., Yao, Y.Y.: Special issue on Advances in Rough Set Theory. Fundamenta Informaticae 108(3-4) (2011)
Delimata, P., Moshkov, M.J., Skowron, A., Suraj, Z.: Inhibitory Rules in Data Analysis: A Rough Set Approach. SCI, vol. 163. Springer, Heidelberg (2009)
Demri, S., Orłowska, E. (eds.): Incomplete Information: Structure, Inference, Complexity. Monographs in Theoretical Computer Sience. Springer, Heidelberg (2002)
Doherty, P., Łukaszewicz, W., Skowron, A., Szałas, A.: Knowledge Engineering: A Rough Set Approach. STUDFUZZ, vol. 202. Springer, Heidelberg (2006)
Dubois, D., Prade, H.: Foreword. In: Rough Sets: Theoretical Aspects of Reasoning about Data [169]
Duda, R., Hart, P., Stork, R.: Pattern Classification. John Wiley & Sons, New York (2002)
Dunin-Kęplicz, B., Jankowski, A., Skowron, A., Szczuka, M. (eds.): Monitoring, Security, and Rescue Tasks in Multiagent Systems (MSRAS 2004). Advances in Soft Computing. Springer, Heidelberg (2005)
Düntsch, I.: A logic for rough sets. Theoretical Computer Science 179, 427–436 (1997)
Düntsch, I., Gediga, G.: Rough set data analysis. In: Encyclopedia of Computer Science and Technology, vol. 43, pp. 281–301. Marcel Dekker (2000)
Düntsch, I., Gediga, G.: Rough set data analysis: A road to non-invasive knowledge discovery. Methodos Publishers, Bangor (2000)
Fahle, M., Poggio, T.: Perceptual Learning. MIT Press, Cambridge (2002)
Fan, T.F., Liau, C.J., Yao, Y.: On modal and fuzzy decision logics based on rough set theory. Fundamenta Informaticae 52(4), 323–344 (2002)
Feng, J., Jost, J., Minping, Q. (eds.): Network: From Biology to Theory. Springer, Berlin (2007)
Frege, G.: Grundgesetzen der Arithmetik, vol. 2. Verlag von Hermann Pohle, Jena (1903)
Friedman, J.H.: Data mining and statistics. What’s the connection? (keynote address). In: Scott, D. (ed.) Proceedings of the 29th Symposium on the Interface: Computing Science and Statistics, Huston, Texas, May 14-17, University of Huston, Huston (1997)
Gabbay, D. (ed.): Fibring Logics. Oxford University Press (1998)
Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.): Handbook of Logic in Artificial Intelligence and Logic Programming. Volume 3: Nonmonotonic Reasoning and Uncertain Reasoning. Calderon Press, Oxford (1994)
Garcia-Molina, H., Ullman, J., Widom, J.: Database Systems: The Complete Book. Prentice-Hall, Upper Saddle River (2002)
Gediga, G., Düntsch, I.: Rough approximation quality revisited. Artificial Intelligence 132, 219–234 (2001)
Gell-Mann, M.: The Quark and the Jaguar - Adventures in the Simple and the Complex. Brown and Co., London (1994)
Goldin, D., Smolka, S., Wegner, P. (eds.): Interactive Computation: The New Paradigm. Springer (2006)
Goldin, D., Wegner, P.: Principles of interactive computation. In: Goldin, et al. [55], pp. 25–37
Gomolińska, A.: A graded meaning of formulas in approximation spaces. Fundamenta Informaticae 60(1-4), 159–172 (2004)
Gomolińska, A.: Rough validity, confidence, and coverage of rules in approximation spaces. In: Peters, Skowron [178], pp. 57–81
Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.): RSCTC 2006. LNCS (LNAI), vol. 4259. Springer, Heidelberg (2006)
Greco, S., Kadzinski, M., Słowiński, R.: Selection of a representative value function in robust multiple criteria sorting. Computers & OR 38(11), 1620–1637 (2011)
Greco, S., Matarazzo, B., Słowiński, R.: Dealing with missing data in rough set analysis of multi-attribute and multi-criteria decision problems. In: Zanakis, S., Doukidis, G., Zopounidis, C. (eds.) Decision Making: Recent Developments and Worldwide Applications, pp. 295–316. Kluwer Academic Publishers, Boston (2000)
Greco, S., Matarazzo, B., Słowiński, R.: Rough set theory for multicriteria decision analysis. European Journal of Operational Research 129(1), 1–47 (2001)
Greco, S., Matarazzo, B., Słowiński, R.: Data mining tasks and methods: Classification: multicriteria classification. In: Kloesgen, W., Żytkow, J. (eds.) Handbook of KDD, pp. 318–328. Oxford University Press, Oxford (2002)
Greco, S., Matarazzo, B., Słowiński, R.: Dominance-based rough set approach to knowledge discovery (I) - General perspective (II) - Extensions and applications. In: Zhong, Liu [319], pp. 513–552, 553–612
Greco, S., Matarazzo, B., Słowiński, R.: Dominance-based rough set approach as a proper way of handling graduality in rough set theory. In: Peters, et al. [187], pp. 36–52
Greco, S., Matarazzo, B., Słowiński, R.: Granular computing and data mining for ordered data: The dominance-based rough set approach. In: Encyclopedia of Complexity and Systems Science, pp. 4283–4305. Springer, Heidelberg (2009)
Greco, S., Matarazzo, B., Słowiński, R.: A summary and update of “Granular computing and data mining for ordered data: The dominance-based rough set approach”. In: Hu, X., Lin, T.Y., Raghavan, V.V., Grzymala-Busse, J.W., Liu, Q., Broder, A.Z. (eds.) 2010 IEEE International Conference on Granular Computing, GrC 2010, San Jose, California, August 14-16, pp. 20–21. IEEE Computer Society (2010)
Greco, S., Słowiński, R., Stefanowski, J., Zurawski, M.: Incremental versus non-incremental rule induction for multicriteria classification. In: Peters, et al. [183], pp. 54–62
Grzymała-Busse, J.W.: Managing Uncertainty in Expert Systems. Kluwer Academic Publishers, Norwell (1990)
Grzymała-Busse, J.W.: LERS – A system for learning from examples based on rough sets. In: Słowiński [266], pp. 3–18
Grzymała-Busse, J.W.: A new version of the rule induction system LERS. Fundamenta Informaticae 31(1), 27–39 (1997)
Grzymała-Busse, J.W.: LERS - A data mining system. In: The Data Mining and Knowledge Discovery Handbook, pp. 1347–1351 (2005)
Grzymala-Busse, J.W.: Generalized parameterized approximations. In: Yao, et al. [310], pp. 136–145
Gurevich, Y.: Interactive algorithms 2005. In: Goldin, et al. [55], pp. 165–181
Harnad, S.: Categorical Perception: The Groundwork of Cognition. Cambridge University Press, New York (1987)
Hassanien, A.E., Suraj, Z., Slezak, D., Lingras, P. (eds.): Rough Computing: Theories, Technologies and Applications. IGI Global, Hershey (2008)
Hastie, T., Tibshirani, R., Friedman, J.H.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, Heidelberg (2001)
Hirano, S., Inuiguchi, M., Tsumoto, S. (eds.): Proceedings of International Workshop on Rough Set Theory and Granular Computing (RSTGC 2001), Matsue, Shimane, Japan, May 20-22. Bulletin of the International Rough Set Society, vol. 5(1-2). International Rough Set Society, Matsue (2001)
Huhns, M.N., Singh, M.P.: Readings in Agents. Morgan Kaufmann, San Mateo (1998)
Inuiguchi, M., Hirano, S., Tsumoto, S. (eds.): Rough Set Theory and Granular Computing. STUDFUZZ, vol. 125. Springer, Heidelberg (2003)
Jain, R., Abraham, A.: Special issue on Hybrid Intelligence using rough sets. International Journal of Hybrid Intelligent Systems 2 (2005)
Jankowski, A., Skowron, A.: A wistech paradigm for intelligent systems. In: Peters, et al. [184], pp. 94–132
Jankowski, A., Skowron, A.: Logic for artificial intelligence: The Rasiowa - Pawlak school perspective. In: Ehrenfeucht, A., Marek, V., Srebrny, M. (eds.) Andrzej Mostowski and Foundational Studies, pp. 106–143. IOS Press, Amsterdam (2008)
Jankowski, A., Skowron, A.: Wisdom technology: A rough-granular approach. In: Marciniak, M., Mykowiecka, A. (eds.) Bolc Festschrift. LNCS, vol. 5070, pp. 3–41. Springer, Heidelberg (2009)
Jensen, R., Shen, Q.: Computational Intelligence and Feature Selection: Rough and Fuzzy Approaches. IEEE Press Series on Cmputationa Intelligence. IEEE Press and John Wiley & Sons, Hoboken, NJ (2008)
Jian, L., Liu, S., Lin, Y.: Hybrid Rough Sets and Applications in Uncertain Decision-Making (Systems Evaluation, Prediction, and Decision-Making). CRC Press, Boca Raton (2010)
Keefe, R.: Theories of Vagueness. Cambridge Studies in Philosophy, Cambridge, UK (2000)
Keefe, R., Smith, P.: Vagueness: A Reader. MIT Press, Massachusetts (1997)
Kloesgen, W., Żytkow, J. (eds.): Handbook of Knowledge Discovery and Data Mining. Oxford University Press, Oxford (2002)
Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: A tutorial. In: Pal, Skowron [154], pp. 3–98
Kostek, B.: Soft Computing in Acoustics, Applications of Neural Networks, Fuzzy Logic and Rough Sets to Physical Acoustics. STUDFUZZ, vol. 31. Physica-Verlag, Heidelberg (1999)
Kostek, B.: Perception-Based Data Processing in Acoustics: Applications to Music Information Retrieval and Psychophysiology of Hearing. SCI, vol. 3. Springer, Heidelberg (2005)
Kotlowski, W., Dembczynski, K., Greco, S., Słowiński, R.: Stochastic dominance-based rough set model for ordinal classification. Information Sciences 178(21), 4019–4037 (2008)
Kryszkiewicz, M., Cichoń, K.: Towards scalable algorithms for discovering rough set reducts. In: Peters, Skowron [185], pp. 120–143
Kryszkiewicz, M., Peters, J.F., Rybiński, H., Skowron, A. (eds.): RSEISP 2007. LNCS (LNAI), vol. 4585. Springer, Heidelberg (2007)
Kuznetsov, S.O., Ślęzak, D., Hepting, D.H., Mirkin, B. (eds.): RSFDGrC 2011. LNCS (LNAI), vol. 6743. Springer, Heidelberg (2011)
Leibniz, G.W.: Discourse on metaphysics. In: Ariew, Garber [4], pp. 35–68
Leśniewski, S.: Grundzüge eines neuen Systems der Grundlagen der Mathematik. Fundamenta Mathematicae 14, 1–81 (1929)
Leśniewski, S.: On the foundations of mathematics. Topoi 2, 7–52 (1982)
Lin, T.Y.: Neighborhood systems and approximation in database and knowledge base systems. In: Emrich, M.L., Phifer, M.S., Hadzikadic, M., Ras, Z.W. (eds.) Proceedings of the Fourth International Symposium on Methodologies of Intelligent Systems (Poster Session), October 12-15, pp. 75–86. Oak Ridge National Laboratory, Charlotte (1989)
Lin, T.Y.: Special issue, Journal of the Intelligent Automation and Soft Computing 2(2) (1996)
Lin, T.Y.: The discovery, analysis and representation of data dependencies in databases. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1: Methodology and Applications. STUDFUZZ, vol. 18, pp. 107–121. Physica-Verlag, Heidelberg (1998)
Lin, T.Y., Cercone, N. (eds.): Rough Sets and Data Mining - Analysis of Imperfect Data. Kluwer Academic Publishers, Boston (1997)
Lin, T.Y., Wildberger, A.M. (eds.): Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, Knowledge Discovery. Simulation Councils, Inc., San Diego (1995)
Lin, T.Y., Yao, Y.Y., Zadeh, L.A. (eds.): Rough Sets, Granular Computing and Data Mining. STUDFUZZ. Physica-Verlag, Heidelberg (2001)
Liu, J.: Autonomous Agents and Multi-Agent Systems: Explorations in Learning, self-Organization and Adaptive Computation. World Scientific Publishing (2001)
Łukasiewicz, J.: Die logischen Grundlagen der Wahrscheinlichkeitsrechnung, 1913. In: Borkowski, L. (ed.) Jan Łukasiewicz - Selected Works, pp. 16–63. North Holland Publishing Company, Polish Scientific Publishers, Amsterdam, London, Warsaw (1970)
Maji, P., Pal, S.K.: Rough-Fuzzy Pattern Recognition: Application in Bioinformatics and Medical Imaging. Wiley Series in Bioinformatics. John Wiley & Sons, Hoboken (2012)
Marcus, S.: The paradox of the heap of grains, in respect to roughness, fuzziness and negligibility. In: Polkowski, Skowron [202], pp. 19–23
Marek, V.W., Rasiowa, H.: Approximating sets with equivalence relations. Theoretical Computer Science 48(3), 145–152 (1986)
Marek, V.W., Truszczyński, M.: Contributions to the theory of rough sets. Fundamenta Informaticae 39(4), 389–409 (1999)
McCarthy, J.: Notes on formalizing contex. In: Proceedings of the 13th International Joint Conference on Artifical Intelligence (IJCAI 1993), pp. 555–560. Morgan Kaufmann Publishers Inc., San Francisco (1993)
de Medeiros, A.K.A., Weijters, A.J.M.M., van der Aalst, W.M.P.: Genetic process mining: An experimental evaluation. Data Mining and Knowledge Discovery 14, 245–304 (2007)
Mill, J.S.: Ratiocinative and Inductive, Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation. In: Parker, Son, Bourn (eds.) West Strand London (1862)
Mitchel, T.M.: Machine Learning. McGraw-Hill Series in Computer Science, Boston, MA (1999)
Moshkov, M., Skowron, A., Suraj, Z.: On testing membership to maximal consistent extensions of information systems. In: Greco, et al. [59], pp. 85–90
Moshkov, M., Skowron, A., Suraj, Z.: On irreducible descriptive sets of attributes for information systems. In: Chan, et al. [33], pp. 21–30
Moshkov, M.J., Piliszczuk, M., Zielosko, B.: Partial Covers, Reducts and Decision Rules in Rough Sets - Theory and Applications. SCI, vol. 145. Springer, Heidelberg (2008)
Moshkov, M.J., Skowron, A., Suraj, Z.: On minimal rule sets for almost all binary information systems. Fundamenta Informaticae 80(1-3), 247–258 (2007)
Moshkov, M.J., Skowron, A., Suraj, Z.: On minimal inhibitory rules for almost all k-valued information systems. Fundamenta Informaticae 93(1-3), 261–272 (2009)
Moshkov, M., Zielosko, B.: Combinatorial Machine Learning - A Rough Set Approach. SCI, vol. 360. Springer, Heidelberg (2011)
Nakamura, A.: Fuzzy quantifiers and rough quantifiers. In: Wang, P.P. (ed.) Advances in Fuzzy Theory and Technology II, pp. 111–131. Duke University Press, Durham (1994)
Nakamura, A.: On a logic of information for reasoning about knowledge. In: Ziarko [322], pp. 186–195
Nakamura, A.: A rough logic based on incomplete information and its application. International Journal of Approximate Reasoning 15(4), 367–378 (1996)
Nguyen, H.S.: Efficient SQL-learning method for data mining in large data bases. In: Dean, T. (ed.) Sixteenth International Joint Conference on Artificial Intelligence, IJCAI, pp. 806–811. Morgan-Kaufmann Publishers, Stockholm (1999)
Nguyen, H.S.: On efficient handling of continuous attributes in large data bases. Fundamenta Informaticae 48(1), 61–81 (2001)
Nguyen, H.S.: Approximate boolean reasoning approach to rough sets and data mining. In: Ślęzak, et al. [263], pp. 12–22 (plenary talk)
Nguyen, H.S.: Approximate boolean reasoning: Foundations and applications in data mining. In: Peters, Skowron [180], pp. 344–523
Nguyen, H.S., Jankowski, A., Skowron, A., Stepaniuk, J., Szczuka, M.: Discovery of process models from data and domain knowledge: A rough-granular approach. In: Yao, J.T. (ed.) Novel Developments in Granular Computing: Applications for Advanced Human Reasoning and Soft Computation, pp. 16–47. IGI Global, Hershey (2010)
Nguyen, H.S., Nguyen, S.H.: Rough sets and association rule generation. Fundamenta Informaticae 40(4), 383–405 (1999)
Nguyen, H.S., Skowron, A.: A rough granular computing in discovery of process models from data and domain knowledge. Journal of Chongqing University of Post and Telecommunications 20(3), 341–347 (2008)
Nguyen, H.S., Ślęzak, D.: Approximate reducts and association rules - correspondence and complexity results. In: Skowron, et al. [234], pp. 137–145
Nguyen, S.H., Bazan, J., Skowron, A., Nguyen, H.S.: Layered learning for concept synthesis. In: Peters, Skowron [185], pp. 187–208
Nguyen, S.H., Nguyen, H.S.: Some efficient algorithms for rough set methods. In: Sixth International Conference on Information Processing and Management of Uncertainty on Knowledge Based Systems, IPMU 1996, Granada, Spain, vol. III, pp. 1451–1456 (1996)
Nguyen, T.T.: Eliciting domain knowledge in handwritten digit recognition. In: Pal, et al. [149], pp. 762–767
Nguyen, T.T., Skowron, A.: Rough set approach to domain knowledge approximation. In: Wang, et al. [303], pp. 221–228
Nguyen, T.T., Skowron, A.: Rough-granular computing in human-centric information processing. In: Bargiela, A., Pedrycz, W. (eds.) Human-Centric Information Processing Through Granular Modelling. SCI, vol. 182, pp. 1–30. Springer, Heidelberg (2009)
Noë, A.: Action in Perception. MIT Press (2004)
Omicini, A., Ricci, A., Viroli, M.: The multidisciplinary patterns of interaction from sciences to computer science. In: Goldin, et al. [55], pp. 395–414
Orłowska, E.: Semantics of vague concepts. In: Dorn, G., Weingartner, P. (eds.) Foundation of Logic and Linguistics, pp. 465–482. Plenum Press, New York (1984)
Orłowska, E.: Rough concept logic. In: Skowron [224], pp. 177–186
Orłowska, E.: Reasoning about vague concepts. Bulletin of the Polish Academy of Sciences, Mathematics 35, 643–652 (1987)
Orłowska, E.: Logic for reasoning about knowledge. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 35, 559–572 (1989)
Orłowska, E.: Kripke semantics for knowledge representation logics. Studia Logica 49(2), 255–272 (1990)
Orłowska, E. (ed.): Incomplete Information: Rough Set Analysis. STUDFUZZ, vol. 13. Springer/Physica-Verlag, Heidelberg (1997)
Orłowska, E., Pawlak, Z.: Representation of non-deterministic information. Theoretical Computer Science 29, 27–39 (1984)
Orłowska, E., Peters, J.F., Rozenberg, G., Skowron, A.: Special volume dedicated to the memory of Zdzisław Pawlak. Fundamenta Informaticae 75(1-4) (2007)
Pal, S.: Computational theory perception (CTP), rough-fuzzy uncertainty analysis and mining in bioinformatics and web intelligence: A unified framework. In: Peters, Skowron [182], pp. 106–129
Pal, S.K., Bandyopadhyay, S., Biswas, S. (eds.): PReMI 2005. LNCS, vol. 3776. Springer, Heidelberg (2005)
Pal, S.K., Mitra, P.: Pattern Recognition Algorithms for Data Mining. CRC Press, Boca Raton (2004)
Pal, S.K., Pedrycz, W., Skowron, A., Swiniarski, R.: Special volume: Rough-neuro computing. Neurocomputing 36 (2001)
Pal, S.K., Peters, J.F. (eds.): Rough Fuzzy Image Analysis Foundations and Methodologies. Chapman & Hall/CRC, Boca Raton, Fl (2010)
Pal, S.K., Polkowski, L., Skowron, A. (eds.): Rough-Neural Computing: Techniques for Computing with Words. Cognitive Technologies. Springer, Heidelberg (2004)
Pal, S.K., Skowron, A. (eds.): Rough Fuzzy Hybridization: A New Trend in Decision-Making. Springer, Singapore (1999)
Pancerz, K., Suraj, Z.: Modelling concurrent systems specified by dynamic information systems: A rough set approach. Electronic Notes in Theoretical Computer Science 82(4), 206–218 (2003)
Pancerz, K., Suraj, Z.: Discovering concurrent models from data tables with the ROSECON system. Fundamenta Informaticae 60(1-4), 251–268 (2004)
Pancerz, K., Suraj, Z.: Discovering concurrent models from data tables with the ROSECON system. Fundamenta Informaticae 60(1-4), 251–268 (2004)
Pancerz, K., Suraj, Z.: Discovery of asynchronous concurrent models from experimental tables. Fundamenta Informaticae 61(2), 97–116 (2004)
Pancerz, K., Suraj, Z.: Restriction-based concurrent system design using the rough set formalism. Fundamenta Informaticae 67(1-3), 233–247 (2005)
Pancerz, K., Suraj, Z.: Reconstruction of concurrent system models described by decomposed data tables. Fundamenta Informaticae 71(1), 121–137 (2006)
Pancerz, K., Suraj, Z.: Towards efficient computing consistent and partially consistent extensions of information systems. Fundamenta Informaticae 79(3-4), 553–566 (2007)
Papageorgiou, E.I., Stylios, C.D.: Fuzzy cognitive maps. In: Pedrycz, et al. [176], pp. 755–774
Pawlak, Z.: Classification of Objects by Means of Attributes, Reports, vol. 429, Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland (1981)
Pawlak, Z.: Information systems - theoretical foundations. Information Systems 6, 205–218 (1981)
Pawlak, Z.: Rough Relations, Reports, vol. 435. Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland (1981)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Rough logic. Bulletin of the Polish Academy of Sciences, Technical Sciences 35(5-6), 253–258 (1987)
Pawlak, Z.: Decision logic. Bulletin of the EATCS 44, 201–225 (1991)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. In: System Theory, Knowledge Engineering and Problem Solving, vol. 9. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z.: Concurrent versus sequential - the rough sets perspective. Bulletin of the EATCS 48, 178–190 (1992)
Pawlak, Z.: Decision rules, Bayes’ rule and rough sets. In: Skowron, et al. [234], pp. 1–9
Pawlak, Z., Skowron, A.: Rough membership functions. In: Yager, R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer Theory of Evidence, pp. 251–271. John Wiley & Sons, New York (1994)
Pawlak, Z., Skowron, A.: Rough sets and boolean reasoning. Information Sciences 177(1), 41–73 (2007)
Pawlak, Z., Skowron, A.: Rough sets: Some extensions. Information Sciences 177(28-40), 1 (2007)
Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Sciences 177(1), 3–27 (2007)
Pedrycz, W., Skowron, S., Kreinovich, V. (eds.): Handbook of Granular Computing. John Wiley & Sons, Hoboken (2008)
Peters, J., Skowron, A.: Special issue on a rough set approach to reasoning about data. International Journal of Intelligent Systems 16(1) (2001)
Peters, J.F., Skowron, A. (eds.): Transactions on Rough Sets III. LNCS, vol. 3400. Springer, Heidelberg (2005)
Peters, J.F., Skowron, A. (eds.): Transactions on Rough Sets IV. LNCS, vol. 3700. Springer, Heidelberg (2005)
Peters, J.F., Skowron, A. (eds.): Transactions on Rough Sets V. LNCS, vol. 4100. Springer, Heidelberg (2006)
Peters, J.F., Skowron, A. (eds.): Transactions on Rough Sets VIII. LNCS, vol. 5084. Springer, Heidelberg (2008)
Peters, J.F., Skowron, A. (eds.): Transactions on Rough Sets XI. LNCS, vol. 5946. Springer, Heidelberg (2010)
Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds.): Transactions on Rough Sets II. LNCS, vol. 3135. Springer, Heidelberg (2004)
Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J.W., Orłowska, E., Polkowski, L. (eds.): Transactions on Rough Sets VI. LNCS, vol. 4374. Springer, Heidelberg (2007)
Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M.S. (eds.): Transactions on Rough Sets I. LNCS, vol. 3100. Springer, Heidelberg (2004)
Peters, J.F., Skowron, A., Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.): Transactions on Rough Sets XIII. LNCS, vol. 6499. Springer, Heidelberg (2011)
Peters, J.F., Skowron, A., Marek, V.W., Orłowska, E., Słowiński, R., Ziarko, W.P. (eds.): Transactions on Rough Sets VII. LNCS, vol. 4400. Springer, Heidelberg (2007)
Peters, J.F., Skowron, A., Rybiński, H. (eds.): Transactions on Rough Sets IX. LNCS, vol. 5390. Springer, Heidelberg (2008)
Peters, J.F., Skowron, A., Sakai, H., Chakraborty, M.K., Ślęzak, D., Hassanien, A.E., Zhu, W.: Transactions on Rough Sets XIV. LNCS, vol. 6600. Springer, Heidelberg (2011)
Peters, J.F., Skowron, A., Słowiński, R., Lingras, P., Miao, D., Tsumoto, S. (eds.): Transactions on Rough Sets XII. LNCS, vol. 6190. Springer, Heidelberg (2010)
Peters, J.F., Skowron, A., Suraj, Z.: An application of rough set methods in control design. Fundamenta Informaticae 43(1-4), 269–290 (2000)
Peters, J.F., Skowron, A., Suraj, Z.: An application of rough set methods in control design. Fundamenta Informaticae 43(1-4), 269–290 (2000)
Peters, J.F., Skowron, A., Wolski, M., Chakraborty, M.K., Wu, W.-Z. (eds.): Transactions on Rough Sets X. LNCS, vol. 5656. Springer, Heidelberg (2009)
Pindur, R., Susmaga, R., Stefanowski, J.: Hyperplane aggregation of dominance decision rules. Fundamenta Informaticae 61(2), 117–137 (2004)
Poggio, T., Smale, S.: The mathematics of learning: Dealing with data. Notices of the AMS 50(5), 537–544 (2003)
Polkowski, L.: Rough Sets: Mathematical Foundations. Advances in Soft Computing. Physica-Verlag, Heidelberg (2002)
Polkowski, L.: Rough mereology: A rough set paradigm for unifying rough set theory and fuzzy set theory. Fundamenta Informaticae 54, 67–88 (2003)
Polkowski, L.: A note on 3-valued rough logic accepting decision rules. Fundamenta Informaticae 61(1), 37–45 (2004)
Polkowski, L.: Approximate Reasoning by Parts. An Introduction to Rough Mereology. ISRL, vol. 20. Springer, Heidelberg (2011)
Polkowski, L., Lin, T.Y., Tsumoto, S. (eds.): Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems. STUDFUZZ, vol. 56. Springer/Physica-Verlag, Heidelberg (2000)
Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning. International Journal of Approximate Reasoning 15(4), 333–365 (1996)
Polkowski, L., Skowron, A. (eds.): RSCTC 1998. LNCS (LNAI), vol. 1424. Springer, Heidelberg (1998)
Polkowski, L., Skowron, A. (eds.): Rough Sets in Knowledge Discovery 1: Methodology and Applications. STUDFUZZ, vol. 18. Physica-Verlag, Heidelberg (1998)
Polkowski, L., Skowron, A. (eds.): Rough Sets in Knowledge Discovery 2: Applications, Case Studies and Software Systems. STUDFUZZ, vol. 19. Physica-Verlag, Heidelberg (1998)
Polkowski, L., Skowron, A.: Towards adaptive calculus of granules. In: Zadeh, L.A., Kacprzyk, J. (eds.) Computing with Words in Information/Intelligent Systems, pp. 201–227. Physica-Verlag, Heidelberg (1999)
Polkowski, L., Skowron, A.: Rough mereological calculi of granules: A rough set approach to computation. Computational Intelligence: An International Journal 17(3), 472–492 (2001)
Polkowski, L., Skowron, A., Żytkow, J.: Rough foundations for rough sets. In: Lin, Wildberger [104], pp. 55–58
Ramsay, J.O., Silverman, B.W.: Applied Functional Data Analysis. Springer, Berlin (2002)
Rasiowa, H.: Axiomatization and completeness of uncountably valued approximation logic. Studia Logica 53(1), 137–160 (1994)
Rasiowa, H., Skowron, A.: Approximation logic. In: Bibel, W., Jantke, K.P. (eds.) Mathematical Methods of Specification and Synthesis of Software Systems. Mathematical Research, vol. 31, pp. 123–139. Akademie Verlag, Berlin (1985)
Rasiowa, H., Skowron, A.: Rough concept logic. In: Skowron [224], pp. 288–297
Rauszer, C.: An equivalence between indiscernibility relations in information systems and a fragment of intuitionistic logic. In: Skowron [224], pp. 298–317
Rauszer, C.: An equivalence between theory of functional dependence and a fragment of intuitionistic logic. Bulletin of the Polish Academy of Sciences, Mathematics 33, 571–579 (1985)
Rauszer, C.: Logic for information systems. Fundamenta Informaticae 16, 371–382 (1992)
Rauszer, C.: Knowledge representation systems for groups of agents. In: Wroński, J. (ed.) Philosophical Logic in Poland, pp. 217–238. Kluwer, Dordrecht (1994)
Read, S.: Thinking about Logic: An Introduction to the Philosophy of Logic. Oxford University Press, Oxford (1994)
Rissanen, J.: Modeling by shortes data description. Automatica 14, 465–471 (1978)
Rissanen, J.: Minimum-description-length principle. In: Kotz, S., Johnson, N. (eds.) Encyclopedia of Statistical Sciences, pp. 523–527. John Wiley & Sons, New York (1985)
Roddick, J., Hornsby, K.S., Spiliopoulou, M.: An Updated Bibliography of Temporal, Spatial, and Spatio-temporal Data Mining Research. In: Roddick, J., Hornsby, K.S. (eds.) TSDM 2000. LNCS (LNAI), vol. 2007, pp. 147–164. Springer, Heidelberg (2001)
Russell, B.: An Inquiry into Meaning and Truth. George Allen & Unwin Ltd. and W. W. Norton, London and New York (1940)
Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds.): RSFDGrC 2009. LNCS, vol. 5908. Springer, Heidelberg (2009)
Serafini, L., Bouquet, P.: Comparing formal theories of context in ai. Artificial Intelligence 155, 41–67 (2004)
Skowron, A.: Rough Sets in Perception-Based Computing (keynote talk). In: Pal, S.K., Bandyopadhyay, S., Biswas, S. (eds.) PReMI 2005. LNCS, vol. 3776, pp. 21–29. Springer, Heidelberg (2005)
Skowron, A. (ed.): SCT 1984. LNCS, vol. 208. Springer, Heidelberg (1985)
Skowron, A.: Boolean Reasoning for Decision Rules Generation. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689, pp. 295–305. Springer, Heidelberg (1993)
Skowron, A.: Extracting laws from decision tables. Computational Intelligence: An International Journal 11, 371–388 (1995)
Skowron, A.: Rough sets in KDD - plenary talk. In: Shi, Z., Faltings, B., Musen, M. (eds.) 16th World Computer Congress (IFIP 2000): Proceedings of Conference on Intelligent Information Processing (IIP 2000), pp. 1–14. Publishing House of Electronic Industry, Beijing (2000)
Skowron, A.: Approximate reasoning by agents in distributed environments. In: Zhong, N., Liu, J., Ohsuga, S., Bradshaw, J. (eds.) Intelligent Agent Technology Research and Development: Proceedings of the 2nd Asia-Pacific Conference on Intelligent Agent Technology, IAT 2001, Maebashi, Japan, October 23-26, pp. 28–39. World Scientific, Singapore (2001)
Skowron, A.: Toward intelligent systems: Calculi of information granules. Bulletin of the International Rough Set Society 5(1-2), 9–30 (2001)
Skowron, A.: Approximate reasoning in distributed environments. In: Zhong, Liu [319], pp. 433–474
Skowron, A.: Perception logic in intelligent systems (keynote talk). In: Blair, S., et al. (eds.) Proceedings of the 8th Joint Conference on Information Sciences (JCIS 2005), Salt Lake City, Utah, July 21-26, pp. 1–5. X-CD Technologies: A Conference & Management Company, Toronto (2005)
Skowron, A.: Rough sets and vague concepts. Fundamenta Informaticae 64(1-4), 417–431 (2005)
Skowron, A., Grzymała-Busse, J.W.: From rough set theory to evidence theory. In: Yager, R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer Theory of Evidence, pp. 193–236. John Wiley & Sons, New York (1994)
Skowron, A., Ohsuga, S., Zhong, N. (eds.): RSFDGrC 1999. LNCS (LNAI), vol. 1711. Springer, Heidelberg (1999)
Skowron, A., Pal, S.K.: Special volume: Rough sets, pattern recognition and data mining. Pattern Recognition Letters 24(6) (2003)
Skowron, A., Pal, S.K., Nguyen, H.S.: Special issue: Rough sets and fuzzy sets in natural computing. Theoretical Computer Science 412(42) (2011)
Skowron, A., Peters, J.: Rough sets: Trends and challenges. In: Wang, et al. [303], pp. 25–34 (plenary talk)
Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Słowiński [266], pp. 331–362
Skowron, A., Stepaniuk, J.: Generalized approximation spaces. In: The Third International Workshop on Rough Sets and Soft Computing Proceedings (RSSC 1994), San Jose, California, USA, November 10-12, pp. 156–163 (1994)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27(2-3), 245–253 (1996)
Skowron, A., Stepaniuk, J.: Information granules: Towards foundations of granular computing. International Journal of Intelligent Systems 16(1), 57–86 (2001)
Skowron, A., Stepaniuk, J.: Information granules and rough-neural computing. In: Pal, et al. [153], pp. 43–84
Skowron, A., Stepaniuk, J.: Ontological framework for approximation. In: Ślęzak, et al. [262], pp. 718–727
Skowron, A., Stepaniuk, J.: Approximation spaces in rough-granular computing. Fundamenta Informaticae 100, 141–157 (2010)
Skowron, A., Stepaniuk, J., Peters, J., Swiniarski, R.: Calculi of approximation spaces. Fundamenta Informaticae 72, 363–378 (2006)
Skowron, A., Stepaniuk, J., Swiniarski, R.: Modeling rough granular computing based on approximation spaces. Information Sciences 184, 20–43 (2012)
Skowron, A., Suraj, Z.: A rough set approach to real-time state identification. Bulletin of the EATCS 50, 264–275 (1993)
Skowron, A., Suraj, Z.: Rough sets and concurrency. Bulletin of the Polish Academy of Sciences, Technical Sciences 41, 237–254 (1993)
Skowron, A., Suraj, Z.: Discovery of concurrent data models from experimental tables: A rough set approach. In: Proceedings of the First International Conference on Knowledge Discovery and Data Mining (KDD 1995), Montreal, Canada, August 20-21, pp. 288–293. AAAI Press, Menlo Park (1995)
Skowron, A., Swiniarski, R.: Rough sets and higher order vagueness. In: Ślęzak, et al. [262], pp. 33–42
Skowron, A., Swiniarski, R., Synak, P.: Approximation spaces and information granulation. In: Peters, Skowron [178], pp. 175–189
Skowron, A., Synak, P.: Complex patterns. Fundamenta Informaticae 60(1-4), 351–366 (2004)
Skowron, A., Szczuka, M. (eds.): Proceedings of the Workshop on Rough Sets in Knowledge Discovery and Soft Computing at ETAPS 2003, April 12-13. Electronic Notes in Computer Science, vol. 82(4). Elsevier, Amsterdam (2003), www.elsevier.nl/locate/entcs/volume82.html
Skowron, A., Szczuka, M.: Toward Interactive Computations: A Rough-Granular Approach. In: Koronacki, J., Raś, Z.W., Wierzchoń, S.T., Kacprzyk, J. (eds.) Advances in Machine Learning II. SCI, vol. 263, pp. 23–42. Springer, Heidelberg (2010)
Skowron, A., Wasilewski, P.: Information systems in modeling interactive computations on granules. Theoretical Computer Science 412(42), 5939–5959 (2011)
Skowron, A., Wasilewski, P.: Toward interactive rough-granular computing. Control & Cybernetics 40(2), 1–23 (2011)
Ślęzak, D.: Approximate reducts in decision tables. In: Sixth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 1996, vol. III, pp. 1159–1164. Granada, Spain (1996)
Ślęzak, D.: Normalized decision functions and measures for inconsistent decision tables analysis. Fundamenta Informaticae 44, 291–319 (2000)
Ślęzak, D.: Various approaches to reasoning with frequency-based decision reducts: A survey. In: Polkowski, et al. [200], pp. 235–285
Ślęzak, D.: Approximate entropy reducts. Fundamenta Informaticae 53, 365–387 (2002)
Ślęzak, D.: Rough sets and Bayes factor. In: Peters, Skowron [178], pp. 202–229
Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.): RSFDGrC 2005, Part I. LNCS (LNAI), vol. 3641. Springer, Heidelberg (2005)
Ślęzak, D., Yao, J., Peters, J.F., Ziarko, W.P., Hu, X. (eds.): RSFDGrC 2005, Part II. LNCS (LNAI), vol. 3642. Springer, Heidelberg (2005)
Ślęzak, D., Ziarko, W.: The investigation of the Bayesian rough set model. International Journal of Approximate Reasoning 40, 81–91 (2005)
Słowiński, R.: New Applications and Theoretical Foundations of the Dominance-based Rough Set Approach. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds.) RSCTC 2010. LNCS, vol. 6086, pp. 2–3. Springer, Heidelberg (2010)
Słowiński, R. (ed.): Intelligent Decision Support - Handbook of Applications and Advances of the Rough Sets Theory. System Theory, Knowledge Engineering and Problem Solving, vol. 11. Kluwer Academic Publishers, Dordrecht (1992)
Słowiński, R., Greco, S., Matarazzo, B.: Rough set analysis of preference-ordered data. In: Alpigini, et al. [2], pp. 44–59
Słowiński, R., Stefanowski, J. (eds.): Special issue: Proceedings of the First International Workshop on Rough Sets: State of the Art and Perspectives, Kiekrz, Poznań, Poland, September 2-4 (1992); Foundations of Computing and Decision Sciences 18(3-4) (1993)
Sowa, J.F.: Knowledge Representation: Logical, Philosophical, and Computational Foundations. Brooks Cole Publishing Co. (2000)
Staab, S., Studer, R. (eds.): Handbook on Ontologies. International Handbooks on Information Systems. Springer, Heidelberg (2004)
Stepaniuk, J.: Approximation spaces, reducts and representatives. In: Polkowski, Skowron [204], pp. 109–126
Stepaniuk, J. (ed.): Rough-Granular Computing in Knowledge Discovery and Data Mining. Springer, Heidelberg (2008)
Stone, P.: Layered Learning in Multi-Agent Systems: A Winning Approach to Robotic Soccer. The MIT Press, Cambridge (2000)
Strąkowski, T., Rybiński, H.: A new approach to distributed algorithms for reduct calculation. In: Peters, Skowron [188], pp. 365–378
Suraj, Z.: Discovery of concurrent data models from experimental tables: A rough set approach. Fundamenta Informaticae 28(3-4), 353–376 (1996)
Suraj, Z.: Rough set methods for the synthesis and analysis of concurrent processes. In: Polkowski, et al. [200], pp. 379–488
Suraj, Z.: Discovering concurrent process models in data: A rough set approach. In: Sakai, et al. [221], pp. 12–19
Suraj, Z., Pancerz, K.: A synthesis of concurrent systems: A rough set approach. In: Wang, et al. [303], pp. 299–302
Suraj, Z., Pancerz, K.: The rosecon system - a computer tool for modelling and analysing of processes. In: 2005 International Conference on Computational Intelligence for Modelling Control and Automation (CIMCA 2005), International Conference on Intelligent Agents, Web Technologies and Internet Commerce (IAWTIC 2005), Vienna, Austria, November 28-30, pp. 829–834. IEEE Computer Society (2005)
Suraj, Z., Pancerz, K.: Some remarks on computing consistent extensions of dynamic information systems. In: Proceedings of the Fifth International Conference on Intelligent Systems Design and Applications (ISDA 2005), Wrocław, Poland, September 8-10, pp. 420–425. IEEE Computer Society (2005)
Suraj, Z., Pancerz, K., Owsiany, G.: On consistent and partially consistent extensions of information systems. In: Ślęzak et al. [262], pp. 224–233
Swift, J.: Gulliver’s Travels into Several Remote Nations of the World (ananymous publisher), London, M, DCC, XXVI (1726)
Swiniarski, R.W., Pancerz, K., Suraj, Z.: Prediction of model changes of concurrent systems described by temporal information systems. In: Proceedings of The 2005 International Conference on Data Mining (DMIN 2005), Las Vegas, Nevada, USA, June 20-23, pp. 51–57. CSREA Press (2005)
Sycara, K.: Multiagent systems. AI Magazine, 79–92 (Summer 1998)
Szczuka, M., Skowron, A., Stepaniuk, J.: Function approximation and quality measures in rough-granular systems. Fundamenta Informaticae 109(3-4), 339–354 (2011)
Szczuka, M.S., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds.): RSCTC 2010. LNCS, vol. 6086. Springer, Heidelberg (2010)
Tarski, A.: Logic, Semantics, Metamathematics. Oxford University Press, Oxford (1983) [translated by J. H. Woodger]
Taylor, G.W., Fergus, R., LeCun, Y., Bregler, C.: Convolutional Learning of Spatio-Temporal Features. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6316, pp. 140–153. Springer, Heidelberg (2010)
Terano, T., Nishida, T., Namatame, A., Tsumoto, S., Ohsawa, Y., Washio, T. (eds.): JSAI-WS 2001. LNCS (LNAI), vol. 2253. Springer, Heidelberg (2001)
Torra, V., Narukawa, Y.: Modeling Decisions Information Fusion and Aggregation Operators. Springer (2007)
Tsumoto, S., Kobayashi, S., Yokomori, T., Tanaka, H., Nakamura, A. (eds.): Proceedings of the The Fourth International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery, November 6-8. University of Tokyo, Tokyo (1996)
Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.): RSCTC 2004. LNCS (LNAI), vol. 3066. Springer, Heidelberg (2004)
Tsumoto, S., Tanaka, H.: PRIMEROSE: Probabilistic rule induction method based on rough sets and resampling methods. Computational Intelligence: An International Journal 11, 389–405 (1995)
Unnikrishnan, K.P., Ramakrishnan, N., Sastry, P.S., Uthurusamy, R.: Network reconstruction from dynamic data. SIGKDD Explorations 8(2), 90–91 (2006)
Vakarelov, D.: A modal logic for similarity relations in Pawlak knowledge representation systems. Fundamenta Informaticae 15(1), 61–79 (1991)
Vakarelov, D.: Modal logics for knowledge representation systems. Theoretical Computer Science 90(2), 433–456 (1991)
Vakarelov, D.: A duality between Pawlak’s knowledge representation systems and bi-consequence systems. Studia Logica 55(1), 205–228 (1995)
Vakarelov, D.: A modal characterization of indiscernibility and similarity relations in Pawlak’s information systems. In: Ślęzak et al. [262], pp. 12–22 (plenary talk)
van der Aalst, W.M.P. (ed.): Process Mining Discovery, Conformance and Enhancement of Business Processes. Springer, Heidelberg (2011)
Vapnik, V.: Statistical Learning Theory. John Wiley & Sons, New York (1998)
Vitória, A.: A framework for reasoning with rough sets. Licentiate Thesis, Linköping University 2004. In: Peters, Skowron [179], pp. 178–276
Wang, G., Li, T.R., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.): RSKT 2008. LNCS (LNAI), vol. 5009. Springer, Heidelberg (2008)
Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.): RSFDGrC 2003. LNCS (LNAI), vol. 2639. Springer, Heidelberg (2003)
Wang, G.-Y., Peters, J.F., Skowron, A., Yao, Y. (eds.): RSKT 2006. LNCS (LNAI), vol. 4062. Springer, Heidelberg (2006)
Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds.): RSKT 2009. LNCS, vol. 5589. Springer, Heidelberg (2009)
Wong, S.K.M., Ziarko, W.: Comparison of the probabilistic approximate classification and the fuzzy model. Fuzzy Sets and Systems 21, 357–362 (1987)
Wróblewski, J.: Theoretical foundations of order-based genetic algorithms. Fundamenta Informaticae 28, 423–430 (1996)
Wu, F.X.: Inference of gene regulatory networks and its validation. Current Bioinformatics 2(2), 139–144 (2007)
Yao, J., Lingras, P., Wu, W.-Z., Szczuka, M.S., Cercone, N.J., Ślęzak, D. (eds.): RSKT 2007. LNCS (LNAI), vol. 4481. Springer, Heidelberg (2007)
Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.): RSKT 2011. LNCS, vol. 6954. Springer, Heidelberg (2011)
Yao, Y.Y.: Generalized rough set models. In: Polkowski, Skowron [203], pp. 286–318
Yao, Y.Y.: Information granulation and rough set approximation. International Journal of Intelligent Systems 16, 87–104 (2001)
Yao, Y.Y.: On generalizing rough set theory. In: Wang, et al. [303], pp. 44–51
Yao, Y.Y.: Probabilistic approaches to rough sets. Expert Systems 20, 287–297 (2003)
Yao, Y.Y., Wong, S.K.M., Lin, T.Y.: A review of rough set models. In: Lin, Cercone [103], pp. 47–75
Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds.): RSKT 2010. LNCS, vol. 6401. Springer, Heidelberg (2010)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Zadeh, L.A.: A new direction in AI: Toward a computational theory of perceptions. AI Magazine 22(1), 73–84 (2001)
Zhong, N., Liu, J. (eds.): Intelligent Technologies for Information Analysis. Springer, Heidelberg (2004)
Zhu, W.: Topological approaches to covering rough sets. Information Sciences 177, 1499–1508 (2007)
Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46, 39–59 (1993)
Ziarko, W. (ed.): Rough Sets, Fuzzy Sets and Knowledge Discovery: Proceedings of the Second International Workshop on Rough Sets and Knowledge Discovery (RSKD 1993), Banff, Alberta, Canada, October 12-15 (1993); Workshops in Computing. Springer & British Computer Society, London, Berlin (1994)
Ziarko, W.: Special issue, Computational Intelligence: An International Journal 11(2) (1995)
Ziarko, W.: Special issue, Fundamenta Informaticae 27(2-3) (1996)
Ziarko, W.: Probabilistic decision tables in the variable precision rough set model. Computational Intelligence 17, 593–603 (2001)
Ziarko, W.P., Yao, Y. (eds.): RSCTC 2000. LNCS (LNAI), vol. 2005. Springer, Heidelberg (2001)
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Chikalov, I. et al. (2013). Rough Sets. In: Three Approaches to Data Analysis. Intelligent Systems Reference Library, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28667-4_2
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