Abstract
This article presents some general remarks on rough sets and their place in general picture of research on vagueness and uncertainty – concepts of utmost interest, for many years, for philosophers, mathematicians, logicians and recently also for computer scientists and engineers particularly those working in such areas as AI, computational intelligence, intelligent systems, cognitive science, data mining and machine learning. Thus this article is intended to present some philosophical observations rather than to consider technical details or applications of rough set theory. Therefore we also refrain from presentation of many interesting applications and some generalizations of the theory.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Apostoli, P., Kanda, A.: Parts of the Continuum: Towards a Modern Ontology of Sciences. Technical Reports in Philosophical Logic 96,97(1), Revised March, The University of Toronto, Department of Philosophy (1999)
Banerjee, M., Chakraborty, M.K.: Rough Consequence and Rough Algebra. In: Ziarko, W.P. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, Proc. Int. Workshop on Rough Sets and Knowledge Discovery (RSKD 1993), Workshops in Computing, pp. 196–207. Springer-Verlag & British Computer Society (1993)
Banerjee, M., Chakraborty, M.K.: Algebras from Rough Sets. In: [27], pp. 157–188 (2004)
Banerjee, M.: Rough truth, consequence, consistency and belief revision. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W., et al. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 95–102. Springer, Heidelberg (2004)
Bazan, J.G., Peters, J.F., Skowron, A.: Behavioral pattern identification through rough set modelling. In: Ślęzak, D., Yao, J., Peters, J.F., Ziarko, W.P., Hu, X. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3642, pp. 688–697. Springer, Heidelberg (2005)
Chakraborty, M.K., Banerjee, M.: Rough Consequence. Bull. Polish Acad. Sc (Math.) 41(4), 299–304 (1993)
Breiman, L.: Statistical Modeling: The Two Cultures. Statistical Science 16(3), 199–231 (2001)
Cantor, G.: Grundlagen einer allgemeinen Mannigfaltigkeitslehre. Leipzig (1883)
Casati, R., Varzi, A.: Parts and Places. In: The Structures of Spatial Representation. MIT Press, Bradford Books (1999)
Doherty, P., Łukaszewicz, W., Skowron, A., Szałas, A.: Knowledge Engineering: A Rough Set Approach. Springer, Heidelberg (2005) (to appear)
Dubois, D., Prade, H.: Foreword. In: Pawlak, Z. (ed.) Rough Sets, Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Frege, G.: Grundlagen der Arithmetik, vol. 2. Verlag von Herman Pohle, Jena (1893)
Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.): Handbook of Logic in Aretificial Intelligence and Logic Programming: Nonmonotonic Reasoning and Uncertain Reasoning, vol. 3. Calderon Press, Oxford (1994)
Greco, S., Matarazzo, B., Słowiński, R.: Rough Set Theory for Multicriteria Decision Analysis. European Journal of Operational Research 129(1), 1–47 (2001)
Grzymała-Busse, J.W.: Managing Uncertainty in Expert Systems. Kluwer Academic Publishers, Norwell (1990)
Friedman, J., Hastie, T., Tibshirani, R.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, Heidelberg (2001)
Keefe, R.: Theories of Vagueness. Cambridge Studies in Philosophy, Cambridge (2000)
Keefe, R., Smith, P. (eds.): Vagueness: A Reader. MIT Press, Massachusetts (1997)
Leśniewski, S.: Grungzüge eines neuen Systems der Grundlagen der Mathematik. Fundamenta Matemaicae 14, 1–81 (1929)
Łukasiewicz, J.: Die Logischen grundlagen der Wahrscheinlichkeitsrechnung. Kraków. In: Borkowski, L. (ed.) Jan Łukasiewicz - Selected Works, North Holland Publishing Company, Polish Scientific Publishers (1913/1970)
Marcus, S.: The paradox of the heap of grains in respect to roughness, fuzziness and negligibility. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 19–23. Springer, Heidelberg (1998)
Nguyen, S.H., Bazan, J.G., Skowron, A., Nguyen, H.S.: Layered learning for concept synthesis. In: 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, pp. 187–208. Springer, Heidelberg (2004)
Orłowska, E.: Semantics of Vague Conepts. In: Dorn, G., Weingartner, P. (eds.) Foundation of Logic and Linguistics, pp. 465–482. Plenum Press, New York (1984)
Orłowska, E.: Reasoning about Vague Concepts. Bull. Polish Acad. Sci. Math. 35, 643–652 (1987)
Pal, S.K., Skowron, A.: Rough Fuzzy Hybridization: A New Trend in Decision-Making. Springer, Singapore (1999)
Pal, S.K., Mitra, P.: Pattern Recognition Algorithms for Data Mining. CRC Press, Boca Raton (2004)
Pal, S.K., Polkowski, L., Skowron, A. (eds.): Rough-Neural Computing: Techniques for Computing with Words. Springer, Heidelberg (2004)
Pawlak, Z.: Rough Sets. Int. J. of Information and Computer Sciences 11(5), 341–356 (1982)
Pawlak, Z.: Rough Logic. Bull. Polish. Acad. Sci. Tech. 35(5-6), 253–258 (1987)
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., Skowron, A.: Rough Membership Functions. In: Yager, R.R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Schafer Theory of Evidence, pp. 251–271. John Wiley and Sons, New York (1994)
Peters, J.F., Skowron, A., Synak, P., Ramanna, S.: Rough Sets and Information Granulation. In: De Baets, B., Kaynak, O., Bilgiç, T. (eds.) IFSA 2003. LNCS, vol. 2715, pp. 370–377. Springer, Heidelberg (2003)
Polkowski, L.: Rough Sets: Mathematical Foundations. Physica, Heidelberg (2002)
Polkowski, L., Skowron, A.: Rough Mereology: A New Paradigm for Approximate Reasoning. International Journal of Approximate Reasoning 15, 333–365 (1996)
Polkowski, L., Skowron, A.: Rough Mereological Calculi of Granules: A Rough Set Approach to Computation. Computational Intelligence 17, 472–492 (2001)
Read, S.: Thinking about Logic. An Introduction to the Philosophy of Logic. Oxford University Press, Oxford (1995)
Russell, B.: The Principles of Mathematics, 1st edn. George Allen & Unwin Ltd., London (1903) (2nd edn. in 1937)
Russell, B.: An Inquiry into Meaning and Truth. George Allen and Unwin, London (1940)
Skowron, A.: Rough Sets in KDD (plenary lecture). In: Shi, Z., Faltings, B., Musen, M. (eds.) 16-th World Computer Congress (IFIP 2000): Proceedings of Conference on Intelligent Information Processing (IIP 2000), pp. 1–17. Publishing House of Electronic Industry, Beijing (2000)
Skowron, A.: Approximate Reasoning in Distributed Environments. In: Zhong, N., Liu, J. (eds.) Intelligent Technologies for Information Analysis, pp. 433–474. Springer, Heidelberg (2004)
Skowron, A.: Rough Sets and Vague Concepts. Fundamenta Informaticae 64(1-4), 417–431 (2005)
Skowron, A., Stepaniuk, J.: Tolerance Approximation Spaces. Fundamenta Informaticae 27(2-3), 245–253 (1996)
Skowron, A., Peters, J.: Rough Sets: Trends and Challenges (plenary talk). In: Wang, G., Liu, Q., Yao, Y.Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 25–34. Springer, Heidelberg (2003)
Skowron, A., Świniarski, R.W., Synak, P.: Approximation spaces and information granulation. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 175–189. Springer, Heidelberg (2005)
Słowiński, R., Vanderpooten, D.: Similarity Relation as a Basis for Rough Approximations. In: Wang, P. (ed.) Advances in Machine Intelligence and Soft Computing, vol. 4, pp. 17–33. Duke University Press (1997)
Swift, J.: Gulliver’s Travels into Several Remote Nations of the World. London, M, DCC, XXVI (1726)
Vapnik, V.: Statistical Learning Theory. John Wiley & Sons, New York (1998)
Vitória, A.: A Framework for Reasoning with Rough Sets. Licentiate Thesis, Linköping University, Transactions on Rough Sets IV: Journal Subline, LNCS. Springer, Heidelberg (2005) (to appear)
Vopenka, P.: Mathematics in the Alternative Set Theory, Teubner, Leipzig (1979)
Ziarko, W.: Variable Precision Rough Set Model. Journal of Computer and System Sciences 46, 39–59 (1993)
Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pawlak, Z. (2005). A Treatise on Rough Sets. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets IV. Lecture Notes in Computer Science, vol 3700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11574798_1
Download citation
DOI: https://doi.org/10.1007/11574798_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29830-4
Online ISBN: 978-3-540-32016-6
eBook Packages: Computer ScienceComputer Science (R0)