Rough Sets and Sorites Paradox

• Autorzy: Jankowski A. , Skowron A. , Wasilewski P.

Identyfikatory

DOI

10.3233/FI-2018-1633

• Języki publikacji: EN

Abstrakty

EN

We discuss the rough set approach to approximation of vague concepts. There are already published several papers on rough sets and vague concepts staring from the seminal papers by Zdzisław Pawlak. However, only a few of them are discussing the relationships of rough sets with the sorites paradox. This paper contains a continuation of discussion on this issue.

Słowa kluczowe

EN

rough set; sorites paradox; vague concept; vagueness

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2018
• Tom: Vol. 157, nr 4
• Strony: 371--384
• Opis fizyczny: Bibliogr. 57 poz., rys.

Twórcy

autor

Jankowski A.

• The Dziubanski Foundation of Knowledge Technology, Nowogrodzka 31, 00-511 Warsaw, Poland

autor

Skowron A.

• Institute of Mathematics, The University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
• Systems Research Institute Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland

autor

Wasilewski P.

• Institute of Informatics, The University of Warsaw, Banacha 2, 02-097 Warsaw, Poland

Bibliografia

• [1] Baker GP, and Hacker PMS. (Eds.), Wittgenstein: Understanding and Meaning: Volume 1 of an Analytical Commentary on the Philosophical Investigations, Part II: Exegesis §§1-184, Blackwell, 2005. (2nd Edition). ISBN-10:1405101768, 13:978-1405101769.
• [2] Banerjee M, and Chakraborty MK. Foundations of vagueness: A category-theoretic approach, Electronic Notes in Theoretical Computer Science 2003;82(4):10-19. URL https://doi.org/10.1016/S1571-0661(04)80701-1.
• [3] Bazan JG, Skowron A, and Swiniarski R. Rough sets and vague concept approximation: From sample approximation to adaptive learning, Transactions on Rough Sets V vol. 4100, 2006 pp. 39-62. URL https://doi.org/10.1007/11847465_3.
• [4] Black M. Vagueness: An exercise in logical analysis, Philosophy of Science 1937;4(4):427-455. URL http://www.jstor.org/stable/184414.
• [5] Bonikowski Z, and Wybraniec-Skardowska U. Vagueness and roughness. Transactions on Rough Sets IX, vol. 5390, 2008 pp. 1-13. URL https://doi.org/10.1007/978-3-540-89876-4_1.
• [6] Bums LC, Vagueness. An Investigation into Natural Languages and the Sorites Paradox, Kluwer, 1991. ISBN: 0792314891, 9780792314899.
• [7] Dubois D, Esteva F, Godo L, and Prade H. An information-based discussion of vagueness, In: Proceedings of the 10th IEEE International Conference on Fuzzy Systems, Melbourne, Australia, December 2-5, 2001, IEEE, IEEE Computer Science Press, 2001 pp. 781-784. doi:10.1109/FUZZ.2001.1009071.
• [8] Dubois D, Godo L, Prade H, and Esteva F. An information-based discussion of vagueness, In: H. Cohen, C. Lefebvre (Eds.), Handbook of Categorization in Cognitive Science, Elsevier, Amsterdam, 2005 pp.892-913. doi:10.1016/b978-0-08-101107-2.00041-5.
• [9] Dubois D, Lang J, and Prade H. Handling uncertainty, context, vague predicates, and partial inconsistency in possibilistic logic, In: D. Driankov, P.W. Eklund, A. L. Ralescu (Eds.), Fuzzy Logic and Fuzzy Control, IJCAI ’91, Workshops on Fuzzy Logic and Fuzzy Control, Sydney, Australia, August 24, 1991, Proceedings, LNCS 833, Springer 1991 pp. 45-55. URL https://doi.org/10.1007/3-540-58279-7_18.
• [10] Dubois D, and Prade H. Modeling uncertain and vague knowledge in possibility and evidence theories, In: R. D. Shachter, T. S. Levitt, L. N. Kanal, J. F. Lemmer (Eds.), UAI ’88: Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence, Minneapolis, MN, USA, July 10-12, 1988, North-Holland, 1988 pp. 303-318. URL http://dl.acm.org/citation.cfm?id=647231.719431.
• [11] Dubois D, and Prade H. Fuzzy sets - a convenient fiction for modeling vagueness and possibility, IEEE Transactions on Fuzzy Systems 1994;2(1):16-21. doi:10.1109/91.273117.
• [12] Dubois D, and Prade H. Modeling uncertain and vague knowledge in possibility and evidence theories, CoRR abs/1304.2349. URL http://arxiv.org/abs/1304.2349.
• [13] Dutta S, Basu S, and Chakraborty MK. Many-valued logics, fuzzy logics and graded consequence: A comparative appraisal, In: K. Lodaya (Ed.), Logic and Its Applications, 5th Indian Conference, ICLA 2013, Chennai, India, January 10-12, 2013, Proceedings, Springer, LNCS 7750, Springer, 2013 pp. 197-209. URL https://doi.org/10.1007/978-3-642-36039-8_18.
• [14] Fine K. Vagueness, truth and logic, Synthese 1975;30:265-300. URL http://www.jstor.org/stable/20115033.
• [15] Frege G. Grundgesetzen der Arithmetik 2, Verlag von Hermann Pohle, 1903.
• [16] Geach P, and Black M. (Eds.), Translations from the Philosophical Writings of Gottlob Frege, Blackwell, 1960.
• [17] Goguen JA. The logic of inexact concepts, Synthese 1968-69;19:325-373. URL http://www.jstor.org/stable/20114646.
• [18] Hastie T, Tibshirani R, and Friedman JH. The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer-Verlag, 2001. ISBN: 0387952845, 9780387952840.
• [19] Hempel CG. Vagueness and logic, Philosophy of Science 1939;6:163-180.
• [20] Hyde D. Vagueness, Logic, and Ontology, Ashgate, 2008. ISBN: 0754615324, 9780754615323.
• [21] Jankowski A. Interactive Granular Computations in Networks and Systems Engineering: A Practical Perspective, Lecture Notes in Networks and Systems 17, Springer, Heidelberg, 2017. ISBN: 978-3-319-57626-8.
• [22] Jankowski A, and Skowron A. A Wistech paradigm for intelligent systems, Transactions on Rough Sets VI, 2007 pp. 94-132. doi:10.1007/978-3-540-71200-8_7.
• [23] Jankowski A, and Skowron A. Wisdom technology: A rough-granular approach, In: M. Marciniak, A. Mykowiecka (Eds.), Bolc Festschrift, Springer, Heidelberg, LNCS vol. 5070, Springer, 2009 pp. 3-41. URL https://doi.org/10.1007/978-3-642-04735-0_1.
• [24] Jankowski A, Skowron A, and Swiniarski RW. Interactive complex granules, Fundamenta Informaticae 2014;133(2-3):181-196. doi:10.3233/FI-2014-1070.
• [25] Jankowski A, and Skowron A. Rough sets and vague concepts, Analele Universitatii din Bucuresti. Seria Informatica 2015;XII(3):119-133.
• [26] Keefe R. Theories of Vagueness, Cambridge Studies in Philosophy, Cambridge, UK, 2000. ISBN:0521650674, 9780521650670.
• [27] Keefe R, and Smith P. Vagueness: A Reader, MIT Press, Massachusetts, MA, 1997. doi:10.1023/A:1005389012304.
• [28] Lawry J, Dubois D. A bipolar framework for combining beliefs about vague propositions, In: G. Brewka, T. Eiter, S. A. McIlraith (Eds.), Principles of Knowledge Representation and Reasoning: Proceedings of KR 2012, Rome, Italy, June 10-14, 2012, AAAI Press, 2012.
• [29] Marcus S. The paradox of the heap of grains, in respect to roughness, fuzziness and negligibility, In: L. Polkowski, A. Skowron (Eds.), Proceedings of RSCTC’1998, Warsaw, June 22-26, 1998, LNAI 1424, Springer-Verlag, 1998 pp. 19-23. URL https://doi.org/10.1007/3-540-69115-4_2.
• [30] Nguyen HS, and Skowron A. Rough Sets: From Rudiments to Challenges. In: A. Skowron, Z. Suraj (eds.), Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam, Intelligent Systems Reference Library 42, Springer 2013 pp. 75-173. URL https://doi.org/10.1007/978-3-642-30344-9_3.
• [31] Orłowska E. Semantics of vague concepts, In: G. Dorn, P. Weingartner (Eds.), Foundation of Logic and Linguistics, Plenum Press, 1984 pp. 465-482. URL https://doi.org/10.1007/978-1-4899-0548-2_20.
• [32] Orłowska E. Reasoning about vague concepts, Bulletin of the Polish Academy of Sciences, Mathematics 35, 1987 pp. 643-652.
• [33] Pal SK, Polkowski L, and Skowron A. (Eds.), Rough-Neural Computing: Techniques for Computing with Words, Cognitive Technologies, Springer-Verlag, 2004. doi:10.1007/978-3-642-18859-6.
• [34] Pawlak Z. Information systems-Theoretical foundations, Information Systems 1981;6(3):205-218. URL https://doi.org/10.1016/0306-4379(81)90023-5.
• [35] Pawlak Z. Rough sets, International Journal of Computer and Information Sciences 1982;11(5):341-356. URL https://doi.org/10.1007/BF01001956.
• [36] Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning about Data, System Theory, Knowledge Engineering and Problem Solving 9, Kluwer Academic Publishers, 1991. ISBN: 0792314727, 9780792314721.
• [37] Pawlak Z. Vagueness and uncertainty: A rough set perspective, Computational Intelligence: An International Journal 1995;11:217-232. doi:10.1111/j.1467-8640.1995.tb00029.x.
• [38] Pawlak Z. Vagueness-A rough set view. In: J. Mycielski, G. Rozenberg, A. Salomaa (Eds.), Structures in Logic and Computer Science, Springer, LNCS 1261, Springer, 1997 pp. 106-117. URL https://doi.org/10.1007/3-540-63246-8_7.
• [39] Pawlak Z, and Skowron A. Rough sets: Some extensions, Information Sciences 2007;177(1):28-40. URL https://doi.org/10.1016/j.ins.2006.06.006.
• [40] Pawlak Z, and Skowron A. Rudiments of rough sets, Information Sciences 2007;177(1):3-27. URL https://doi.org/10.1016/j.ins.2006.06.003.
• [41] Polkowski L, and Semeniuk-Polkowska M. Boundries, borders, fences, hedges. Fundamenta Informaticae 2014;129(1-2):149-159. doi:10.3233/FI-2014-966.
• [42] Polkowski L, and Skowron A. Rough mereological calculi of granules: A rough set approach to computation, Computational Intelligence: An International Journal 2001;17(3):472-492. doi:10.1111/0824-7935.00159.
• [43] Prade H. A two-layer fuzzy pattern matching procedure for the evaluation of conditions involving vague quantifiers, Journal of Intelligent and Robotic Systems 1990;3(2):93-101. URL https://doi.org/10.1007/BF00242158.
• [44] Prade H, and Testemale C. Generalizing database relational algebra for the treatment of incomplete/uncertain information and vague queries, Information Sciences 1984;34(2):115-143. URL https://doi.org/10.1016/0020-0255(84)90020-3.
• [45] Read S. Thinking about Logic: An Introduction to the Philosophy of Logic, Oxford University Press, 1994.
• [46] Ronzitti G. (Ed.), Vagueness: A Guide, Logic, Epistemology, and The Unity of Science Series, vol. 19, Springer, 2011. doi:10.1007/978-94-007-0375-9.
• [47] Russell B. Vagueness, The Australian Journal of Psychology and Philosophy 1923;1:84-92.
• [48] Seising R. Pioneers of vagueness, haziness, and fuzziness in the 20th century, in: M. Nikravesh, J. Kacprzyk, L.A. Zadeh (Eds.), Forging New Frontiers: Fuzzy Pioneers I, Studies in Fuzziness and Soft Computing 217, Springer, 2007, 55-81. URL https://doi.org/10.1007/978-3-540-73182-5_4.
• [49] Shapiro S. (Ed.) Vagueness in Context, Clarendon Press, 2006. doi:10.1093/acprof:oso/9780199280391.001.0001.
• [50] Skowron A. Rough sets and vague concepts, Fundamenta Informaticae 2005;64(1-4):417-431.
• [51] Skowron A, and Swiniarski R. Rough sets and higher order vagueness, In: D. Ślęzak, G. Wang, M. Szczuka, I. Düntsch, Y. Yao (Eds.), Proceedings of RSFDGrC’2005, Regina, Canada, August 31-September 3, 2005, Part I, LNAI 3641, Springer-Verlag, 2005 pp. 33-42. URL https://doi.org/10.1007/11548669_4.
• [52] Ślęzak D, and Wasilewski P. Foundations of rough sets from vagueness perspective, In: A. E. Hassanien, Z. Suraj, D. Ślęzak, P. Lingras (Eds.), Rough Computing: Theories, Technologies and Applications, IGI Global, 2007 pp. 1-37.
• [53] Tanaka K, Berto F, Mares E, and Paoli F. (Eds.), Paraconsistency: Logic and Applications, Logic, Epistemology, and the Unity of Science 26, Springer, 2013. doi:10.1007/978-94-007-4438-7.
• [54] Thiele LP. The Heart of Judgment: Practical Wisdom, Neuroscience, and Narrative, Cambridge University Press, 2010. ISBN: 10:0521248914, 13:978-0521248914.
• [55] Verdée P, van der Waart van Gulik S.. A generic framework for adaptive vague logics, Studia Logica 2008;90(3):385-405. URL https://doi.org/10.1007/s11225-008-9158-x.
• [56] Wolski M. Science and semantics: A note on vagueness, In: A. Skowron, Z. Suraj (Eds.), Rough Sets and Intelligent Systems. Professor Zdzisław Pawlak in Memoriam, Series Intelligent Systems Reference Library 42, Springer 2013 pp. 623-643. URL https://doi.org/10.1007/978-3-642-30344-9_24.
• [57] Q. Zhang Q, Wang J, Wang G, and Yu H. The approximation set of a vague set in rough approximation space, Information Sciences 2015;300:1-19. URL https://doi.org/10.1016/j.ins.2014.12.023.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).