Skip to main content

Toward Adaptive Rough Sets

  • Conference paper
  • First Online:
Rough Sets (IJCRS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10313))

Included in the following conference series:

Abstract

In this paper we take an attempt to depart from the closed way of presenting information table characterizing a vague concept with respect to a closed sample of objects, a fixed set of attributes, and a static time point. The aim is rather to have an interactive information system which is open to incorporate new information based on the interactions of an agent with the physical reality. This in turn prepares the ground for the notion of adaptive information system which incorporates the possibility of adapting decision strategies based on the history of making decisions over a period of time through interactions of an agent with the physical reality.

The original version of this chapter was revised: The acknowledgement was modified. The correction to this chapter is available at https://doi.org/10.1007/978-3-319-60837-2_54

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Change history

  • 01 December 2018

    The acknowledgement section of this paper originally referred to grant DEC-2013/09/B/ST6/01568. The reference to this grant has been removed from the acknowledgement section at the request of one of the authors.

References

  1. Anderson, J.R.: How Can the Human Mind Occur in the Physical Universe?. Oxford University Press, New York (2007)

    Book  Google Scholar 

  2. Baker, G.P., Hacker, P.M.S. (eds.): Wittgenstein: Understanding and Meaning: Volume 1 of an Analytical Commentary on the Philosophical Investigations, Part II: Exegesis, 2nd edn. pp. 1–184. Blackwell, Hoboken (2005)

    Google Scholar 

  3. Banerjee, M., Chakraborty, M.K.: Foundations of vagueness: a category-theoretic approach. Electron. Notes Theor. Comput. Sci. 82(4), 10–19 (2003)

    Article  Google Scholar 

  4. Barwise, J., Seligman, J.: Information Flow: The Logic of Distributed Systems. Cambridge University Press, Cambridge (1997)

    Book  Google Scholar 

  5. Batens, D.: Inconsistency-adaptive logics. In: Orlowska, E. (ed.) Logic at Work: Essays Dedicated to the Memory of Helena Rasiowa, pp. 445–472. Physica Verlag (Springer), Heidelberg (1999)

    Google Scholar 

  6. Batens, D.: Tutorial on inconsistency-adaptive logics. In: Beziau, J.-Y., Chakraborty, M., Dutta, S. (eds.) New Directions in Paraconsistent Logic, Springer Proceedings in Mathematics & Statistics, vol. 152, pp. 3–38. Springer, Heidelberg (2016)

    Chapter  Google Scholar 

  7. Bazan, J.G.: Hierarchical classifiers for complex spatio-temporal concepts. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX: Journal Subline. LNCS, vol. 5390, pp. 474–750. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89876-4_26

    Chapter  Google Scholar 

  8. Bazan, J., Skowron, A., Swiniarski, R.: Rough sets and vague concept approximation: from sample approximation to adaptive learning. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 39–62. Springer, Heidelberg (2006). 10.1007/11847465_3

    Chapter  MATH  Google Scholar 

  9. Bonikowski, Z., Wybraniec-Skardowska, U.: Vagueness and roughness. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 1–13. Springer, Heidelberg (2008). 10.1007/978-3-540-89876-4_1

    Chapter  Google Scholar 

  10. Bums, L.C.: Vagueness. In: An Investigation into Natural Languages and the Sorites Paradox. Kluwer, Dordrecht (1991)

    Google Scholar 

  11. Dubois, D., Esteva, F., Godo, L., Prade, H.: An information-based discussion of vagueness. In: Proceedings of 10th IEEE International Conference on Fuzzy Systems, Melbourne, Australia, 2–5 December 2001, pp. 781–784. IEEE Computer Science Press (2001)

    Google Scholar 

  12. Dubois, D., Godo, L., Prade, H., Esteva, F.: An information-based discussion of vagueness. In: Cohen, H., Lefebvre, C. (eds.) Handbook of Categorization in Cognitive Science, pp. 892–913. Elsevier, Amsterdam (2005)

    Google Scholar 

  13. Dubois, D., Lang, J., Prade, H.: Handling uncertainty, context, vague predicates, and partial inconsistency in possibilistic logic. In: Driankov, D., Eklund, P.W., Ralescu, A.L. (eds.) IJCAI 1991. LNCS, vol. 833, pp. 45–55. Springer, Heidelberg (1994). 10.1007/3-540-58279-7_18

    Chapter  Google Scholar 

  14. Dubois, D., Prade, H.: Modeling uncertain and vague knowledge in possibility and evidence theories. In: Shachter, R.D., Levitt, T.S., Kanal, L.N., Lemmer, J.F. (eds.) Proceedings of 4th Annual Conference on Uncertainty in Artificial Intelligence (UAI 1988), Minneapolis, MN, USA, 10–12 July 1988, LNCS, vol. 7750, pp. 303–318. North-Holland, Amsterdam (1988)

    Google Scholar 

  15. Dubois, D., Prade, H.: Fuzzy sets - a convenient fiction for modeling vagueness and possibility. IEEE Trans. Fuzzy Syst. 2(1), 16–21 (1994)

    Article  Google Scholar 

  16. Dubois, D., Prade, H., Modeling uncertain and vague knowledge in possibility and evidence theories. CoRR abs/1304.2349. http://arxiv.org/abs/1304.2349

  17. Dutta, S., Basu, S., Chakraborty, M.K.: Many-valued logics, fuzzy logics and graded consequence: a comparative appraisal. In: Lodaya, K. (ed.) ICLA 2013. LNCS, vol. 7750, pp. 197–209. Springer, Heidelberg (2013). 10.1007/978-3-642-36039-8_18

    Chapter  MATH  Google Scholar 

  18. Goguen, J.A.: The logic of inexact concepts. Synthese 19, 325–373 (1968–1969)

    Google Scholar 

  19. Harnad, S.: Categorical Perception: The Groundwork of Cognition. Cambridge University Press, New York (1987)

    Google Scholar 

  20. Harnad, S.: The symbol grounding problem. Physica D 42, 335–346 (1990)

    Article  Google Scholar 

  21. Hastie, T., Tibshirani, R., Friedman, J.H.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, Heidelberg (2001)

    Book  Google Scholar 

  22. Heller, M.: The Ontology of Physical Objects. Four Dimensional Hunks of Matter. Cambridge Studies in Philosophy. Cambridge University Press, Cambridge (1990)

    Book  Google Scholar 

  23. Jankowski, A.: Interactive Granular Computations in Networks and Systems Engineering: A Practical Perspective. LNNS. Springer, Heidelberg (2017, in print)

    Google Scholar 

  24. Jankowski, A., Skowron, A.: A wistech paradigm for intelligent systems. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 94–132. Springer, Heidelberg (2007). 10.1007/978-3-540-71200-8_7

    Chapter  Google Scholar 

  25. Jankowski, A., Skowron, A.: Wisdom technology: a rough-granular approach. In: Marciniak, M., Mykowiecka, A. (eds.) Aspects of Natural Language Processing. LNCS, vol. 5070, pp. 3–41. Springer, Heidelberg (2009). 10.1007/978-3-642-04735-0_1

    Chapter  Google Scholar 

  26. Jankowski, A., Skowron, A., Dutta, S.: Toward problem solving support based on big data and domain knowledge: interactive granular computing and adaptive judgement. In: Japkowicz, N., Stefanowski, J. (eds.) Big Data Analysis: New Algorithms for a New Society, Series Big Data, vol. 16, pp. 44–90. Springer, Heidelberg (2015)

    Google Scholar 

  27. Jankowski, A., Skowron, A., Swiniarski, R.W.: Perspectives on uncertainty and risk in rough sets and interactive rough-granular computing. Fundamenta Informaticae 129(1–2), 69–84 (2014)

    MathSciNet  MATH  Google Scholar 

  28. Keefe, R.: Theories of Vagueness. Cambridge Studies in Philosophy. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  29. Lawry, J., Dubois, D., A bipolar framework for combining beliefs about vague propositions. In: Brewka, G., Eiter, T., McIlraith, S.A. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of KR 2012, Rome, Italy, 10–14 June 2012, pp. 530–540. AAAI Press (2012)

    Google Scholar 

  30. 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, vol. 1424, pp. 19–22. Springer, Heidelberg (1998). 10.1007/3-540-69115-4_2

    Chapter  Google Scholar 

  31. Martin, W.M. (ed.): Theories of Judgment. Psychology, Logic, Phenomenology. Cambridge University Press, New York (2006)

    Google Scholar 

  32. Noë, A.: Action in Perception. MIT Press, Cambridge (2004)

    Google Scholar 

  33. Orłowska, E.: Semantics of vague concepts. In: ICS PAS Reports 450/82, pp. 1–20. Institute of Computer Science Polish Academy of Sciences (ICS PAS), Warsaw, Poland (1982)

    Google Scholar 

  34. Orłowska, E., Pawlak, Z.: Expressive power of knowledge representation systems. In: ICS PAS Reports 432/81, pp. 1–31. Institute of Computer Science Polish Academy of Sciences (ICS PAS), Warsaw, Poland (1981)

    Google Scholar 

  35. Pal, S.K., Polkowski, L., Skowron, A. (eds.): Rough-Neural Computing: Techniques for Computing with Words. Cognitive Technologies. Springer-, Heidelberg (2004)

    Google Scholar 

  36. Pawlak, Z.: Mathematical foundation of information retrieval. In: Proceedings of International Symposium and Summer School on Mathematical Foundations of Computer Science, Strbske Pleso, High Tatras, Czechoslovakia, pp. 135–136. Mathematical Institute of the Slovak Academy of Sciences (1973)

    Google Scholar 

  37. Pawlak, Z.: Mathematical foundations of information retrieval. In: CC PAS Reports 101/73, pp. 1–8. Computation Center Polish Academy of Sciences (CC PAS), Warsaw, Poland (1973)

    Google Scholar 

  38. Pawlak, Z.: Information systems - theoretical foundations. Inf. Syst. 6, 205–218 (1981)

    Article  Google Scholar 

  39. Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11, 341–356 (1982)

    Article  Google Scholar 

  40. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data, System Theory, Knowledge Engineering and Problem Solving, vol. 9. Kluwer Academic Publishers, Dordrecht (1991)

    Book  Google Scholar 

  41. Pawlak, Z.: Vagueness and uncertainty: a rough set perspective. Comput. Intell.: Int. J. 11, 217–232 (1995)

    Article  MathSciNet  Google Scholar 

  42. Pawlak, Z.: Vagueness — a rough set view. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds.) Structures in Logic and Computer Science. LNCS, vol. 1261, pp. 106–117. Springer, Heidelberg (1997). 10.1007/3-540-63246-8_7

  43. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inf. Sci. 177(1), 3–27 (2007)

    Article  MathSciNet  Google Scholar 

  44. Polkowski, L., Semeniuk-Polkowska, M.: Boundaries, borders, fences, hedges. Fundamenta Informaticae 129(1–2), 149–159 (2014)

    MathSciNet  MATH  Google Scholar 

  45. Polkowski, L., Skowron, A.: Rough mereological calculi of granules: a rough set approach to computation. Comput. Intell.: Int. J. 17(3), 472–492 (2001)

    Article  MathSciNet  Google Scholar 

  46. Prade, H.: A two-layer fuzzy pattern matching procedure for the evaluation of conditions involving vague quantifiers. J. Intell. Rob. Syst. 3, 93–101 (1990)

    Article  Google Scholar 

  47. Prade, H., Testemale, C.: Generalizing database relational algebra for the treatment of incomplete/uncertain information and vague queries. Inf. Sci. 34, 115–143 (1984)

    Article  MathSciNet  Google Scholar 

  48. Read, S.: Thinking about Logic: An Introduction to the Philosophy of Logic. Oxford University Press, Oxford (1994)

    Google Scholar 

  49. Skowron, A.: Rough sets and vague concepts. Fundamenta Informaticae 64(1–4), 417–431 (2005)

    MathSciNet  MATH  Google Scholar 

  50. Skowron, A., Dutta, S.: From information systems to interactive information systems. In: Wang, G., Skowron, A., Yao, Y., Slezak, D., Polkowski, L. (eds.) Thriving Rough Sets. SCI, vol. 708, pp. 207–223. Springer, Heidelberg (2017). 10.1007/978-3-319-54966-8_10

    Chapter  Google Scholar 

  51. Skowron, A., Jankowski, A.: Rough sets and vague concepts. Ann. Univ. Buchar. Inform. Ser. LXI LXII(3), 119–133 (2015)

    Google Scholar 

  52. Skowron, A., Jankowski, A.: Interactive computations: toward risk management in interactive intelligent systems. Nat. Comput. 15(3), 465–476 (2016)

    Article  MathSciNet  Google Scholar 

  53. Skowron, A., Jankowski, A.: Rough sets and interactive granular computing. Fundamenta Informaticae 147, 371–385 (2016)

    Article  MathSciNet  Google Scholar 

  54. Skowron, A., Jankowski, A.: Toward W2T foundations: interactive granular computing and adaptive judgement. In: Zhong, N., Ma, J., Liu, J., Huang, R., Tao, X. (eds.) Wisdom Web of Things (W2T), pp. 47–71. Springer, Heidelberg (2016)

    Chapter  Google Scholar 

  55. Skowron, A., Jankowski, A., Dutta, S.: Interactive granular computing. Granul. Comput. 1, 95–113 (2016). Springer, Heidelberg. 10.1007/s41066-015-0002-1

  56. Skowron, A., Jankowski, A., Wasilewski, P.: Risk management and interactive computational systems. J. Adv. Math. Appl. 1, 61–73 (2012)

    Google Scholar 

  57. Skowron, A., Jankowski, A., Wasilewski, P.: Rough sets and sorites paradox. In: Schlingloff, H. (ed.) International Workshop on Concurrency, Specification and Programming (CS&P 2016), Rostock, Germany, 28–30 September, CEUR-WS.org 2016, CEUR Workshop Proceedings, vol. 1698, pp. 49–60 (2017)

    Google Scholar 

  58. Skowron, A., Nguyen, H.S.: Rough sets: from rudiments to challenges. In: Skowron, A., Suraj, Z. (eds.) Rough Sets and Intelligent Systems. Professor Zdzislaw Pawlak in Memoriam. Intelligent Systems Reference Library, vol. 42, pp. 75–173. Springer, Heidelberg (2013). 10.1007/978-3-642-30344-9_3

    Chapter  Google Scholar 

  59. Skowron, A., Swiniarski, R.: Rough sets and higher order vagueness. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS, vol. 3641, pp. 33–42. Springer, Heidelberg (2005). 10.1007/11548669_4

    Chapter  MATH  Google Scholar 

  60. Skowron, A., Szczuka, M.: Toward interactive computations: a rough-granular approach. In: Koronacki, J., Raś, Z., Wierzchoń, S., Kacprzyk, J. (eds.) Advances in Machine Learning II: Dedicated to the Memory of Professor Ryszard S. Michalski. SCI, vol. 263, pp. 23–42. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  61. Skowron, A., Wasilewski, P.: Interactive information systems: toward perception based computing. Theoret. Comput. Sci. 454, 240–260 (2012)

    Article  MathSciNet  Google Scholar 

  62. Ślȩzak, D., Wasilewski, P.: Foundations of rough sets from vagueness perspective. In: Hassanien, A.E., Suraj, Z., Ślȩzak, D., Lingras, P. (eds.) Rough Computing: Theories, Technologies and Applications, pp. 1–37. IGI Global, Hershey (2008)

    Google Scholar 

  63. Vapnik, V.: Statistical Learning Theory. Wiley, New York (1998)

    MATH  Google Scholar 

  64. Wolski, M.: Science and semantics: a note on vagueness. In: Skowron, A., Suraj, Z. (eds.) Rough Sets and Intelligent Systems. Professor Zdzislaw Pawlak in Memoriam. Intelligent Systems Reference Library, vol. 42, pp. 623–643. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

Download references

Acknowledgments

This work was partially supported by the Polish National Science Centre (NCN) grant DEC-2011/01/D /ST6/06981, as well as by the Polish National Centre for Research and Development (NCBiR) under the grant DZP/RID-I-44 / 8 /NCBR/2016.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andrzej Skowron .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Dutta, S., Skowron, A. (2017). Toward Adaptive Rough Sets. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10313. Springer, Cham. https://doi.org/10.1007/978-3-319-60837-2_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-60837-2_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60836-5

  • Online ISBN: 978-3-319-60837-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics