Skip to main content
SpringerLink
Log in

Adaptive Rough Sets and Vague Concepts

  • Chapter
  • First Online:
Ewa Orłowska on Relational Methods in Logic and Computer Science

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 17))

  • 242 Accesses

Abstract

In this chapter our attempt is to point out different ways of addressing different perspectives of understanding a vague concept from the angle of rough set semantics. In this attempt, we propose 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. To do that we introduce an interactive information system which is open to incorporate new information based on the interaction of an agent with the physical reality. Moreover, we propose an outline of an 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.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Baker, G. P. & Hacker, P. M. S. (Eds.). (2005). Wittgenstein: Understanding and Meaning: Volume 1 of an Analytical Commentary on the Philosophical Investigations, Part II: Exegesis §§1–184 (2nd edn.). Wiley-Blackwell.

    Google Scholar 

  • Banerjee, M. & Chakraborty, M. K. (2003). Foundations of vagueness : A category theoretic approach. Electronic Notes on Theoretical Computer Science, 82(4), 10–19.

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Bazan, J. G. (2008). Hierarchical classifiers for complex spatio-temporal concepts. Transactions on Rough Sets, IX(LNCS 6390), 474–750.

    Google Scholar 

  • Bazan, J. G., Skowron, A., & Świniarski, R. W. (2006). Rough sets and vague concept approximation: From sample approximation to adaptive learning. Transactions on Rough Sets, V(LNCS 4100), 39–62.

    Google Scholar 

  • Black, M. (1937). Vagueness: An exercise in logical analysis. Philosophy of Science, 4(4), 427–455.

    Article  Google Scholar 

  • Bonikowski, Z. & Wybraniec-Skardowska, U. (2008). Vagueness and roughness. Transactions on Rough Sets, IX, (LNCS 5390), 1–13).

    Google Scholar 

  • Burns, L. (1991). Vagueness. An Investigation into Natural Languages and the Sorites Paradox. Kluwer Academic Publishers.

    Google Scholar 

  • Dubois, D. & Prade, H. (1988). 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 4th Annual Conference on Uncertainty in Artificial Intelligence (pp. 303–318). Minneapolis, USA: North-Holland.

    Chapter  Google Scholar 

  • Dubois, D. & Prade, H. (1994). Fuzzy sets-a convenient fiction for modeling vagueness and possibility. IEEE Transactions on Fuzzy Systems, 2(1), 16–21.

    Article  Google Scholar 

  • Dubois, D. & Prade, H. (2013). Modeling uncertain and vague knowledge in possibility and evidence theories. CoRR. arXiv:1304.2349.

  • Dubois, D., Lang, J., & Prade, H. (1991). Handling uncertainty, context, vague predicates, and partial inconsistency in possibilistic logic. In D. Driankov, P. W. Eklund, & A. L. Ralescu (Eds.), Proceedings of Workshops Fuzzy Logic and Fuzzy Control, IJCAI ’91 (Vol. 833, pp. 45–55). Lecture Notes in Computer Science. Sydney, Australia: Springer.

    Chapter  Google Scholar 

  • Dubois, D., Esteva, F., Godo, L., & Prade, H. (2001). An information-based discussion of vagueness. In Proceedings of the 10th IEEE International Conference on Fuzzy Systems (pp. 781–784). Melbourne, Australia: IEEE.

    Google Scholar 

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

    Google Scholar 

  • Dutta, S., Basu, S., & Chakraborty, M. K. (2013). Many-valued logics, fuzzy logics and graded consequence: A comparative appraisal. In K. Lodaya (Ed.), Proceedings of Logic and Its Applications, 5th Indian Conference, ICLA 2013 (Vol. 7750, pp. 197–209). Lecture Notes in Computer Science. Chennai, India: Springer.

    Google Scholar 

  • Fine, K. (1975). Vagueness, truth and logic. Synthese, 30(3/4), 265–300.

    Article  Google Scholar 

  • Frege, G. (1903). Grundgesetze der Arithmetik. Jena: Verlag von Hermann Pohle.

    Google Scholar 

  • Geach, P. & Black, M. (Eds.). (1960). Translations from the Philosophical Writings of Gottlob Frege. Oxford: Blackwell.

    Google Scholar 

  • Goguen, J. A. (1969). The logic of inexact concepts. Synthese, 19(3/4), 325–373.

    Article  Google Scholar 

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

    Chapter  Google Scholar 

  • Hempel, C. G. (1939). Vagueness and logic. Philosophy of Science, 6, 163–180.

    Article  Google Scholar 

  • Jankowski, A. (2017). Interactive Granular Computations in Networks and Systems Engineering: A Practical Perspective. Lecture Notes in Networks and Systems. Heidelberg: Springer.

    Book  Google Scholar 

  • Jankowski, A. & Skowron, A. (2007). A wistech paradigm for intelligent systems. Transactions on Rough Sets, VI(LNCS 4374), 94–132.

    Google Scholar 

  • Jankowski, A. & Skowron, A. (2009). Wisdom technology: A rough-granular approach. In M. Marciniak & A. Mykowiecka (Eds.), Aspects of Natural Language Processing, Essays Dedicated to Leonard Bolc on the Occasion of his 75th Birthday (Vol. 5070, pp. 3–41). Lecture Notes in Computer Science. Berlin: Springer.

    Chapter  Google Scholar 

  • Jankowski, A., Skowron, A., & Wasilewski, P. (2012). Risk management and interactive computational systems. Journal of Advanced Mathematics and Applications, 1(1), 61–73.

    Article  Google Scholar 

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

    Google Scholar 

  • Jankowski, A., Skowron, A., & Wasilewski, P. (2016). Rough sets and sorites paradox. In B.-H. Schlingloff (Ed.), Proceedings of the 25th International Workshop on Concurrency, Specification and Programming 2016 (Vol. 1698, pp. 49–60). CEUR Workshop Proceedings. Rostock, Germany: CEUR-WS.org.

    Google Scholar 

  • Kacprzyk, J. & Pedrycz, W. (2015). Springer Handbook of Computational Intelligence. Heidelberg: Springer.

    Chapter  Google Scholar 

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

    Google Scholar 

  • Keefe, R. & Smith, P. (1997). Vagueness: A Reader. Cambridge: MIT Press.

    Google Scholar 

  • Konrad, E., Orłowska, E., & Pawlak, Z. (1981). Knowledge representation systems (No. 433). ICS PAS Reports.

    Google Scholar 

  • Konrad, E., Orłowska, E., & Pawlak, Z. (1982). On approximate concept learning. In Proceedings of the European Conference on AI (pp. 17–19). See also Technische Universität Berlin, Bericht No. 81/87, 1981. Orsay, France.

    Google Scholar 

  • Lawry, J. & Dubois, D. (2012). 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 the 13th International Conference, KR 2012. Rome, Italy: AAAI Press.

    Google Scholar 

  • Marcus, S. (1998). The paradox of the heap of grains in respect to roughness, fuzziness and negligibility. In L. Polkowski & A. Skowron (Eds.), Proceedings of Rough Sets and Current Trends in Computing, 1st International Conference, RSCTC’98 (Vol. 1424, pp. 19–23). Lecture Notes in Computer Science. Warsaw, Poland: Springer.

    Google Scholar 

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

    Google Scholar 

  • Orłowska, E. (1982a). Logic of vague concepts. Bulletin of the Section of Logic, 11(3/4), 115–126.

    Google Scholar 

  • Orłowska, E. (1982b). Semantics of vague concepts (No. 450). ICS PAS Reports.

    Google Scholar 

  • Orłowska, E. (1983a). Semantics of vague concepts. In G. Dorn & P. Weingartner (Eds.), Foundations of Logic and Linguistics. Problems and Their Solutions. Selected Contributions to the 7th International Congress of Logic, Methodology and Philosophy of Science, Salzburg 1983 (pp. 465–482). London/New York: Plenum Press.

    Chapter  Google Scholar 

  • Orłowska, E. (1983b). Semantics of vague concepts. In Abstracts of the 7th International Congress of Logic, Methodology and Philosophy of Science (Vol. 2, pp. 127–130). Salzburg, Austria.

    Google Scholar 

  • Orłowska, E. (1987). Reasoning about vague concepts. Bulletin of the Polish Academy of Sciences, 35, 643–652.

    Google Scholar 

  • Orłowska, E. (1988). Representation of vague information. Information Systems, 13(2), 167–174.

    Article  Google Scholar 

  • Orłowska, E. & Pawlak, Z. (1981a). Expressive power of knowledge representation systems (No. 432). ICS PAS Reports.

    Google Scholar 

  • Orłowska, E. & Pawlak, Z. (1981b). Representation of nondeterministic information (No. 450). ICS PAS Reports.

    Google Scholar 

  • Orłowska, E. & Pawlak, Z. (1984a). Expressive power of knowledge representation systems. International Journal of Man-Machine Studies, 20(5), 485–500.

    Article  Google Scholar 

  • Orłowska, E. & Pawlak, Z. (1984b). Logical foundations of knowledge representation (No. 537). ICS PAS Reports.

    Google Scholar 

  • Orłowska, E. & Pawlak, Z. (1984c). Measurement and indiscernibility. Bulletin of the Polish Academy of Sciences, 32(9–10), 617–624.

    Google Scholar 

  • Orłowska, E. & Pawlak, Z. (1984d). Representation of nondeterministic information. Theoretical Computer Science, 29, 27–39.

    Article  Google Scholar 

  • Pal, S. K., Polkowski, L., & Skowron, A. (Eds.). (2004). Rough-neural Computing: Techniques for Computing with Words. Cognitive Technologies. Berlin: Springer.

    Google Scholar 

  • Pawlak, Z. (1973a). Mathematical foundation of information retrieval. In Mathematical Foundations of Computer Science: Proceedings of Symposium and Summer School (pp. 135–136). Strbské Pleso, Czechoslovakia: Mathematical Institute of the Slovak Academy of Sciences.

    Google Scholar 

  • Pawlak, Z. (1973b). Mathematical foundation of information retrieval (No. 101). ICS PAS Reports.

    Google Scholar 

  • Pawlak, Z. (1981). Information systems–theoretical foundations. Information Systems, 6(3), 205–218.

    Article  Google Scholar 

  • Pawlak, Z. (1982). Rough sets. International Journal of Parallel Programming, 11(5), 341–356.

    Google Scholar 

  • Pawlak, Z. (1991). Rough Sets: Theoretical Aspects of Reasoning About Data. Dordrecht: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Pawlak, Z. (1995). Vagueness and uncertainty: A rough set perspective. Computational Intelligence, 11, 277–232.

    Article  Google Scholar 

  • Pawlak, Z. (1997). Vagueness - a rough set view. In J. Mycielski, G. Rozenberg, & A. Salomaa (Eds.), Structures in Logic and Computer Science, A Selection of Essays in Honor of Andrzej Ehrenfeucht (Vol. 1261, pp. 106–117). Lecture Notes in Computer Science. Berlin: Springer.

    Google Scholar 

  • Pawlak, Z. & Skowron, A. (2007). Rudiments of rough sets. Information Sciences, 177(1), 3–27.

    Article  Google Scholar 

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

    Google Scholar 

  • Polkowski, L. & Skowron, A. (2001). Rough mereological calculi of granules: A rough set approach to computation. Computational Intelligence, 17(3), 472–492.

    Article  Google Scholar 

  • Prade, H. (1990). A two-layer fuzzy pattern matching procedure for the evaluation of conditions involving vague quantifiers. Journal of Intelligent and Robotic Systems, 3(2), 93–101.

    Article  Google Scholar 

  • Prade, H. & Testemale, C. (1984). Generalizing database relational algebra for the treatment of incomplete/uncertain information and vague queries. Information Sciences, 34(2), 115–143.

    Article  Google Scholar 

  • Read, S. (1994). Thinking About Logic: An Introduction to the Philosophy of Logic. Oxford-New York: Oxford University Press.

    Google Scholar 

  • Ronzitti, G. (Ed.). (2011). Vagueness: A Guide. Logic, Epistemology, and the Unity of Science. Berlin: Springer.

    Google Scholar 

  • Russell, B. (1923). Vagueness. The Australian Journal of Psychology and Philosophy, 1(2), 84–92.

    Article  Google Scholar 

  • Seising, R. (2007). 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 (pp. 55–81). Berlin-Heidelberg: Springer.

    Google Scholar 

  • Shapiro, S. (2006). Vagueness in Context. Oxford: Clarendon Press.

    Google Scholar 

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

    Google Scholar 

  • Skowron, A. & Jankowski, A. (2015). Rough sets and vague concepts. Annals of the University of Bucharest (Informatics series), LXII(3), 119–133.

    Google Scholar 

  • Skowron, A. & Jankowski, A. (2016). Rough sets and interactive granular computing. Fundamenta Informaticae, 147(2–3), 371–385.

    Article  Google Scholar 

  • Skowron, A. & Nguyen, H. S. (2013). Rough sets: From rudiments to challenges. In A. Skowron & Z. Suraj (Eds.), Rough Sets and Intelligent Systems: Professor Zdzisław Pawlak in Memoriam (Vols. 2, 43, pp. 75–173). Intelligent Systems Reference Library. Berlin: Springer.

    Google Scholar 

  • Skowron, A. & Świniarski, R. W. (2005). Rough sets and higher order vagueness. In D. Ślęzak, G. Wang, M. S. Szczuka, I. Düntsch, & Y. Yao (Eds.), Proceedings of Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, 10th International Conference, RSFDGrC 2005, Part I (Vol. 3641, pp. 33–42). Lecture Notes in Computer Science. Regina, Canada: Springer.

    Google Scholar 

  • Skowron, A. & Szczuka, M. S. (2010). Toward interactive computations: A rough granular approach. In J. Koronacki, Z.W. Raś, S. T.Wierzchoń, & J. Kacprzyk (Eds.), Advances in Machine Learning II, Dedicated to the Memory of Professor Ryszard S. Michalski (Vol. 263, pp. 23–42). Studies in Computational Intelligence. Berlin: Springer.

    Chapter  Google Scholar 

  • Skowron, A. & Wasilewski, P. (2012). Interactive information systems: Toward perception based computing. Theoretical Computer Science, 454, 240–260.

    Article  Google Scholar 

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

    Google Scholar 

  • Wolski, M. (2013). Science and semantics: A note on vagueness. In A. Skowron & Z. Suraj (Eds.), Rough Sets and Intelligent Systems: Professor Zdzisław Pawlak in Memoriam (Vols. 2, 43, pp. 623–643). Intelligent Systems Reference Library. Berlin: Springer.

    Google Scholar 

  • Zadeh, L. A. (2012). Computing with Words–Principal Concepts and Ideas. Studies in Fuzziness and Soft Computing. Berlin: Springer.

    Book  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the referees for their valuable comments which helped to improve the manuscript. This work was partially supported 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

  1. Institute of Mathematics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  2. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Andrzej Skowron

  3. Vistula University, Stokłosy 3, 02-787, Warsaw, Poland

    Soma Dutta

  4. Department of Mathematics and Computer Science, University of Warmia and Mazury, Sloneczna Str. 54, 10-710, Olsztyn, Poland

    Soma Dutta

Authors
  1. Andrzej Skowron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Soma Dutta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrzej Skowron .

Editor information

Editors and Affiliations

  1. Institute of Philosophy, University of Warsaw, Warsaw, Poland

    Joanna Golińska-Pilarek

  2. Department of Logic and Methodology of Science, University of Lodz, Łódź, Poland

    Michał Zawidzki

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Skowron, A., Dutta, S. (2018). Adaptive Rough Sets and Vague Concepts. In: Golińska-Pilarek, J., Zawidzki, M. (eds) Ewa Orłowska on Relational Methods in Logic and Computer Science. Outstanding Contributions to Logic, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-97879-6_13

Download citation

Publish with us

Policies and ethics

Search

Navigation