Skip to main content

Solving Zadeh’s Challenge Problems with the Application of RDM-Arithmetic

  • Conference paper
Artificial Intelligence and Soft Computing (ICAISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9119))

Included in the following conference series:

Abstract

The paper presents a simple method of CwW that is based on RDM-models of intervals and on the multidimensional RDM-interval arithmetic. The method is explained on the example of popular Zadeh’s challenge problem known as ‘Balls in a box’ problem. On the base of presented calculations, the general methodology of solving CwW problems with the application of simplified RDM-models of quantifiers is formulated.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aliev, R., Pedrycz, W., Fazlollahi, B., Huseynov, O.H., Alizadeh, A.V., Guirimov, B.G.: Fuzzy logic-based generalized decision theory with imperfect information. Information Sciences 189, 18–42 (2012)

    Article  MathSciNet  Google Scholar 

  2. Dymova, L.: Soft computing in economics and finance. Springer, Heidelberg (2011)

    Book  Google Scholar 

  3. Hansen, E.R.: A generalized interval arithmetic. In: Nickel, K. (ed.) Interval Mathematics. LNCS, vol. 29, pp. 7–18. Springer, Heidelberg (1975)

    Chapter  Google Scholar 

  4. Hanss, M.: Applied fuzzy arithmetic. Springer, Heidelberg (2005)

    Google Scholar 

  5. Kaufmann, A., Gupta, M.M.: Introduction to fuzzy arithmetic. Van Nostrand Reinhold, New York (1991)

    Google Scholar 

  6. Moore, R.E.: Interval analysis. Prentice Hall, Englewood Cliffs (1966)

    Google Scholar 

  7. Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to interval analysis. Society for Industrial and Applied Mathematics, Philadelphia (2009)

    Book  Google Scholar 

  8. Landowski, M.: Differences between Moore’s and RDM interval arithmetic. In: Angelov, P., et al. (eds.) Intelligent Systems’2014. AISC, vol. 322, pp. 331–340. Springer, Heidelberg (2015)

    Google Scholar 

  9. Piegat, A.: Fuzzy modeling and control. Physica Verlag, Heidelberg (2001)

    Book  Google Scholar 

  10. Piegat, A., Landowski, M.: Is the conventional interval-arithmetic correct? Journal of Theoretical and Applied Computer Science 6(2), 27–44 (2012)

    Google Scholar 

  11. Piegat, A., Landowski, M.: Two interpretations of multidimensional RDM interval arithmetic: multiplication and division. International Journal of Fuzzy Systems 15(4), 486–496 (2013)

    MathSciNet  Google Scholar 

  12. Piegat, A., Landowski, M.: Multidimensional approach to interval-uncertainty calculations. In: New Trends in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, pp. 137–152. System Research Institute of Polish Academy of Sciences, Warsaw (2013)

    Google Scholar 

  13. Rajati, M.R., Mendel, J.M., Wu, D.: Solving Zadeh’s Magnus challenge problem on linguistic probabilities via linguistic weighted averages. In: Proceedings of IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 2177–2184 (2011)

    Google Scholar 

  14. Rajati, M.R., Wu, D., Mendel, J.M.: On solving Zadeh’s tall Swedes problem. In: Proceedings of 2011 World Conference on Soft Computing (2011)

    Google Scholar 

  15. Rajati, M.R., Mendel, J.M.: Lower and upper probability calculations using compatibility measures for solving Zadeh’s challenge problems. In: Proceedings of IEEE International Conference on Fuzzy Systems, pp. 1–8 (2012)

    Google Scholar 

  16. Sevastjanov, P., Dymova, L.: A new method for solving interval and fuzzy equations: linear case. Information Sciences 17, 925–937 (2009)

    Article  MathSciNet  Google Scholar 

  17. Zadeh, L.A.: Fuzzy logic = computing with words. IEEE Transactions on Fuzzy Systems 4(2), 103–111 (1996)

    Article  MathSciNet  Google Scholar 

  18. Zadeh, L.A.: Linguistic characterization of preference relations as a basis for choice in social systems. In: Fuzzy Sets, fuzzy Logic, and Fuzzy Systems, pp. 336–354. World Scientific Publishing Co., Inc. (1996)

    Google Scholar 

  19. Zadeh, L.A.: A new direction in AI – toward a computational theory of perceptions. AI Magazine 22(1), 73–84 (2001)

    Google Scholar 

  20. Zadeh, L.A.: From computing with numbers to computing with words – from manipulation of measurements to manipulation of perceptions. International Journal of Applied Mathematics and Computer Science 12(3), 307–324 (2002)

    MathSciNet  Google Scholar 

  21. Zadeh, L.A.: A note on web intelligence, world knowledge and fuzzy logic. Data & Knowledge Engineering 50, 291–304 (2004)

    Article  Google Scholar 

  22. Zadeh, L.A.: Generalized theory of uncertainty (GTU) – principal concepts and ideas. Computational Statistics & Data Analysis 51, 15–46 (2006)

    Article  MathSciNet  Google Scholar 

  23. Zadeh, L.A.: Computations with imprecise probabilities. In: Proceedings of 7-th International Conference on Applications of Fuzzy Systems and Soft Computing (ICAFS 2008), pp. 1–3 (2008)

    Google Scholar 

  24. Zadeh, L.A.: Computing with words and perceptions – a paradigm shift. In: Proceedings of the 2009 IEEE International Conference on Information Reuse and Integration, pp. viii–x (2009)

    Google Scholar 

  25. Zadeh, L.A.: Computing with Words: Principal concepts and ideas. Springer (2012)

    Google Scholar 

  26. Zadeh, L.A., Kacprzyk, J.: Computing with Words in Information/Intelligent Systems 1: Foundations. Studies in Fuzziness and Soft Computing, vol. 33. Physica-Verlag HD (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marcin Pluciński .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Pluciński, M. (2015). Solving Zadeh’s Challenge Problems with the Application of RDM-Arithmetic. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2015. Lecture Notes in Computer Science(), vol 9119. Springer, Cham. https://doi.org/10.1007/978-3-319-19324-3_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19324-3_22

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19323-6

  • Online ISBN: 978-3-319-19324-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics