Skip to main content

Statistical Approach to Fuzzy Cognitive Maps

  • Chapter
  • First Online:

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 391))

Abstract

Fuzzy cognitive maps are studied from statistical standpoint. An analogy between these maps and linear regression and logistic regression models is drawn. Practical examples are also provided.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   249.99
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

Learn about institutional subscriptions

References

  1. R. Axelrod, Structure of Decision. The Cognitive Maps of Political Elites (Princeton University Press, Princeton, 1976)

    Google Scholar 

  2. H. Bandemer, W. Näther, Fuzzy Data Analysis (Kluwer, Dordrecht, 1992)

    Book  Google Scholar 

  3. M. Buruzs, M. Hatwágner L.T. Kóczy, Expert-based method of integrated waste management systems for developing fuzzy cognitive map, in Complex System Modelling and Control Through Intelligent Soft Computations. Studies in Fuzziness and Soft Computing, vol. 319, ed. by Q. Zhu, A. Azar (2015), pp. 111–137

    Google Scholar 

  4. J.P. Carvalho, J. Tome, Rule based fuzzy cognitive maps in socio-economic systems, in Proceedings of the IFSA Congress (Lisbon, 2009), pp. 1821–1826

    Google Scholar 

  5. S. Chiu, Fuzzy model identification based on cluster estimation. J. Intell. Fuzzy Syst. 2, 267–278 (1994)

    Article  Google Scholar 

  6. V. Dimitrov, B. Hodge, Social Fuzziology—Study of Fuzziness of Social Complexity (Physica Verlag, Heidelberg, 2002)

    MATH  Google Scholar 

  7. D. Freedman, Statistical models: Theory and practice (Cambridge University Press, Cambridge, 2005)

    Book  Google Scholar 

  8. Fuzzy Logic User’s Guide 2018a, Mathworks, 2018, www.mathworks.com/help/pdf_doc/fuzzy/fuzzy.pdf

  9. M. Glykas (ed.), Fuzzy Cognitive Maps (Springer, Heidelberg, 2010)

    MATH  Google Scholar 

  10. P. Grzegorzewski, O. Hryniewicz, M. Gil, Soft Methods in Probability. Statistics and Data Analysis (Physica Verlag, Heidelberg, 2002)

    Book  Google Scholar 

  11. M. Hatwagner, V. Niskanen L. Koczy, Behavioral analysis of fuzzy cognitive map models by simulation, in Proceedings of the IFSA ’17 Congress, Otsu, Japan, https://ieeexplore.ieee.org/abstract/document/8023345/

  12. S. Kim, C. Lee, Fuzzy implications of fuzzy cognitive map with emphasis on fuzzy causal relationship and fuzzy partially causal relationship. Fuzzy Sets Syst. 97(3), 303–3013 (1998)

    Article  MathSciNet  Google Scholar 

  13. B. Kosko, Fuzzy Engineering (Prentice Hall, Upper Saddle River, New Jersey, 1997)

    Google Scholar 

  14. K.C. Lee, W.J. Lee, O.B. Kwon, J.H. Han, P.I. Yu, Strategic planning simulation based on fuzzy cognitive map knowledge and differential game. Simulation 71(5), 316–327 (1998)

    Article  Google Scholar 

  15. R. Kruse, K. Meyer, Statistics with Vague Data (Reidel, Dordrecht, 1987)

    Book  Google Scholar 

  16. J. Metsämuuronen, Essentials in Research Methods in Human Sciences, Multivariate Analysis (Sage, London, 2017)

    Google Scholar 

  17. J. Metsämuuronen, Essentials in Research Methods in Human Sciences, Advanced Analysis (Sage, London, 2017)

    Google Scholar 

  18. V.A. Niskanen, Application of logistic regression analysis to fuzzy cognitive maps, in Fuzzy Logic Theory and Applications, vol. 2, ed. by L. Zadeh, R. Aliev (World Scientific Publishing, Singapore, 2019)

    Google Scholar 

  19. V.A. Niskanen, Concept map approach to approximate reasoning with fuzzy extended logic, in Fuzzy Technology: Present Applications and Future Technology, Studies in Fuzziness and Soft Computing, vol. 335, ed. by M. Fedrizzi, M. Collan, J. Kacprzyk, (Springer, Heidelberg, 2016), pp. 47–70

    Google Scholar 

  20. J. Novak, Learning, Creating, and Using Knowledge: Concept Maps as Facilitative Tools in Schools and Corporations (Lawrence Erlbaum Associates Inc, New Jersey, 1998)

    Book  Google Scholar 

  21. E. Papageorgiou, E. Stylios, P. Groumpos, Fuzzy cognitive map learning based on nonlinear Hebbian rule, in AI 2003. LNCS (LNAI), vol. 2903, ed. by T. Gedeon, L. Fung (Springer, 2003), pp. 256–268

    Google Scholar 

  22. W. Pedrycz, A. Jastrzebska, W. Homenda, Design of fuzzy cognitive maps for modeling time series. IEEE Transactions of Fuzzy Systems 24(1), 120–130 (2016)

    Article  Google Scholar 

  23. W. Stach, L. Kurgan, W. Pedrycz, Expert-based and computational methods for developing fuzzy cognitive maps, in Fuzzy Cognitive Maps, ed. by M. Glykas (Springer, 2010), pp. 24–41

    Google Scholar 

  24. W. Stach, L.A. Kurgan W. Pedrycz, Numerical and linguistic prediction of time series with the use of fuzzy cognitive maps. IEEE Trans. Fuzzy Syst. 16 (2008)

    Article  Google Scholar 

  25. W. Stach, L. Kurgan, W. Pedrycz, M. Reformat, Genetic learning of fuzzy cognitive maps. Fuzzy Sets Syst. 153, 371–401 (2005)

    Article  MathSciNet  Google Scholar 

  26. W. Stach, L. Kurgan, W. Pedrycz, A survey of fuzzy cognitive map learning methods. Issues Soft Comput. Theory Appl., pp. 71–84 (2005)

    Google Scholar 

  27. C. Stylios, P. Groumpos, Modeling complex systems using fuzzy cognitive maps. IEEE Trans. Syst. Man Cybern. Part A 34(1), 155–162 (2004)

    Article  Google Scholar 

  28. F. Wenstøp, Quantitative analysis with linguistic values. Fuzzy Sets Syst. 4, 99–115 (1980)

    Article  Google Scholar 

  29. L. Zadeh, Fuzzy logic = computing with words. IEEE Trans. Fuzzy Syst. 2, 103–111 (1996)

    Article  Google Scholar 

  30. L. Zadeh, Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 90(2), 111–127 (1997)

    Article  MathSciNet  Google Scholar 

  31. L. Zadeh, From computing with numbers to computing with words—from manipulation of measurements to manipulation of perceptions. IEEE Trans. Circ. Syst. 45, 105–119 (1999)

    Article  MathSciNet  Google Scholar 

  32. L. Zadeh, Toward a perception-based theory of probabilistic reasoning with imprecise probabilities. J. Stat. Plann. Infer. 105(2), 233–264 (2002)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

I express my thanks to the distinguished Editors for having this opportunity to be one of the contributors of this book. This article is dedicated to the memory of my mentor and friend, the great Professor Lotfi Zadeh.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vesa A. Niskanen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Niskanen, V.A. (2020). Statistical Approach to Fuzzy Cognitive Maps. In: Shahbazova, S., Sugeno, M., Kacprzyk, J. (eds) Recent Developments in Fuzzy Logic and Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 391. Springer, Cham. https://doi.org/10.1007/978-3-030-38893-5_3

Download citation

Publish with us

Policies and ethics