Skip to main content

A Concept Map Approach to Approximate Reasoning with Fuzzy Extended Logic

  • Chapter
  • First Online:
Fuzzy Technology

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 335))

Abstract

Concept maps and Lotfi Zadeh’s fuzzy extended logic are applied to such computerized approximate reasoning models as modus ponens and modus tollens. A statistical application is also sketched. A pedagogical approach is mainly adopted, but these ideas are also applicable to the conduct of inquiry in general.

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 EPUB and 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
Hardcover Book
USD 109.99
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

  1. Ausubel, D.: Educational Psychology: A Cognitive View, Holt. Rinehart & Winston, New York (1968)

    Google Scholar 

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

    Google Scholar 

  3. Bai, S.H., Chen, S.M.: Automatically constructing concept maps based on fuzzy rules for adapting learning systems. Expert Syst. Appl. 35(1–2), 41–49 (2008)

    Article  Google Scholar 

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

    Google Scholar 

  5. Barabasi, A.L.: Linked. Plume, New York (2003)

    Google Scholar 

  6. Carnap, R.: The Logical Foundations of Probability, The University of Chicago Press, Chicago (1962)

    Google Scholar 

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

    Google Scholar 

  8. Fullér, R.: Fuzzy Reasoning and Fuzzy Optimization. TUCS General Publications No. 9, Turku Centre for Computer Science, Turku (1998)

    Google Scholar 

  9. Gadamer, H.-G.: Truth and Method. Sheed & Ward, London (1975)

    Google Scholar 

  10. Haack, S.: Philosophy of Logics. Cambridge University Press, Cambridge (1978)

    Book  MATH  Google Scholar 

  11. Hempel, C.: Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. The Free Press, New York (1965)

    Google Scholar 

  12. Hempel, C.: Philosophy of Natural Science. Prentice Hall, Englewood Cliffs (1966)

    Google Scholar 

  13. Hintikka, J., Suppes, P. (eds.): Information and Inference. Reidel, Dordrecht (1970)

    MATH  Google Scholar 

  14. Kemeny, J., Oppenheim, P.: Degree of factual support. Philos. Sci. 19(4), 307–324 (1952)

    Article  Google Scholar 

  15. Kim, S., Lee, C.: 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  MATH  Google Scholar 

  16. Kosko, B.: Fuzzy Engineering, Prentice Hall, Upper Saddle River (1997)

    Google Scholar 

  17. Lau, R., et al.: Towards fuzzy domain ontology based concept map generation for E-learning. Lecture Notes in Computer Science, vol. 4823, pp. 90–101 (2008)

    Google Scholar 

  18. Miao, Y., et al.: Dynamical cognitive network—an extension of fuzzy cognitive map. IEEE Trans. Fuzzy Syst. 9(5), 760–770 (2001)

    Google Scholar 

  19. Niiniluoto, I.: Tieteellinen päättely ja selittäminen (Scientific Reasoning and Explanation). Otava, Keuruu (1983)

    Google Scholar 

  20. Niiniluoto, I.: Truthlikeness. Reidel, Dordrecht (1987)

    Book  MATH  Google Scholar 

  21. Niskanen, V.A.: A Meta-level approach to approximate probability. In: Setchi, R., et al. (eds.) Lecture Notes in Artificial Intelligence, vol. 6279, pp. 116–123. Springer, Heidelberg (2010)

    Google Scholar 

  22. Niskanen, V.A.: Application of approximate reasoning to hypothesis verification. J. Intell. Fuzzy Syst. 21(5), 331–339 (2010)

    MathSciNet  MATH  Google Scholar 

  23. Niskanen, V.A.: Soft Computing Methods in Human Sciences, Studies in Fuzziness and Soft Computing, vol. 134. Springer, Berlin (2004)

    Book  MATH  Google Scholar 

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

    Google Scholar 

  25. Popper, K.: Conjectures and Refutations. Routledge & Kegan Paul, London (1963)

    Google Scholar 

  26. Popper, K.: The Logic of Scientific Discovery. Hutchinson, London (1959)

    MATH  Google Scholar 

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

    Google Scholar 

  28. Tseng, S., et al.: A new approach for constructing the concept map. Comput. Educ. 49, 691–707 (2007)

    Google Scholar 

  29. Wenstøp, F.: Quantitative Analysis with Linguistic Values. Fuzzy Sets Syst. 4, 99–115 (1980)

    Article  MATH  Google Scholar 

  30. von Wright, G.H.: The Logical Foundations of Probability. Blackwell, Oxford (1957)

    Google Scholar 

  31. Zadeh, L.: A note on modal logic and possibility theory. Inf. Sci. 279, 908–913 (2014)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  33. Zadeh, L.: From search engines to question answering systems? The problems of world knowledge, relevance, deduction and precisiation. In: Sanchez, E. (ed.) Fuzzy Logic and the Semantic Web. Elsevier, Amsterdam (2006)

    Google Scholar 

  34. Zadeh, L.: Fuzzy logic and approximate reasoning. Synthese 30, 407–428 (1975)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  36. Zadeh, L.: Toward extended fuzzy logic—a first step. Fuzzy Sets Syst. 160, 3175–3181 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  37. Zadeh, L.: 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  MATH  Google Scholar 

  38. Zadeh, L.: Toward a perception-based theory of probabilistic reasoning with imprecise probabilities. J. Stat. Plan. Inference 105(2), 233–264 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  39. Zar, J.: Biostatistical Analysis. Prentice Hall, Englewood Cliffs (1984)

    Google Scholar 

Download references

Acknowledgments

I express my thanks to Prof. Christer Carlsson in Ã…bo Akademi University who has constantly supported me in my scientific activities. I also thank Academician Janusz Kacprzyk for this opportunity to give my contribution for this book.

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

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Niskanen, V.A. (2016). A Concept Map Approach to Approximate Reasoning with Fuzzy Extended Logic. In: Collan, M., Fedrizzi, M., Kacprzyk, J. (eds) Fuzzy Technology. Studies in Fuzziness and Soft Computing, vol 335. Springer, Cham. https://doi.org/10.1007/978-3-319-26986-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26986-3_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26984-9

  • Online ISBN: 978-3-319-26986-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics