Skip to main content

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 243))

  • 1338 Accesses

Introduction

In 1977 as a (relatively) young assistant professor I was invited to deliver a tutorial on fuzzy sets in decision making at the meeting on subjective probability, utility and decision making (SPUDM) in Warsaw. Apparently, the well-known Polish social psychologist and methodologist Maria Nowakowska with whom I had been in correspondence for some years had suggested my name to the local organizers of the meeting. The invitation was naturally a great honor to me although the meaning of the word “tutorial” was not known to me at the time. It turned out that I was to give a plenary lecture to an international audience of distinguished decision analysts, psychologists, methodologists and management scientists. In those days the fuzzy systems were not considered standard background knowledge of people working on individual decision making. Sometimes I doubt that times have changed much in this regard.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bellman, R., Zadeh, L.A.: Decision-Making in a Fuzzy Environment. Management Science (17), B-141–B-164 (1970)

    Article  MathSciNet  Google Scholar 

  2. Bezdek, J.C., Spillman, B., Spillman, R.: Fuzzy Relation Space for Group Decision Theory. Fuzzy Sets and Systems (1), 255–268 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  3. Blin, J.M.: Fuzzy Relations in Group Decision Theory. Journal of Cybernetics (4), 17–22 (1974)

    Article  Google Scholar 

  4. Bunge, M.: Scientific Research, vol. I. Springer, Berlin (1967)

    MATH  Google Scholar 

  5. Coughlin, P.: Pareto Optimality of Policy Proposals with Probabilistic Voting. Public Choice (39), 427–433 (1982)

    Article  Google Scholar 

  6. Downs, A.: An Economic Theory of Democracy. Harper and Row (1957)

    Google Scholar 

  7. Fine, K.: Vagueness, Truth and Logic. Synthese (30), 265–300 (1975)

    Article  MATH  Google Scholar 

  8. Hinich, M., Ordeshook, P., Ledyard, J.: A Theory of Electoral Equilibrium: A Spatial Analysis Based on the Theory of Games. Journal of Politics (35), 154–193 (1973)

    Article  Google Scholar 

  9. Intriligator, M.D.: A Probabilistic Model of Social Choice. Review of Economic Studies (40), 553–560 (1973)

    Article  Google Scholar 

  10. Intriligator, M.D.: Probabilistic Models of Choice. Mathematical Social Sciences (2), 157–166 (1982)

    Article  MATH  Google Scholar 

  11. Knopfmacher, J.: On Measures of Fuzziness. Journal of Mathematical Analysis and Applications (49), 529–534 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  12. McKelvey, R.D.: General Conditions for Global Intransitivities in Formal Voting Models. Econometrica (47), 1085–1112 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  13. Negoita, C.V., Ralescu, D.A.: Applications of Fuzzy Sets to Systems Analysis. Birkhäuser, Basel (1975)

    MATH  Google Scholar 

  14. Nurmi, H.: Approaches to Collective Decision Making with Fuzzy Preference Relations. Fuzzy Sets and Systems (6), 249–259 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  15. Nurmi, H.: Probability and Fuzziness: Some Methodological Considerations. In: Sjöberg, L., Tyszka, T., Wise, J.M. (eds.) Human Decision Making, Doxa (1983)

    Google Scholar 

  16. Nurmi, H.: Probabilistic Voting: A Fuzzy Interpretation and Extension. Political Methodology (10), 81–95 (1984)

    Google Scholar 

  17. Nurmi, H., Kacprzyk, J.: Fuzzy Sets in Political Science: An Overview. New Mathematics and Natural Computation (3), 281–299 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  18. Page, B.: The Theory of Political Ambiguity. American Political Science Review (70), 742–752 (1976)

    Article  Google Scholar 

  19. Pawlak, Z.: Rough Sets. International Journal of Information & Computer Sciences (11), 341–356 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  20. Pawlak, Z.: Rough Sets – Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)

    MATH  Google Scholar 

  21. Pawlak, Z., Słowinski, R.: Decision Analysis Using Rough Sets. International Transactions in Operational Research (1), 107–114 (1994)

    Article  MATH  Google Scholar 

  22. Saari, D.G.: Mathematical Structure of Voting Paradoxes. Economic Theory (15), 1–53 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  23. Salmon, W.C.: The Foundations of Scientific Inference. University of Pittsburgh Press, Pittsburgh (1967)

    Google Scholar 

  24. Salmon, W.C.: Statistical Explanation. In: Salmon, W.C. (ed.) Statistical Explanation and Statistical Relevance. University of Pittsburgh Press, Pittsburgh (1971)

    Google Scholar 

  25. Schofield, N.: Generic Instability of Majority Rule. Review of Economic Studies (50), 695–705 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  26. Shepsle, K.: Parties, Voters and Risk Environment. In: Niemi, R., Weisberg, H. (eds.) Probability Models of Collective Decision-Making. Merrill, Ohio (1972)

    Google Scholar 

  27. Simon, H.: How Complex Are Complex Systems. In: Suppe, F., Asquith, P. (eds.) PSA 1976, Philosophy of Science Association, vol. 2 (1976)

    Google Scholar 

  28. Terano, T., Sugeno, M.: Conditional Fuzzy Measures and Their Applications. In: Zadeh, L.A., Fu, K.-S., Tanaka, K., Shimura, M. (eds.) Fuzzy Sets and Their Applications to Cognitive and Decision Processes. Academic Press, New York (1975)

    Google Scholar 

  29. Weaver, W.: Science and Complexity. American Scientist 36, 536 (1948)

    Google Scholar 

  30. Zadeh, L.A.: Fuzzy Sets. Information and Control (8), 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Nurmi, H. (2009). Probability and Fuzziness – Echoes from 30 Years Back. In: Seising, R. (eds) Views on Fuzzy Sets and Systems from Different Perspectives. Studies in Fuzziness and Soft Computing, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93802-6_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-93802-6_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-93801-9

  • Online ISBN: 978-3-540-93802-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics