Skip to main content

Fuzzy Concepts: Logic, Motivation, Application

  • Chapter
Systems Theory in the Social Sciences

Abstract

The present paper should mainly be considered as an elementary introduction to the motivations for using fuzzy concepts. We laid especial stress on providing arguments of rationality for the underlying logic. Some generalizations and applications of fuzzy sets have also been considered. For lack of space it was however not possible even to mention some applications in the following interesting fields: game — and decision theory, automata and algorithms, pattern recognition and cluster analysis. Also we will not report about progress in fuzzy algebra, fuzzy topological spaces, fuzzy graphs and so on. Some of these topics will be treated by other authors in this book some other fields, especially decision theory and its foundation, will be investigated by the present author in the near future.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Bellman, R., M. Giertz, On the analytic formalism of the theory of fuzzy sets, Univ. of Southern California, Techn. Rep. No. 71–20 (1971).

    Google Scholar 

  2. Birkhoff, G., Lattice Theory, Amer.Math.Soc.Colloq. Publ.Vol. 25, 1967.

    Google Scholar 

  3. Blin, J.M., K.S. Fu, A.B. Whinston, Application of pattern recognition to some problems in economics, Purdue Univ. H.C. Krannert Graduate School Reprint Series No. 416.

    Google Scholar 

  4. Blin, J.M., K.S. Fu, K.B. Moberg, A.B. Whinston, Pattern recognition and quantitative political theory, Purdue Univ. H.C. Krannert Graduate School Reprint Series No. 441.

    Google Scholar 

  5. Borkowski, L., (ed.) Jan Lukasiewicz, Selected Works, North-Holland, Amsterdam, 1970.

    Google Scholar 

  6. Carnap, R., R.C. Jeffrey, Studies in Inductive Logic and Probability I, Univ. of California Press, 1971.

    Google Scholar 

  7. Destouches-Février, P., La structure des théories physiques, PUF, Paris, 1951.

    Google Scholar 

  8. Finch, P.D., On the structure of quantum logic, J.Symb.Logic 34 (1969), pp. 275–282.

    Article  Google Scholar 

  9. deFinetti, B., La Prévision: ses lois logiques, ses sources subjectives, Ann.Inst.H.Poincaré 7 (1937), pp. 1–68.

    Google Scholar 

  10. Goguen, J.A., L-fuzzy sets, J.Math.Anal.Appl. 18 (1967), pp. 145–174.

    Article  Google Scholar 

  11. Grattan-Guinness, I., Fuzzy Membership Mapped onto Intervals and Many-Valued Quantities, mimeographed.

    Google Scholar 

  12. Hatten, M.L., A.B. Whinston, K.S. Fu, Fuzzy set and automata theory applied to economics, Purdue Univ. H.C. Krannert Graduate School Reprint Series No. 533.

    Google Scholar 

  13. Karp, C.R., Languages with Expressions of Infinite Length, North-Holland, Amsterdam, 1964.

    Google Scholar 

  14. Kochen, S., E.P. Specker, Logical structures arising in quantum theory, in: J.W. Addison, L. Henkin, A. Tarski (eds.), The Theory of Models, North-Holland, Amsterdam, 1972.

    Google Scholar 

  15. Lorenz, K., Dialogspiele als Semantische Grundlage von Logikkalkülen I, II, Arch.f.Math., Logik und Grundlagenforschung 11 (1968), pp. 32–55, 73–100.

    Article  Google Scholar 

  16. Lorenzen, P., Metamathematik, B. I., Mannheim, 1962.

    Google Scholar 

  17. Lukasiewicz, J., Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls, Comptes rendus des séances de la Société des Sciences et des Lettres de.Varsovie 23 (193o), Classe III, pp. 51–77.

    Google Scholar 

  18. Luxemburg, W.A.J., Non-Standard Analysis, Math.Dep., C.I. T., Pasadena, 1962.

    Google Scholar 

  19. Moore, R.E., Interval Analysis, Englewood Cliffs, 1966.

    Google Scholar 

  20. Prior, A.N., Three-valued logic and future Contingents, The Philosophical Quarterly 3 (1953), pp. 317–326.

    Article  Google Scholar 

  21. Reichenbach, H., Philosophische Grundlagen der Quantenmechanik, Birkhäuser, Basel, 1949.

    Google Scholar 

  22. Rosser, J.B., A.R. Turquette, Many-Valued Logics, North-Holland, Amsterdam, 1952.

    Google Scholar 

  23. Rosser, J.B., Simplified Independence Proofs, Academic Press, New York, 1969.

    Google Scholar 

  24. Scott, D., P. Krauss, Assigning probabilities to logical formulas, in Aspects of Inductive Logic (eds. J. Hintikka, P. Suppes ), pp. 113–132, North-Holland, Amsterdam, 1966.

    Google Scholar 

  25. Scott, D., A proof of the indeprendence of the Continuum Hypothesis, Math. Systems Theory 1(1967), pp. 89.-111.

    Google Scholar 

  26. Skala, H.J., Non-Archimedeàn Utility Theory, Reidel, Dordrecht/Boston, 1975.

    Book  Google Scholar 

  27. Skala, H.J., On the problem of imprecision, to appear.

    Google Scholar 

  28. Skala, H.J., Not necessarily additive realizations of comparative probability relations, to appear.

    Google Scholar 

  29. Skolem, T., Bemerkungen zum Komprehensionsaxiom, Zeitschrift f. math. Logik u. Grundlagen d. Math. 3 (1957 a), pp. 1–17.

    Google Scholar 

  30. Skolem, T., Mengenlehre gegründet auf einer Logik mit unendlich vielen Wahrheitswerten, Sitzungsberichte der Berliner Math. Gesellschaft (1957–58), pp. 41–56.

    Google Scholar 

  31. Varadarajan, V.S., Probability in physics and a theorem on simultaneous observability, Communications in Pure and Applied Mathematics 15 (1962), pp. 189–217.

    Article  Google Scholar 

  32. Zadeh, L.A., Fuzzy sets, Information and Control 8 (1965), pp. 338–353.

    Article  Google Scholar 

  33. Zadeh, L.A., A Fuzzy-Algorithmic Approach to the Definition of Complex or Imprecise Concepts, University of California, Berkeley, Memorandum No. ERL-M 474 (1974).

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1976 Springer Basel AG

About this chapter

Cite this chapter

Skala, H.J. (1976). Fuzzy Concepts: Logic, Motivation, Application. In: Systems Theory in the Social Sciences. Interdisciplinary Systems Research / Interdisziplinäre Systemforschung. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5495-5_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-5495-5_13

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-0822-3

  • Online ISBN: 978-3-0348-5495-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics