Skip to main content

Representations of Transitive Fuzzy Relations

  • Chapter
Aspects of Vagueness

Part of the book series: Theory and Decision Library ((TDLU,volume 39))

Abstract

Since Zadeh (1971) introduced similarity relations and fuzzy orderings, a great deal of work has been done in studying properties of these relations and their applications. The reader is referred to recent volumes edited by Gupta and Sanchez (1982), Yager (1982), and Gupta, Ragade and Yager (1979) for a representative sample of publications in this area.

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
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Altwegg, M.: 1950, ‘Zur axiomatik der teiweise geordneten mengen’ Comm.Math.Helv. 24, 149–155.

    Article  Google Scholar 

  • Bezdek, J.C.: 1981, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press.

    Google Scholar 

  • Birkhoff, G.: 1979, Lattice Theory, AMS Colloquium Publications, vol.25.

    Google Scholar 

  • Blin, J.M., and Whinston, A.B.: 1974, ‘Fuzzy sets and social choice’, J. of Cybernetics 3, 28–36.

    Article  Google Scholar 

  • Dugundji, J.: 1966, Topology, Allyn and Bacon, Inc., Boston.

    Google Scholar 

  • Fishburn, P.C.: 1973, ‘Binary choice probabilities: on the varieties of stochastic transitivity’, J. of Math.Psych.10, 327–352.

    Article  Google Scholar 

  • Goguen, J.A.: 1967, ‘L-fuzzy sets’, J. Math. Anal. and Appl. 18, 145–174.

    Article  Google Scholar 

  • Goodman, I.R.: 1982, ‘Fuzzy sets as equivalence classes of random sets’ in Yager 1982.

    Google Scholar 

  • Gupta, M.M., and Sanchez, E. (eds): 1982, Fuzzy Information and Decision Processes, North-Holland.

    Google Scholar 

  • Gupta, M.M., Ragade, R.K., and Yager, R.R. (eds): 1979, Advances in Fuzzy Set Theory and Applications, North-Holland.

    Google Scholar 

  • Klement, E.P.: 1981, ‘Operations on fuzzy sets and fuzzy numbers related to triangular norms’, in Proc. of the Ilth Intern. Symp. on Multiple-Valued Logic, Norman, Oklahoma, U.S.A., 218–225.

    Google Scholar 

  • Krantz, D.H., Luce, R.D., Suppes, P., and Tversky, A. : 1971, Foundations of Measurement, vol.1, Academic Press, N.Y.

    Google Scholar 

  • Luce, R.D., and Suppes, P. : 1965, ‘Preference, utility and subjective probability’, in Handbook of Mathematical Psychology, vol.III, John Willey and Sons, Inc., 249–410.

    Google Scholar 

  • Menger, K.: 1951, ‘Probabilistic theories of relations’, Proc.Nat.Acad.Sci. 37, no.3, 178–180.

    Article  Google Scholar 

  • Nurmi, H.: 1981, ‘Approaches to collective decision-making with fuzzy preference relations’, Fuzzy Sets and Systems 6, 249–259.

    Article  Google Scholar 

  • Ovchinnikov, S.V.: 1981, ‘Structure of fuzzy binary relations’ Fuzzy Sets and Systems 6, 169–165.

    Article  Google Scholar 

  • Ovchinnikov, S.V.: 1982a, ‘Social choice and Lukasiewicz logic’ in Proc. of the 12th Int. symp. on Multipl-Valued Logic, Paris, France, 163–166.

    Google Scholar 

  • Ovchinnikov, S.V.: 1982b, ‘Choice theory for cardinal scales’ in Gupta and Sanchez 1982, 323–338.

    Google Scholar 

  • Ovchinnikov, S.V., and Riera, T. : 1982, ‘On fuzzy classifications’, in Yager 1982, 119–132.

    Google Scholar 

  • Saaty, T.L.: 1980, The Analytic Hierarchy Process, McGraw-Hill International.

    Google Scholar 

  • Schweizer, B., and Sklar, A. : 1967, ‘Associative functions and abstract semigroups’, Publ.Math.Debrecen 10, 69–81.

    Google Scholar 

  • Skala, H.J. : 1982, ‘Modelling vagueness,’ in Gupta and Sanchez 1982.

    Google Scholar 

  • Szpilrajn, E.: 1930, ‘Sur l’extension de l’ordre partiel’, Fundamenta Mathematicae 16, 386–389.

    Google Scholar 

  • Yager, R.R. (ed): 1982, Recent Developments in Fuzzy Set and Possibility Theory, Pergamon Press.

    Google Scholar 

  • Zadeh, L.A.: 1971, ‘Similarity relations and fuzzy orderings’ Inf.Sci. 3, 177–200.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 D. Reidel Publishing Company

About this chapter

Cite this chapter

Ovchinnikov, S.V. (1984). Representations of Transitive Fuzzy Relations. In: Skala, H.J., Termini, S., Trillas, E. (eds) Aspects of Vagueness. Theory and Decision Library, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6309-2_7

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-6309-2_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-6311-5

  • Online ISBN: 978-94-009-6309-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics