Fuzzy Sets pp 87-91 | Cite as

Developments in the Wake of the Theory of Possibility

  • Ellen Hisdal


The theory of possibility has introduced new concepts into the theory of fuzzy subsets of multidimensional universes, and has clarified some of the concepts which were already in use. It has also contributed to our seeing the theory of fuzzy sets in a wider perspective. Boolean sets, max-min fuzzy sets and probabilistic sets can be considered as special cases of a more generalized class of fuzzy set systems.


Fuzzy Subset Conjunctive Proposition Fuzzy Connective Possibilistic Variable Joint Relation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Bellman and M. Giertz, “On the Analytic Formalism of the Theory of Fuzzy Sets,” Information Sciences 5 (1973), 149–156.CrossRefGoogle Scholar
  2. 2.
    B. R. Gaines, “Foundations of Fuzzy Reasoning,” Int. J. Man-Machine Studies 8 (1976), 623–668.CrossRefGoogle Scholar
  3. 3.
    J. A. Goguen, “The Logic of Inexact Concepts,” Synthese 19 (1969), 325–373.CrossRefGoogle Scholar
  4. 4.
    E. Hisdal, “Conditional Possibilities, Independence and Noninteraction,” Fuzzy Sets and Systems 1 (1978), 283–297.CrossRefGoogle Scholar
  5. 5.
    E. Hisdal, “Possibilistically Dependent Variables and a General Theory of Fuzzy Sets,” in: Advances in Fuzzy Set Theory and Applications, M. M. Gupta, R. K. Ragade, R. R. Yager, eds., North Holland (1979).Google Scholar
  6. 6.
    E. Hisdal, “Generalized Fuzzy Set Systems and Particularization,” Fuzzy Sets and Systems, to be published. Institute of Informatics, University of Oslo, Box 1080, Blindem, Oslo 3, Norway.Google Scholar
  7. 7.
    H. T. Nguyen, “On Conditional Possibility Distributions,” Fuzzy Sets and Systems 1 (1978), 299–309.CrossRefGoogle Scholar
  8. 8.
    U. Thole, H.-J. Zimmermann, P. Zysno, “On the Suitability of Minimum and Product Operators for the Intersection of Fuzzy Sets,” Fuzzy Sets and Systems 2 (1979), 167–180.CrossRefGoogle Scholar
  9. 9.
    R. R. Yager, “On a General Class of Fuzzy Connectives,” Tech. Report No. RRY 78–18, Iona College, New Rochelle, NY 10801.Google Scholar
  10. 10.
    L. A. Zadeh, “Fuzzy Sets as a Basis for a Theory of Possibility,” Fuzzy Sets and Systems 1 (1978), 3–28.CrossRefGoogle Scholar
  11. 11.
    L. A. Zadeh, “Calculus of Fuzzy Restrictions,” in: Fuzzy Sets and their Applications to Cognitive and Decision Processes, L. A. Zadeh, K. S. Fu, K. Tanaka, M. Shimura, eds., Academic Press, New York, (1975).Google Scholar
  12. 12.
    L. A. Zadeh, “Outline of a New Approach to the Analysis of Complex Systems and Decision Processes,” IEEE Transactions on Systems, Man and Cybernetics SMC-3 (1973), 28–44.Google Scholar
  13. 13.
    L. A. Zadeh, “PRUF—A Meaning Representation Language for Natural Languages,” Int. J. Man-Machine Studies 10 (1978), 395–460.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Ellen Hisdal
    • 1
  1. 1.Institute of InformaticsUniversity of OsloOslo 3Norway

Personalised recommendations