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The Mathematical Framework of Fuzzy Logic

  • Bernard Fustier
Part of the Economic Studies in Inequality, Social Exclusion and Well-Being book series (EIAP, volume 3)

Keywords

Fuzzy Logic Fuzzy Number Membership Degree Fuzzy Subset Duality Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bellman RE, Giertz M (1973) On the Analytic Formalism of the Theory of Fuzzy Sets. Information Sciences 5:149–156.zbMATHCrossRefMathSciNetGoogle Scholar
  2. Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Management Science 17:141–164.MathSciNetCrossRefGoogle Scholar
  3. Bonissone PP, Decker KS (1986) Selecting Uncertainty Calculi and Granularity: An Experiment in Trading-Off Precision and Complexity. In: Kanal and Lemmer (eds), Uncertainty in Artificial Intelligence, Amsterdam, pp 217–247.Google Scholar
  4. Bouchon-Meunier B (1995) La logique floue et ses applications. Editions Addison-Wesley France, ParisGoogle Scholar
  5. Dubois D, Grabisch M (1994) Agrégation multicritère et optimisation. In: Logique floue, ARAGO 14-OFTA. Masson, Paris, pp 179–199.Google Scholar
  6. Dubois D, Prade H (1979) Fuzzy Real Algebra: Some Results. Fuzzy Sets and Systems 2:327–348.zbMATHCrossRefMathSciNetGoogle Scholar
  7. Dubois D, Prade H (1980) Fuzzy Sets and Systems: Theory and Applications. Academic Press, New YorkzbMATHGoogle Scholar
  8. Dubois D, Prade H (1985) A Review of Fuzzy Sets Aggregation Connectives. Information Sciences 36:85–121.zbMATHCrossRefMathSciNetGoogle Scholar
  9. Dubois D, Prade H (1986) Weighted Minimum and Maximum Operations. Fuzzy Sets Theory. Information Sciences 39:12–28.CrossRefMathSciNetGoogle Scholar
  10. Dubois D, Prade H (1991) On the ranking of ill-known values in possibility theory. Fuzzy Sets and Systems 43:311–317.zbMATHCrossRefMathSciNetGoogle Scholar
  11. Fodor J, Roubens M (1992) Aggregation and Scoring Procedures in Multicriteria Decision Making Methods. In: FUZZ-IEEE’92 (Actes de la 1ère Conférence Internationale sur les Systèmes Flous), San Diego, pp 13–21.Google Scholar
  12. Fodor J, Roubens M (1994) Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, DordrechtzbMATHGoogle Scholar
  13. Fustier B (1994) Approche qualitative d’un problème d’évaluation. Journal de Mathématiques du Maroc 2:81–86.Google Scholar
  14. Fustier B (2000) Evaluation, prise décision et logique floue. Economie appliquée 1:155–174.Google Scholar
  15. Fustier B, Serra D (2001) Sensibilité des sites touristiques. Une approche fondée sur la logique floue. Teoros 3:45–53.Google Scholar
  16. Lukasiewicz J (1928) Elements of Mathematical logic. Course given at the University of Warsaw, edited by Pergamon-Polish Scientific Publisher in 1963Google Scholar
  17. Mizumoto M (1989a) Pictoral Representations of Fuzzy Connectives: Cases of t-norms, t-conorms and Averaging Operators. Fuzzy Sets and Systems 31:217–242.CrossRefMathSciNetGoogle Scholar
  18. Mizumoto M (1989b) Pictoral Representations of Fuzzy Connectives: Cases of Compensatory Operators and Self-dual Operators. Fuzzy Sets and Systems 32:45–79.zbMATHCrossRefMathSciNetGoogle Scholar
  19. Ponsard C (1981a) An application of fuzzy subsets theory to the analysis of the consumer’s spatial preferences. Fuzzy Sets and Systems 5:235–244.zbMATHCrossRefMathSciNetGoogle Scholar
  20. Ponsard C (1981b) L’équilibre spatial du consommateur dans un contexte imprécis. Sistemi Urbani 3:107–133.Google Scholar
  21. Ponsard C (1982) Partial spatial equilibria with fuzzy constraints. Journal of Regional Science 22:159–175.CrossRefGoogle Scholar
  22. Ponsard C (1988) Les espaces économiques flous. In: Ponsard C (ed) Analyse économique spatiale, PUF, Paris, pp 355–389.Google Scholar
  23. Ponsard C, Fustier B (1986) Fuzzy Economics and Spatial Analysis. Collection de I’IME-CNRS: 32, Librairie de l’Université (diffuseur), DijonGoogle Scholar
  24. Werners B (1988) Aggregation Models in Mathematical Programming. In: Mitra G (ed) Mathematical Models for Decision Support, Berlin, New York, London, Paris, pp 295–319.Google Scholar
  25. Zadeh LA (1965) Fuzzy Sets. Information and Control 8:338–353.zbMATHCrossRefMathSciNetGoogle Scholar
  26. Zimmermann HJ (1991) Fuzzy set theory and its applications, Second edition. Kluwer Academic Publishers, NorwellzbMATHGoogle Scholar
  27. Zimmermann HJ (1993) The German Fuzzy Boom. Les clubs CRIN, La Lettre 4:3–4.zbMATHGoogle Scholar
  28. Zimmermann H J, Zysno P (1980) Latent Connectives in Human Decision Making. Fuzzy Sets and Systems 4:37–51.zbMATHCrossRefGoogle Scholar
  29. Zimmermann H J, Zysno P (1983) Decisions and Evaluations by Hierarchical Aggregation of Information. Fuzzy Sets and Systems 10:243–260.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Bernard Fustier
    • 1
  1. 1.University of CorsicaFrance

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