Aggregation Operators for Fuzzy Rationality Measures

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 12)


Fuzzy rationality measures represent a particular class of aggregation operators. Following the axiomatic approach developed in [1,3,4,5] rationality of fuzzy preferences may be seen as a fuzzy property of fuzzy preferences. Moreover, several rationality measures can be aggregated into a global rationality measure. We will see when and how this can be done. We will also comment upon the feasibility of their use in real life applications. Indeed, some of the rationality measures proposed, though intuitively (and axiomatically) sound, appear to be quite complex from a computational point of view.


aggregation rules fuzzy preferences decision making. 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. Cutello and J. Montero. An axiomatic approach to fuzzy rationality. In: K.C. Min, Ed., IFS A’93 (Korea Fuzzy Mathematics and Systems Society, Seou1, 1993 ), 634–636.Google Scholar
  2. 2.
    V. Cutello and J. Montero. A characterization of rational amalgamation operations. International Journal of Approximate Reasoning 8: 325–344 (1993).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    V. Cutello and J. Montero. Equivalence of Fuzzy Rationality Measures. In: H.J. Zimmermann, Ed., EUFIT’93 ( Elite Foundation, Aachen, 1993 ), vol. 1, 344–350.Google Scholar
  4. 4.
    V. Cutello and J. Montero. Fuzzy rationality measures. Fuzzy sets and Systems 62: 39–54 (1994).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    V. Cutello and J. Montero. Equivalence and Composition of Fuzzy rationality measures. Fuzzy sets and Systems, 1995. To Appear.Google Scholar
  6. 6.
    J.C. Fodor and M. Roubens. Preference modelling and aggregation procedures with valued binary relations. In: R. Lowen and M. Roubens, Eds., Fuzzy Logic ( Kluwer Academic Press, Amsterdam, 1993 ), 29–38.CrossRefGoogle Scholar
  7. 7.
    J.C. Fodor and M. Roubens. Valued preference structures. European Journal of Operational Research 79: 277–286 (1994).zbMATHCrossRefGoogle Scholar
  8. 8.
    J.C. Fodor and M. Roubens. Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Pub., Dordrecht, 1994.zbMATHCrossRefGoogle Scholar
  9. 9.
    M.R. Garey and D.S. Johnson. Computer and Intractability: a Guide to the Theory of NP-Completeness. Freeman, San Francisco, 1978.Google Scholar
  10. 10.
    M. Gondran and M. Minoux. Graphs and Algorithms. Wiley, Chichester, 1984.zbMATHGoogle Scholar
  11. 11.
    L. Kitainik. Fuzzy Decision Procedures with Binary Relations- Kluwer Academic Pub., Boston, 1993.Google Scholar
  12. 12.
    J. Montero. Arrow’s theorem under fuzzy rationality. Behavioral Science, 32: 267–273 (1987).MathSciNetCrossRefGoogle Scholar
  13. 13.
    J. Montero. Social welfare functions in a fuzzy environment. Kybernetes, 16: 241–245 (1987).MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    J. Montero. Rational aggregation rules. Fuzzy Sets and Systems 62: 267–276 (1994).MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    J. Montero, J. Tejada and V. Cutello. A general model for deriving preference structures from data. European Journal of Operational Research,to appear.Google Scholar
  16. 16.
    S.E. Orlovski. Calculus of Decomposable Properties, Fuzzy Sets and Decisions. Allerton Press, New York. 1994.zbMATHGoogle Scholar
  17. 17.
    U. Thole, H.J. Zimmermann and P. Zysno. On the suitability of minimum and product operators for the intersection of fuzzy sets. Fuzzy sets and Systems, 2: 167–180 (1979).zbMATHCrossRefGoogle Scholar
  18. 18.
    R..R. Yager. On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on Systems, Man and Cybernetics, 18: 183–190 (1988).MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    R.R. Yager. Connectives and quantifiers in fuzzy sets. Fuzzy sets and Systems, 40: 39–75 (1991).MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    R.R. Yager. Families of owa operators. Fuzzy sets and Systems, 59: 125–148 (1993).MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    L.A. Zadeh. Similarity relations and fuzzy orderings. Information Science, 3: 177–200 (1971).MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CataniaCataniaItaly
  2. 2.Faculty of MathematicsComplutense UniversityMadridSpain

Personalised recommendations