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Associative Aggregation Operators

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Aggregation Operators

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 97))

Abstract

An aggregation process occurs in many situations like in decision making or in statistical and economic measurement by aggregating expert’s opinions or by synthesizing judgements. So the typical situation is as follows:

Having n numerical values x 1,..., x n lying in an interval I of real numbers, the aggregation operator M defined on I n aggregates these numbers to a value of ℝ in an appropriate way so that the properties of M represent a model of the concrete situation.

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References

  1. Alsina, C., Frank, M.J., Schweizer, B. Associative functions on intervals. Bookmanuscript.

    Google Scholar 

  2. Calvo, T., De Baets, B. On a generalization of the absorption equation. Manuscript.

    Google Scholar 

  3. Calvo, T., De Baets, B., Fodor, J. The functional equation of Alsina and Frank for uninorms and nullnorms, Fuzzy Sets and Systems 120 (2001), 15–24.

    Article  Google Scholar 

  4. Czogala, E., Drewniak, J. Associative monotonic operations in fuzzy set theory. Fuzzy Seta and Systems 12 (1984), 249–269.

    Article  MathSciNet  MATH  Google Scholar 

  5. De Baets, B. Idempotent uninorms. Europ. J. Oper. Research 118 (1999), 631–642.

    Article  MATH  Google Scholar 

  6. Fodor, J.C. An extension of Fung-Fu’s theorem. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 4 (1996), 51–58.

    Article  MathSciNet  Google Scholar 

  7. Fodor, J., Calvo, T. Aggregation functions defined by t-norms and tconorms. In: Studies and Fuzziness, Ed. B. Bouchon-Meunier, PhysicaVerlag 1998, 36–48.

    Google Scholar 

  8. Fodor, J.C., Roubens, M. Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994).

    MATH  Google Scholar 

  9. Fodor, J.C., Yager,R.R, Rybalov, A. Structure of uninorms. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 5 (1997), 411–427.

    Article  MathSciNet  MATH  Google Scholar 

  10. Fung, L.W., Fu, K.S. An axiomatic approach to rational decision making in a fuzzy environment. In Zadeh, L.A., Fu, K.S., Tanaka, S., Shimura, M., editors, Fuzzy Sets and Their Applications to Cognitive and Decision Processes (1975), 227–256, Academic Press, New York.

    Google Scholar 

  11. Grabisch, M., Nguyen, H., Walker, E.A. Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference. Kluwer Academic Publishers, Dordrecht (1995)

    Google Scholar 

  12. Hajek, P. Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998).

    Book  MATH  Google Scholar 

  13. Klement, E.P., Mesiar, R., Pap, E. Triangular Norms. Kluwer Academic Publishers, Dordrecht-Boston-London (2000).

    MATH  Google Scholar 

  14. Klir, G.J., Yuan, B. Fuzzy Sets And Fuzzy Logic, Theory and Applications. Prentice Hall PTR, Upper Saddle River-New Jersey (1995).

    Google Scholar 

  15. Klement, E.P., Mesiar, R., Pap, E. on the relationship of associative compensatory operators to triangular norms and conorms. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 4 (1996), 129–144.

    MathSciNet  MATH  Google Scholar 

  16. Kolmogorov, A.N. Sur la notion de la moyenne. A.cad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. 12 (1930), 388–391.

    Google Scholar 

  17. Koch, R.J. Note on weak cutpoints in clans. Duke Math.J. 24 (1957), 611–615.

    Article  MathSciNet  MATH  Google Scholar 

  18. Kruse, R.L., Deely, J.J. Joint continuity of monotonic functions. Amer. Math. Soc. 76 (1969), 74–76.

    MathSciNet  MATH  Google Scholar 

  19. Li, Y-M., Shi,Z-K. Weak uniform aggregation operators Information Sciences 124 (2000), 317–323.

    MATH  Google Scholar 

  20. Ling, C.M. Representations of associative functions. Publ. Math. Debrecen 12 (1965), 189–212.

    MathSciNet  Google Scholar 

  21. Marichal, J.-L. Aggregation operators for multicriteria decision aid.PH.D. thesis, Institute of Mathematics, University of Liege, Belgium, 1999.

    Google Scholar 

  22. Mas, M., Mayor, G., Torrens, J. t-operators. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 7 (1999), 31–50.

    Article  MathSciNet  MATH  Google Scholar 

  23. Mostert P.S., Shields, A.L. On the structure of semigroups on a compact manifold with boundary. Ann. of Math. 65 (1957), 117–143.

    Article  MathSciNet  MATH  Google Scholar 

  24. Nagumo, M. Ober eine Klasse der Mittelwerte.Japan. J. of Math 6 (1930), 71–79.

    Google Scholar 

  25. Nelsen, R.B. An introduction to copulas. Volume 139 of Lecture Notes in Statistics (1999).

    Google Scholar 

  26. Paalman-De Miranda, A.B. Topological Semigroups. Volume 11 of Mathematical Centre Tracts. Matematisch Centrum, Amsterdam (1964).

    Google Scholar 

  27. Schweizer, B., Sklar, A. Probabilistic Metric Spaces. North-Holland, New York (1983).

    MATH  Google Scholar 

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© 2002 Physica-Verlag Heidelberg

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Sander, W. (2002). Associative Aggregation Operators. In: Calvo, T., Mayor, G., Mesiar, R. (eds) Aggregation Operators. Studies in Fuzziness and Soft Computing, vol 97. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1787-4_3

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  • DOI: https://doi.org/10.1007/978-3-7908-1787-4_3

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-00319-0

  • Online ISBN: 978-3-7908-1787-4

  • eBook Packages: Springer Book Archive

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