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Extremal fuzzy integrals

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Abstract

Fuzzy integral is a monotone idempotent functional on a fuzzy measure. The extremal fuzzy integrals are introduced. Regular fuzzy integrals do not distinguish functions not distinguishable by the underlying fuzzy measures. These integrals include Choquet, Sugeno, Shilkret and several other well known integrals.

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References

  1. Benvenuti P, Mesiar R (2000) Integrals with respect to a general fuzzy measure. In: Grabisch M, Murofushi T, Sugeno M (eds) Fuzzy measures and integrals. Theory and applications. Physica-Verlag, Heidelberg, pp 205–232

  2. Benvenuti P, Mesiar R, Vivona D (2002) Monotone set functions-based integral. In: Pap E (ed) Handbook of measure theory. Elsevier, Amsterdam

  3. Calvo T, Kolesárová A, Komorní ková M, Mesiar R (2002) Aggregation operators: properties, classes and construction methods. In: Calvo T, Mayor G, Mesiar R (eds) Studies in fuzziness and soft computing, vol 97. Springer, Berlin Heidelberg New York, pp 3–104

  4. Choquet G (1953–1954) Theory of capacities. Ann Inst Fourier 5: pp 131–295

    Google Scholar 

  5. Denneberg D (1994) Non-additive measure and integral. Kluwer, Dordrecht

  6. Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York

  7. Fodor JC, Roubens M (1994) Fuzzy preference modelling and multicriteria decision support. Kluwer, Dordrecht

  8. Grabisch M, Murofushi T, Sugeno M (eds) (2000) Fuzzy measures and integrals. Theory and applications. Physica-Verlag, Heidelberg (2000)

  9. Klement EP, Mesiar R, Pap E (2000) Triangular norms. Trends in Logic, vol 8. Studia Logica Library, Kluwer, Dordrecht

  10. Klement EP, Mesiar R, Pap E (2004) Measure-based aggregation operators. Fuzzy Sets and Syst 142: pp 3–14

    Google Scholar 

  11. Mesiar R, Mesiarová A (2004) Fuzzy integrals. LNAI 3131. Springer, Berlin Heidelberg New York pp 7–14

  12. Mesiar R, Mesiarová A Fuzzy integrals – what they are? Submitted

  13. Nelsen RB (1999) An introduction to copulas. Lecture notes in statistics, vol 139. Springer, Berlin Heidelberg New York

  14. Pap E (1995) Null-additive set functions. Ister Science Bratislava & Kluwer, Dordrecht

  15. Shilkret N (1971) Maxitive measures and integration. Indag Math 33: pp 109–116

    Google Scholar 

  16. Sugeno M (1974) Theory of fuzzy integrals and applications. PhD Thesis, Tokyo Inst. of Technology, Tokyo

  17. Vitali G (1925) Sulla definizione di integrale delle funzioni di una variabile. Ann Mat Pura Ed Appl IV 2: pp 111–121

    Google Scholar 

  18. Wang Z, Klir G (1992) Fuzzy measure theory. Plenum Press, NY, USA

  19. Weber S (1986) Two integrals and some modified versions: critical remarks. Fuzzy Sets Syst 20: pp 97–105

    Google Scholar 

  20. Zadeh LA (1968) Probability measure of fuzzy events. J Math Anal Appl 23: pp 421–427

    Google Scholar 

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Correspondence to P. Struk.

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Struk, P. Extremal fuzzy integrals. Soft Comput 10, 502–505 (2006). https://doi.org/10.1007/s00500-005-0525-5

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