Characterization of invariant aggregation operators

Fuzzy Sets and Systems

Volumn 142, Issue 1, 2004, Pages 63-73

  Mesiar, Radko ^a   Rückschlossová, Tatiana ^a  

^a SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

Author keywords

Aggregation operator; Choquet integral; Invariant aggregation operator; Invariant set

Indexed keywords

FUNCTIONS; FUZZY SETS; INTEGRAL EQUATIONS; INTEGRATION; INVARIANCE; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING; THEOREM PROVING;

CHOQUET INTEGRAL; INVARIANT AGGREGATION OPERATOR; INVARIANT SETS;

MATHEMATICAL OPERATORS;

EID: 0348230695     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2003.10.032     Document Type: Conference Paper

References (17)

1. L. Bartlomiejczyk, J. Drewniak, A characterization of sets and operations invariant under bijections, Aequatione Math., to be published.
2. Benvenuti P., Mesiar R. Integrals with respect to a general fuzzy measure. Grabisch M., Murofushi T., Sugeno M. Fuzzy Measures and Integrals. 2000;205-232 Physica-Verlag, Heidelberg.
3. Calvo T., Kolesárová A., Komorníková M., Mesiar R. A Review of Aggregation Operators. 2001;University of Alcala Press, Alcala de Henares.
4. Klir G.J., Folger T.A. Fuzzy Sets, Uncertainty, and Information. 1988;Prentice-Hall, Englewood Cliffs, NJ.
5. Kolesárová A., Komorníková M. Triangular norm-based iterative compensatory operators. Fuzzy Sets and Systems. 104:1999;109-120.
6. J.-L. Marichal, Aggregation operators for multicriteria decision aid, Ph.D. Thesis, University of Liége, Liége, Belgium, 1998.
7. Marichal J.-L. On Sugeno integral as an aggregation function. Fuzzy Sets and Systems. 114(3):2000;347-365.
8. J.-L. Marichal, On order invariant synthesizing functions, Proc. IPMU'2002', Annecy, pp. 1343-1348.
9. J.-L. Marichal, M. Roubens, Characterization of some stable aggregation functions, Proc. Internat. Conf. on Industrial Engineering and Production Management, Mons, Belgium, 1993, pp. 187-196.
10. R. Mesiar, Scale invariant operators, Proc. EUSFLAT'2001, Leicester, 2001, pp. 479-481.
11. Mesiar R., Komorníková M. Triangular norm-based aggregation of evidence under fuzziness. Bouchon-Meunier B. Aggregation and Fusion of Imperfect Information. 1998;11-35 Physica-Verlag, Heidelberg.
12. Ovchinnikov S., Dukhovny A. Integral representation of invariant functionals. J. Math. Anal. Appl. 244:2000;228-232.
13. Pap E. Null-Additive Set Functions. 1995;Kluwer Academic Publishers, Dordrecht.
14. T. Rückschlossová, Invariant aggregation operators, Proc. SCAM 2001, Bratislava, 2001, pp. 26-27.
15. T. Rückschlossová, Invariant subsets and monotone invariant operators, Proc. "Uncertainty Modelling", Bratislava, 2001, pp. 138-141.
16. Silvert W. Symmetric summation. a class of operations on fuzzy sets IEEE Trans. Systems Man Cybernet. 1:1979;657-659.
17. Wang Z., Klir G.J. Fuzzy Measure Theory. 1992;Plenum Press, New York.