On the closure of families of fuzzy measures under eventwise aggregations

Fuzzy Sets and Systems

Volumn 153, Issue 1, 2005, Pages 45-70

  Bronevich, A G ^a  

^a SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

Aggregation operator; Coherent lower probability; Distortion function; Fuzzy measure; k monotonicity; Multilinear extension

Indexed keywords

ALGEBRA; DECOMPOSITION; FUNCTIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PROBABILITY;

AGGREGATION OPERATOR; COHERENT LOWER PROBABILITY; DISTORTION FUNCTIONS; FUZZY MEASURE; K-MONOTONICITY; MULTILINEAR EXTENSION;

FUZZY SETS;

EID: 18144409135     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2004.12.005     Document Type: Article

References (34)

1. A.G. Bronevich, An investigation of ideals in the set of fuzzy measures, Fuzzy Sets and Systems (2004) 18, accepted.
2. A.G. Bronevich, and A.N. Karkishchenko The structure of fuzzy measure families induced by upper and lower probabilities C. Bertoluzza M.A. Gil D.A. Ralescu Statistical Modeling, Analysis and Management of Fuzzy Data 2002 Physica-Verlag Heidelberg, New York 160 172
3. A.G. Bronevich, and A.E. Lepskiy Convolution operators of fuzzy measures Soft Methods in Probability, Statistics and Data Analysis 2002 Physica-Verlag Heidelberg, New York 84 91
4. M. Brüning, Products of monotone measures, Möbius transform, and k -monotonicity, Ph.D. Thesis, Bremen University, 2003.
5. T. Calvo, G. Mayor, R. Mesiar (Eds.), Aggregation Operators: Properties, Classes and Construction Methods, Aggregation Operators: New Trends and Applications, Physica-Verlag, Heidelberg, New York, 2002.
6. A. Chateauneuf Decomposable capacities, distorted probabilities and concave capacities Math. Social Sci. 31 1996 19 37
7. A. Chateauneuf, and J.Y. Jaffray Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion Math. Social Sci. 17 1989 263 283
8. G. Choquet Theory of capacities Ann. Inst. Fourier 5 1954 131 295
9. D. Denneberg Non-additive Measure and Integral 1997 Kluwer Dordrecht
10. D. Dubois Belief structure's possibility theory and decomposable confidence measures on finite sets Comput. Artif. Intell. 5 1986 403 416
11. D. Dubois, and H. Prade Possibility Theory 1988 Plenum Press New York
12. D. Dubois, and H. Prade Aggregation of possibility measures J. Kacprzyk M. Fedrizzi Multiperson Decision Making Using Fuzzy Sets and Possibility Theory 1990 Kluwer Academic Publishers Dordrecht 55 63
13. D. Dubois, J.C. Fodor, H. Prade, and M. Roubens Aggregation of decomposable measures with application to utility theory Theory and Decision 41 1996 59 95
14. A.O. Gelfond Calculi of Finite Differences 1967 Nauka Press Moscow (in Russian)
15. M. Grabisch k -order additive discrete fuzzy measures and their representation Fuzzy Sets and Systems 92 1997 167 189
16. M. Grabisch The interaction and Möbius representations of fuzzy measures on finite spaces, k -additive measures: a survey M. Grabisch T. Murofushi M. Sugeno Fuzzy Measures and Integrals - Theory and Applications, Studies on Fuzziness and Soft Computing 2000 Physica-Verlag Heidelberg
17. M. Grabisch, J.-L. Marichal, and M. Roubens Equivalent representations of set functions Math. Oper. Res. 25 2000 157 178
18. M. Grabisch, H.T. Nguyen, and E.A. Walker Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference 1995 Kluwer Academic Publishers New York
19. P.L. Hammer, and S. Rudeanu Boolean Methods in Operational Research and Related Areas 1968 Springer Berlin, Germany
20. K. Lehrer, and C.G. Wagner Rational Consensus in Science and Society 1981 D. Reidel Publ. Co. Boston
21. K. McConway Marginalization and linear opinion polls J. Amer. Statist. Assoc. 76 1981 410 414
22. R. Mesiar Choquet-like integrals J. Math. Anal. Appl. 194 1995 477 488
23. G. Owen Multilinear extensions of games A.E. Roth The Shapley Value. Essays in Honor of Lloyd S. Shapley 1988 Cambridge University Press Cambridge, UK 139 151
24. R. Pelessoni, and P. Visig Convex imprecise previsions, Basic issues and applications Proc. 3rd Internat. Symp. on Imprecise Probabilities and their Applications 2003 Lugano, Switzerland 421 434
25. A.W. Roberts, and D.E. Verberg Convex Functions 1973 Academic Press New York
26. G. Shafer A Mathematical Theory of Evidence 1976 Princeton University Press Princeton, NJ
27. M. Sugeno, Theory of fuzzy integrals and its applications, Doctoral Thesis, Tokyo Institute of Technology, 1974.
28. C.G. Wagner Consensus for belief functions and related uncertainty measures Theory and Decision 26 1989 295 304
29. P. Walley Statistical Reasoning with Imprecise Probabilities 1991 Chapman & Hall London
30. P. Walley Measures of uncertainty in expert systems Artificial Intelligence 83 1996 1 58
31. P. Walley Towards a unified theory of imprecise probability Int. J. Approx. Reason. 24 2000 125 148
32. A. Wallner Bi-elastic Neighbourhood models Proc. 3rd Internat. Symp. on Imprecise Probabilities and their Applications 2003 Lugano, Switzerland 591 605
33. S. Weber ⊥ -decomposable measures and integrals for Archimedean t -norms ⊥ J. Math. Anal. Appl. 101 1984 114 138
34. Q. Zhong On fuzzy measure and fuzzy integral on fuzzy set Fuzzy Sets and Systems 37 1990 77 92