An investigation of ideals in the set of fuzzy measures

Fuzzy Sets and Systems

Volumn 152, Issue 2, 2005, Pages 271-288

  Bronevich, A G ^a  

^a SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

Convex sum; Fuzzy measure; Ideal; Product

Indexed keywords

ALGEBRA; FUNCTIONS; MATHEMATICAL MODELS; PROBABILITY; RANDOM PROCESSES; THEOREM PROVING;

CONVEX SUM; FUZZY MEASURE; IDEAL; PRODUCT;

FUZZY SETS;

EID: 17444426659     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2004.09.012     Document Type: Article

References (14)

1. A.G. Bronevich, and A.N. Karkishchenko About ideals on the set of fuzzy measures Soft Methods in Probability, Statistics and Data Analysis 2002 Physica-Verlag Heidelberg, New York 76 83
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. Chateauneuf, and J.Y. Jaffray Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion Math. Social Sci. 17 1989 263 283
4. S.N. Chernikov Linear Inequalities 1971 Moscow Nauka (in Russian)
5. A.P. Dempster Upper and lower probabilities induced by multivalued mapping Ann. Math. Statist. 38 1967 325 339
6. D. Denneberg Non-additive measure and integral, basic concepts and their role for applications M. Grabisch T. Murofushi M. Sugeno Fuzzy Measures and Integrals - Theory and Applications. Studies on Fuzzyness and Soft Computing 2000 Physica-Verlag Heidelberg 42 69
7. D. Dubois, and H. Prade A set-theoretic view of belief functions - Logical operations and approximation by fuzzy sets Internat. J. General Systems 12 1986 193 226
8. D. Dubois, and H. Prade Possibility Theory 1988 Plenum Press New York
9. D. Dubois, and H. Prade When upper probabilities are possibility measures Fuzzy Sets and Systems 24 1992 279 300
10. M. Grabisch, H.T. Nguyen, and E.A. Walker Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference 1995 Kluwer Academic Publishers New York
11. V.V. Prasolov Polynomials 2001 MCNMO Publishers Moscow (in Russian)
12. G. Shafer A Mathematical Theory of Evidence 1976 Princeton University Press Princeton, NJ
13. M. Sugeno Fuzzy measure and fuzzy integral Trans. SICE 8 1972 95 102
14. P. Walley Statistical Reasoning with Imprecise Probabilities 1991 Chapman & Hall London