Some inequalities and convergence theorems for Choquet integrals

Journal of Applied Mathematics and Computing

Volumn 35, Issue 1-2, 2011, Pages 305-321

  Wang, Rui Sheng ^a  

^a RENMIN UNIVERSITY OF CHINA   (China)

Author keywords

Choquet integral; Convergence theorem; Inequality

Indexed keywords

ADDITIVES;

CHOQUET INTEGRAL; CLASSICAL PROBABILITIES; CONVERGENCE THEOREM; INEQUALITY; INTEGRAL INEQUALITIES; MEASURE THEORY; NON-ADDITIVE MEASURE; PROBABILITY MEASURES;

INTEGRAL EQUATIONS;

EID: 78651377364     PISSN: 15985865     EISSN: None     Source Type: Journal    
DOI: 10.1007/s12190-009-0358-y     Document Type: Article

References (22)

1. S. Auephanwiriyakul J. Keller P. Gader 2002 Generalized Choquet fuzzy integral fusion Inf. Fusion 3 69 85 10.1016/S1566-2535(01)00054-9
2. G. Choquet 1953 Theory of capacities Ann. Inst. Fourier 5 131 295 80760
3. L.M. de Campos M.J. Bolanos 1992 Characterization and comparison of Sugeno and Choquet integrals Fuzzy Sets Syst. 52 61 67 0782.28011 10.1016/0165-0114(92)90037-5
4. Denneberg, D.: Nonadditive Measure and Integral. Kluwer Academic, Dordrecht (1994)
5. L.C. Jang 1997 Some properties of Choquet integrals of set-valued functions Fuzzy Sets Syst. 91 1 95 98 0920.28018 10.1016/S0165-0114(96)00124-8 1481272
6. P. Meyera M. Roubensb 2006 On the use of the Choquet integral with fuzzy numbers in multiple criteria decision support Fuzzy Sets Syst. 157 927 938 10.1016/j.fss.2005.11.014
7. T. Murofushi M. Sugeno 1993 Some quantities represented by Choquet integral Fuzzy Sets Syst. 56 229 235 0816.28012 10.1016/0165-0114(93)90148-B 1223212
8. Pap, E.: Null-Additive Set Functions. Kluwer Academic, Dordrecht (1995)
9. D. Ralescu G. Adams 1980 The fuzzy integral J. Math. Anal. Appl. 75 562 570 0438.28007 10.1016/0022-247X(80)90101-8 581840
10. H. Román-Flores Y. Chalco-Cano 2007 Sugeno integral and geometric inequalities Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 15 1 1 11 1118.28012 10.1142/S0218488507004340
11. H. Román-Flores A. Flores-Franulič Y. Chalco-Cano 2007 A Jensen type inequality for fuzzy integrals Inf. Sci. 177 3192 3201 1127.28013 10.1016/j.ins.2007.02.006
12. H. Román-Flores A. Flores-Franulič Y. Chalco-Cano 2008 A convolution type inequality for fuzzy integrals Appl. Math. Comput. 195 94 99 1149.26033 10.1016/j.amc.2007.04.072 2379199
13. Sugeno, M.: Theory of fuzzy integrals and its applications. Ph.D. Thesis, Tokyo Inst. of Tech. (1974)
14. H. Tahani J.M. Keller 1990 Information fusion in computer vision using the fuzzy integral IEEE Trans. Syst. Man Cybern. 20 3 733 741 10.1109/21.57289
15. Z. Wang 1997 Convergence theorems for sequences of Choquet integrals Int. J. Gen. Syst. 26 133 143 0880.28015 10.1080/03081079708945174
16. Wang, Z., Klir, G.: Fuzzy Measure Theory. Plenum, New York (1992)
17. Z. Wang G.J. Klir W. Wang 1996 Monotone set functions defined by Choquet integrals Fuzzy Sets Syst. 81 241 250 0878.28011 10.1016/0165-0114(95)00181-6 1392784
18. R.S. Wang M.H. Ha 2006 On Choquet integrals of fuzzy-valued functions J. Fuzzy Math. 14 1 89 102 1100.28011 2211690
19. R.S. Wang M.H. Ha 2008 On the properties of sequences of fuzzy-valued Choquet integrable functions Fuzzy Optim. Decis. Mak. 7 4 417 431 1182.28024 10.1007/s10700-008-9040-3 2461183
20. R.S. Wang L.M. Wang M.H. Ha 2006 Choquet integrals on L-fuzzy sets J. Fuzzy Math. 14 1 151 164 1098.28009 2211694
21. C. Wu S. Wang M. Ma 1993 Generalized fuzzy integrals: part I. Fundamental concepts Fuzzy Sets Syst. 57 219 226 0786.28016 10.1016/0165-0114(93)90162-B 1229838
22. D. Zhang Z. Wang 1993 On set-valued fuzzy integrals Fuzzy Sets Syst. 56 63 67 10.1016/0165-0114(93)90361-K