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http://dx.doi.org/10.5391/JKIIS.2004.14.1.033

On comonotonically additive interval-valued functionals and interval-valued Choquet integrals(II)  

Jang, Lee-Chae (건국대 전산수학과)
Kim, Tae-Kyun (공주대 과학교육연구소)
Jeon, Jong-Duek (경희대 수학과)
Publication Information
Journal of the Korean Institute of Intelligent Systems / v.14, no.1, 2004 , pp. 33-38 More about this Journal
Abstract
In this paper, we will define comonotonically additive interval-valued functionals which are generalized comonotonically additive real-valued functionals in Schmeidler[14] and Narukawa[12], and prove some properties of them. And we also investigate some relations between comonotonically additive interval-valued functionals and interval-valued Choquet integrals on a suitable function space, cf.[9,10,11,13].
Keywords
fuzzy measures; interval-valued Choquet integrals; comonotonically additive functionals; Hausdorff metric;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 Y. Narukawa, T.Murofushi and M. Sugeno, Regular fuzzy measure and representation of comonotonically additive functional, Fuzzy Sets and Systems vol.112 pp.177-186, 2000.   DOI   ScienceOn
2 S. Ovchinnikov and A. Dukhovny, On order invariant aggregation functionals, J. of Mathematical Psychology, vol. 46, pp. 12-18, 2002.   DOI   ScienceOn
3 M. Sugeno, Y. Narukawa and T. Murofushi, Choquet integral and fuzzy measures on locally compact space, Fuzzy Sets and Systems, vol. 99, pp. 205 -211, 1998.   DOI   ScienceOn
4 F. Hiai and H. Umegaki, Integrals, conditional expectations, and martingales of multivalued functions, J. Multi. Analysis vol.7 pp. 149-182, 1977.   DOI
5 T. Murofushi and M. Sugeno, A theory of Fuzzy measures: representations, the Choquet integral, and null sets, J. Math. Anal. and Appl. vol. 159 pp. 532-549, 1991.   DOI
6 D. Schmeidler, Integral representation without additivity, Proc. Amer. Math. Soc., vol. 97, pp. 253-261, 1986.
7 L.C. Jang and T. Kim, On set-valued Choquet intgerals and convergence theorems, Advanced Studies and Contemporary Mathematics vol. 6, no. 1 pp. 63-76, 2003.
8 Y. Syau, On convex and concave fuzzy mappings, Fuzzy Sets and Systems , vol. 103, pp. 163-168, 1999.   DOI   ScienceOn
9 Y. Narukawa, T. Murofushi and M. Sugeno, Extension and representation of comonotonically additive functionals, Fuzzy Sets and Systems, vol. 121, pp. 217-226, 2001.   DOI   ScienceOn
10 L.C. Jang and J.S. Kwon, On the representation of Choquet integrals of set-valued functions and null sets, Fuzzy Sets and Systems vol.112 pp.233-239, 2000.   DOI   ScienceOn
11 L. C. Jang, B. M. Kil, Y. K. Kim and J. S. Kwon, Some properties of Choquet integrals of set -valued functions, Fuzzy Sets and Systems vol.91 pp.95-98, 1997.   DOI   ScienceOn
12 R. J. Aumann, Integrals of set-valued functions, J. Math. Appl. vol. 12 pp.1-12, 1965.
13 L.C. Jang and T. Kim, On set-valued Choquet intgerals and convergence theorems (II), J. of Fuzzy Logic and Intelligent Systems vol.12, no.4 pp.323-327, 2002.   과학기술학회마을   DOI   ScienceOn
14 L. M. Campos and M. J. Bolauos, Characterization and comparision of Sugeno and Choquet integrals, Fuzzy Sets and Systems vol. 52 pp. 61-67, 1992.   DOI   ScienceOn
15 T. Murofushi and M. Sugeno, An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure, Fuzzy Sets and Systems vol. 29 pp. 201-227, 1989.   DOI   ScienceOn
16 D. Zhang, On measurability of fuzzy number -valued functions, Fuzzy Sets and Systems, vol.120,pp.505-509, 2001.   DOI   ScienceOn
17 J. Aubin, Set-valued analysis, 1990, Birkauser Boston.