[1] Ouyang Yao, Li Jun,. Some properties of monotone set functions definedby Choquet integral [J]. Journal of Southeast University (English Edition), 2003, 19 (4): 423-426. [doi:10.3969/j.issn.1003-7985.2003.04.025]

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Some properties of monotone set functions definedby Choquet integral()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

19

Issue:

2003 4

Page:

423-426

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2003-12-30

Info

Title:

Some properties of monotone set functions definedby Choquet integral

Author(s):

Ouyang Yao;  Li Jun

Department of Mathematics, Southeast University, Nanjing 210096, China

Keywords:

non-additive measure;  monotone set function;  Choquet integral

PACS:

O159

DOI:

10.3969/j.issn.1003-7985.2003.04.025

Abstract:

In this paper, some properties of the monotone set function defined by the Choquet integral are discussed. It is shown that several important structural characteristics of the original set function, such as weak null-additivity, strong order continuity, property(s)and pseudometric generating property, etc., are preserved by the new set function. It is also shown that C-integrability assumption is inevitable for the preservations of strong order continuous and pseudometric generating property.

References:

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[3] Wang Z, Klir G J. Fuzzy measure theory [M]. New York: Plenum Press, 1992. 95-111.
[4] Pap E. Null-additive set functions [M]. Dordrecht: Kluwer Academic Publishers, 1995. 10-218.
[5] Li J. Order continuity of monotone set function and convergence of measurable functions sequence [J]. Applied Mathematics and Computation, 2003, 135(2-3): 211-218.
[6] Sun Q. Property(s)of fuzzy measure and Riesz’s theorem [J]. Fuzzy Sets and Systems, 1994, 62(1): 117-119.
[7] Li J, Yasuda M, Jiang Q, et al. Convergence of sequence of measurable functions on fuzzy measure spaces [J]. Fuzzy Sets and Systems, 1997, 87(3): 317-323.
[8] Royden H L. Real analysis [M]. New York: Macmillan Com-pany, 1966.
[9] Jiang Q, Wang S, Ziou D, et al. Pseudometric generating property and autocontinuity of fuzzy measures [J]. Fuzzy Sets and Systems, 2000, 112(2): 207-216.
[10] Zhang Q, Xu Y, Du W. Lebesgue decomposition theorem for σ-finite signed fuzzy measures [J]. Fuzzy Sets and Systems, 1999, 101(3): 445-451.

Memo

Memo:

Biographies: Ouyang Yao(1973—), male, graduate; Li Jun(corresponding author), male, doctor, professor, lijun@seu.edu.cn.

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