A NOTE ON THE MONOTONE INTERVAL-VALUED SET FUNCTION DEFINED BY THE INTERVAL-VALUED CHOQUET INTEGRAL

- Journal title : Communications of the Korean Mathematical Society
- Volume 22, Issue 2, 2007, pp.227-234
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2007.22.2.227

Title & Authors

A NOTE ON THE MONOTONE INTERVAL-VALUED SET FUNCTION DEFINED BY THE INTERVAL-VALUED CHOQUET INTEGRAL

Jang, Lee-Chae;

Jang, Lee-Chae;

Abstract

At first, we consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. In this paper we investigate some properties and structural characteristics of the monotone interval-valued set function defined by an interval-valued Choquet integral.

Keywords

interval-valued set functions;interval-valued functions;fuzzy measures;Choquet integrals;

Language

English

Cited by

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THE AUTOCONTINUITY OF MONOTONE INTERVAL-VALUED SET FUNCTIONS DEFINED BY THE INTERVAL-VALUED CHOQUET INTEGRAL,;

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On Choquet Integrals with Respect to a Fuzzy Complex Valued Fuzzy Measure of Fuzzy Complex Valued Functions,;;

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Some Properties of Choquet Integrals with Respect to a Fuzzy Complex Valued Fuzzy Measure,;;

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References

1.

J. Aubin, Set-valued analysis, 1990, Birkauser Boston

3.

M. J. Bilanos, L. M. de Campos and A. Gonzalez, Convergence properties of the monotone expectation and its application to the extension of fuzzy measures, Fuzzy Sets and Systems 33 (1989), 201-212

4.

L. M. de Campos and M. J. Bilanos, Characterization and comparison of Sugeno and Choquet integrals, Fuzzy Sets and Systems 52 (1992), 61-67

5.

W. Cong, RSu integral of interval-valued functions and fuzzy-valued functions redefined, Fuzzy Sets and Systems 84 (1996), 301-308

6.

L. C. Jang and J. S. Kwon, On the representation of Choquet integrals of set-valued functions and null sets, Fuzzy Sets and Systems 112 (2000), 233-239

7.

L. C. Jang, T. Kim, and J. D. Jeon, On set-valued Choquet intgerals and convergence theorems, Advanced Studies and Contemporary Mathematics 6 (2003), no. 1, 63-76

8.

L. C. Jang, T. Kim, and J. D. Jeon, On set-valued Choquet intgerals and convergence theorems (II), Bull. Korean Math. Soc. 40 (2003), no. 1, 139-147

9.

L. C. Jang, T. Kim, and D. Park, A note on convexity and comonotonically additivity of set-valued Choquet intgerals, Far East J. Appl. Math. 11 (2003), no. 2, 137-148

10.

L. C. Jang, T. Kim, J. D. Jeon, and W. J. Kim, On Choquet intgerals of measurable fuzzy number-valued functions , Bull. Korean Math. Soc. 41 (2004), no. 1, 95-107

11.

L. C. Jang, Interval-valued Choquet integrals and their applications, J. of Applied Mathematics and computing 16 (2004), no. 1-2, 429-443

12.

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 29 (1989), 201-227

13.

T. Murofushi and M. Sugeno, A theory of Fuzzy measures: representations, the Choquet integral, and null sets, J. Math. Anal. and Appl. 159 (1991), 532-549

14.

T. Murofushi and M. Sugeno, RSome quantities represented by Choquet integral, Fuzzy Sets and Systems 56 (1993), 229-235

15.

H. Suzuki, On fuzzy measures de칗ed by fuzzy integrals, J. of Math. Anal. Appl. 132 (1998), 87-101

16.

Z. Wang, The autocontinuity of set function and the fuzzy integral, J. of Math. Anal. Appl. 99 (1984), 195-218

17.

Z. Wang, On the null-additivity and the autocontinuity of fuzzy measure, Fuzzy Sets and Systems 45 (1992), 223-226

18.

Z. Wang, G. J. Klir, and W. Wang, Fuzzy measures defined by fuzzy integral and their absolute continuity, J. Math. Anal. Appl. 203 (1996), 150-165

19.

Z. Wang, G. J. Klir, and W. Wang, Monotone set functions defined by Choquet integral, Fuzzy measures defined by fuzzy integral and their absolute continuity, Fuzzy Sets and Systems 81 (1996), 241-250