JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE AUTOCONTINUITY OF MONOTONE INTERVAL-VALUED SET FUNCTIONS DEFINED BY THE INTERVAL-VALUED CHOQUET INTEGRAL
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 30, Issue 1,  2008, pp.171-183
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2008.30.1.171
 Title & Authors
THE AUTOCONTINUITY OF MONOTONE INTERVAL-VALUED SET FUNCTIONS DEFINED BY THE INTERVAL-VALUED CHOQUET INTEGRAL
Jang, Lee-Chae;
  PDF(new window)
 Abstract
In a previous work [18], the authors investigated autocontinuity, converse-autocontinuity, uniformly autocontinuity, uniformly converse-autocontinuity, and fuzzy multiplicativity of monotone set function defined by Choquet integral([3,4,13,14,15]) instead of fuzzy integral([16,17]). We consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. Then the interval-valued Choquet integral determines a new nonnegative monotone interval-valued set function which is a generalized concept of monotone set function defined by Choquet integral in [18]. These integrals, which can be regarded as interval-valued aggregation operators, have been used in [10,11,12,19,20]. In this paper, we investigate some characterizations of monotone interval-valued set functions defined by the interval-valued Choquet integral such as autocontinuity, converse-autocontinuity, uniform autocontinuity, uniform converse-autocontinuity, and fuzzy multiplicativity.
 Keywords
monotone interval-valued set functions;interval-valued functions;fuzzy measures;Choquet integrals;
 Language
English
 Cited by
 References
1.
J. Aubin, Set-valued analysis, 1990, Birkauser Boston.

2.
R. J. Aumann, Integrals of set-valued Junctions, J. Math. Anal. Appl. 12 (1965), 1-12. crossref(new window)

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. crossref(new window)

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. crossref(new window)

5.
J. Fan and W. Xie, Distance measure and induced fuzzy entropy, Fuzzy Sets and Systems 52 (1992), 61-67. crossref(new window)

6.
L. C. Jang, B.M. Kil, YK. Kim and J. S. Kwon, Some properties of Choquet integrals of set-valued Junctions, Fuzzy Sets and Systems 91 (1997), 95-98. crossref(new window)

7.
L. C. Jang and J. S. Kwon, On the representation of Choquet integrals of set-valued Junctions and null sets, Fuzzy Sets and Systems 112 (1), 233-239. crossref(new window)

8.
L.C. Jang, T. Kim and J.D. Jeon, On set-valued Choquet intgerals and convergence theorems, Advanced Studies and Contemporary Mathematics 6(1) (2003), 63-76.

9.
L.C. Jang, T. Kim and J.D. Jeon, On set-valued Choquet intgerals and convergence theorems (II), Bull. Korean Math. Soc. 40(1) (2003), 139-147. crossref(new window)

10.
L.C. Jang, Interval-valued Choquet integrals and their applications, J. of Applied Mathematics and computing 16(1-2) (2004), 429-445.

11.
L.C. Jang, The application of interval-valued Choquet integrals in multicriteria decision aid, J. of Applied Mathematics and computing 20(1-2) (2006), 549-556.

12.
L.C. Jang, A note on the monotone interval-valued set Junction defined by interval-valued Choquet integral, Commun. Korean Math. Soc. 22(2) (2007), ***- *** crossref(new window)

13.
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. crossref(new window)

14.
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. crossref(new window)

15.
T.Murofushi and M. Sugeno, Some quantities represented by Choquet integral, Fuzzy Sets and Systems 56 (1993), 229-235. crossref(new window)

16.
Z. Wang, The autocontinuity of set Junction and the fuzzy integral, J. of Math. Anal. Appl. 99 (1984), 195-218. crossref(new window)

17.
Z. Wang, On the null-additivity and the autocontinuity of fuzzy measure, Fuzzy Sets and Systems 45 (1992), 223-226. crossref(new window)

18.
Z. Wang, G.J. Klir and W. Wang, Monotone set Junctions defined by Choquet integral, Fuzzy measures defined by fuzzy integral and their absolute continuity, Fuzzy Sets and Systems 81 (1996), 241-250. crossref(new window)

19.
W. Zeng and H. Li, Relationship between similarity measure and entropy of interval-valued fuzzy sets, Fuzzy Sets and Systems 157 (2006), 1477-1484. crossref(new window)

20.
D. Zhang, C.Guo and D. Liu, Set-valued Choquet integrals revisited, Fuzzy Sets and Systems 147 (2004), 475-485. crossref(new window)