Canonical hierarchical decomposition of Choquet integral over finite set with respect to null additive fuzzy measure

International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems

Volumn 6, Issue 4, 1998, Pages 345-363

  Fujimoto, Katsushige ^a   Murofushi, Toshiaki ^b   Sugeno, Michio ^b  

^a TOHOKU UNIVERSITY   (Japan)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Canonical hierarchical decomposition; IEC; Pre IEC; Semiatom

Indexed keywords

EID: 0006935658     PISSN: 02184885     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021848859800029X     Document Type: Article

References (14)

1. A. Chateauneuf and J.Y. Jaffray, "Some Characterization of Lower Probabilities and other monotone Capacities Through the Use of Möbius Inversion", Mathematical Social Sciences vol. 17, pp. 263-283, 1989.
2. K. Fujimoto, "On hierarchical decomposition of Choquet integral model", Doctoral Thesis, Tokyo Institute of Technology, 1995.
3. K. Fujimoto, T. Murofushi, "Some characterization of the systems represented by Choquet and multi-linear functionals through the use of Möbius inversion", International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 5, No. 5, pp. 547-562, 1997.
4. M. Grabisch and J.M. Nicolas, "Classification by fuzzy integral - performance and tests -", Fuzzy Sets and Systems, vol. 65, pp.255-271, 1994.
5. T. Murofushi and M. Sugeno, "A Theory of fuzzy measure: representation, the Choquet integral and null sets", J. Math. Anal. Appl., vol. 159, pp. 532-549, 1991.
6. T. Murofushi and K. Fujimoto, "Mathematical properties of semiatoms in the fuzzy measure theory", Proc. 4th Workshop for Fzzy Systems, pp. 6-9, 1994.
7. T. Murofushi, M. Sugeno, and K. Fujimoto, "Separated hierarchical decomposition of Choquet integral", International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 5, No. 5, pp. 563-586, 1997.
8. T. Murofushi, M. Sugeno, and M. Machida "Non-monotonic fuzzy measures and Choquet integral", Fuzzy sets and Systems. vol.64, pp. 73-86.1994.
9. G.A. Shafer, "A mathematical theory of evidence", Princeton Univ. Press., 1976.
10. M. Sugeno, "Theory of fuzzy integrals and its applications", Doctoral Thesis, Tokyo Institute of Technology, 1974.
11. M. Sugeno and S.H. Kwon, "A new approach to time series modeling with fuzzy measures and the Choquet integral", Proc. of FUZZ-IEEE/IFES '95, pp.799-804, 1995.
12. M. Sugeno, K. Fujimoto and T. Murofushi, "A hierarchical decomposition of Choquet integral model", International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems vol. 3, No. 1,pp. 1-15, 1995.
13. K. Tanaka and M. Sugeno, "A study on subjective evaluation of printed color image", International Journal of Apporoximate Reasoning vol. 5, pp. 213-222, 1991.
14. K. Tahani and J.M. Keller, "Information fusion on computer vision using the fuzzy integral", IEEE trans. on Systems, Man and Cybernetics, vol. 20, pp. 733-741, 1990.