Miranda Menéndez, Pedro and Grabisch, Michel
(2004)
*p-symmetric bi-capacities.*
Kybernetika, 40
(4).
pp. 421-440.
ISSN 0023-5954

PDF
Restricted to Repository staff only until 2020. 1MB |

Official URL: http://dml.cz/dmlcz/135605

## Abstract

Bi-capacities have been recently introduced as a natural generalization of capacities (or fuzzy measures) when the underlying scale is bipolar. They allow to build more flexible models in decision making, although their complexity is of order 3(n), instead of 2(n) for fuzzy measures. In order to reduce the complexity, the paper proposes the notion of p-symmetric bi-capacities, in the same spirit as for p-symmetric fuzzy measures. The main idea is to partition the set of criteria (or states of nature, individuals, ... ) into subsets whose elements are all indifferent for the decision maker.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | bi-capacity, bipolar scales, p-symmetry |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 17085 |

References: | A. Chateauneuf and J.-Y. Jaffray: Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion. Math. Social Sci. 17 (1989), 263-283. G. Choquet: Theory of capacities. Annales de l'Institut Fourier 5 (1953), 131-295. D. Denneberg: Non-additive Measures and Integral. Kluwer, Dordrecht 1994. D. Dubois and H. Prade: A class of fuzzy measures based on triangular norms. Internat. J. Gen. Systems 8 (1982), 43-61. M. Grabisch: Pattern classification and feature extraction by fuzzy integral. In: 3rd European Congress on Intelligent Techniques and Soft Computing (EUFIT, Aachen, Germany, August 1995), pp. 1465-1469. M. Grabisch: Fuzzy measures and integrals: A survey of applications and recent issues. In: Fuzzy Sets Methods in Information Engineering: A Guide Tour of Applications (D. Dubois, H. Prade, and R. Yager, eds.), Wiley, New York 1997, pp. 507-530. M. Grabisch: k-order additive discrete fuzzy measures. In: Proc 6th Internat. Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), Granada (Spain), 1996, pp. 1345-1350, M. Grabisch: k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems 92 (1997), 167-189. M. Grabisch and C. Labreuche: Bi-capacities. In: Proc. First Internat. Conference on Soft Computing and Intelligent Systems (SCIC), Tsukuba (Japan), 2002. M. Grabisch and C. Labreuche: Bi-capacities for decision making on bipolar scales. In: Proc Seventh Meeting of the EURO Working Group on Fuzzy Sets (EUROFUSE) Varenna (Italy), September 2002, pp. 185-190. M. Grabisch and Ch. Labreuche: Capacities on lattices and k-ary capacities. In: 3rd Internat. Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2003), Zittau, Germany, September 2003, pp. 304-307. P. L. Hammer and R. Holzman: On approximations of pseudo-boolean functions. Z. Oper. Res. - Math. Methods Oper. Res. 36 (1992), 3-21. T.W. Hungerford: Algebra. Springer-Verlag, Berlin 1980. R. Mesiar: k-order additive measures. Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 7(1999), 423-428. P. Miranda and M. Grabisch: p-symmetric fuzzy measures. In: Proc. Ninth Internat. Conference of Information Processing and Management of Uncertainty in Knowledgebased Systems (IPMU), Annecy (France), July 2002, pp. 545-552. P. Miranda, M. Grabisch, and P. Gil: p-symmetric fuzzy measures. Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 10 (2002), 105-123. Supplement. P. Miranda and E. F. Combarro, and P. Gil: p-symmetric bi-capacities. In: Proc. Second Internat. Summer School on Aggregation Operators and Their Applications (AGOP), Alcala de Henares (Spain), 2003, pp. 123-128. G. C. Rota: On the foundations of combinatorial theory I. Theory of Mobius functions. Z. Wahrschein. und Verwandte Gebiete 2 (1964), 340-368. M. Sugeno: Theory of Fuzzy Integrals and Its Applications. PhD Thesis, Tokyo Institute of Technology, 1974. M. Sugeno, K. Fujimoto, and T. Murofushi: A hierarchical decomposition of Choquet integral model. Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 1 (1995), 1-15. M. Sugeno and T. Terano: A model of learning based on fuzzy information. Kybernetes 6 (1977), 157-166. A. Tversky and D. Kahneman: Advances in prospect theory: cumulative representation of uncertainty. J. Risk and Uncertainty 5 (1992), 297-323. J. Sipos: Integral with respect to a pre-measure. Math. Slovaca 29 (1979), 141-155. S. Weber: J_-decomposable measures and integrals for archimedean t-conorms _L. J. Math. Anal. Appl. 101 (1984), 114-138. R. R. Yager: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Systems Man Cybernet. 18 (1988), 183-190. |

Deposited On: | 13 Nov 2012 10:05 |

Last Modified: | 07 Feb 2014 09:41 |

Repository Staff Only: item control page