Miranda Menéndez, Pedro and Combarro, Elías F.
(2007)
*On the structure of some families of fuzzy measures.*
IIEEE Transactions on Fuzzy Systems, 15
(6).
pp. 1068-1081.
ISSN 1063-6706

PDF
Restricted to Repository staff only until 2020. 524kB |

Official URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4387919

## Abstract

The generation of fuzzy measures is an important question arising in the practical use of these operators. In this paper, we deal with the problem of developing a random generator of fuzzy measures. More concretely, we study some of the properties that any random generator should satisfy. These properties lead to some theoretical problems concerning the group of isometries that we tackle in this paper for some subfamilies of fuzzy measures.

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

Uncontrolled Keywords: | fuzzy measures; isometric transformations; random generation |

Subjects: | Sciences > Mathematics > Operations research |

ID Code: | 17042 |

References: | G. Beliakov, R. Mesiar, and L. Valáˇsková, “Fitting generated aggregation operators to empirical data,” Int. J. Uncertain., Fuzz. Knowl Based Syst., vol. 12, no. 2, pp. 219–236, 2004. A. Chateauneuf, “Modelling attitudes towards uncertainty and risk through the use of Choquet integral,” Ann. Oper. Res., no. 52, pp. 3–20, 1994. A. Chateauneuf and J.-Y. Jaffray, “Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion,” Math. Social Sci., no. 17, pp. 263–283, 1989. G. Choquet, “Theory of capacities,” Annales de l’Institut Fourier, no. 5, pp. 131–295, 1953. E. F. Combarro and P. Miranda, “Identification of fuzzy measures from sample data with genetic algorithms,” Comput. Oper. Res., vol. 33, no. 10, pp. 3046–3066, 2006. E. F. Combarro and P. Miranda, “On some theoretical results relatin random generation of fuzzy measures,” in Proc. 11th Int. Conf. on Inf. Process. Manage. Uncertain. Knowl.-Based Syst. (IPMU’06), Paris, France, 2006, pp. 1678–1675. R. Dedekind, “Über Zerlegungen von Zahlen durch ihre Bgrössten gemeinsamen Teiler,” in Festschrift Hoch raunschweig Ges. Werke (in German).: , 1897, vol. II, pp. 103–148. D. Denneberg, Non-Additive Measures and Integral. Norwell, MA: Kluwer Academic, 1994. D. Dubois and H. Prade, “A class of fuzzy measures based on triangular norms,” Int. J. General Syst., vol. 8, pp. 43–61, 1982. C. A. B. e Costa and J.-C. Vansnick, “MACBETH—An interative path towards the construction of cardinal value function,” Int. Trans. Oper. Res., vol. 1, no. 4, pp. 489–500, 1994. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning. Reading, MA: Addison-Wesley, 1989. M. Grabisch, “A new algorithm for identifying fuzzy measures and its application to pattern recognition,” in Proc. Int. Joint Conf. 4th IEEE Int. Conf. Fuzzy Syst. 2nd Int. Fuzzy Eng. Symp., Yokohama, Japan, Mar. 1995, pp. 145–150. M. Grabisch, “k-order additive discrete fuzzy measures,” in Proc. 6th Int. Conf. Inf. Process. Manage. Uncertain. Knowl Based Syst. IPMU), Granada, Spain, 1996, pp. 1345–1350. M. Grabisch, “Alternative representations of discrete fuzzy measures for decision making,” Int. J. Uncertain., Fuzz. Knowl.-Based Syst., vol. 5, pp. 587–607, 1997. M. Grabisch, “k-order additive discrete fuzzy measures and their representation" Fuzzy Sets Syst., no. 92, pp. 167–189, 1997. M. Grabisch and J.-M. Nicolas, “Classification by fuzzy integral-performance and tests,” Fuzzy Sets Syst. (Special Issue on Pattern Recognition), no. 65, pp. 255–271, 1994. P. L. Hammer and R. Holzman, “On approximations of pseudo- Boolean functions,” Zeitschrift für Oper. Res. Math. Meth. Oper. Res., no. 36, pp. 3–21, 1992. G. Klir and T. Folger, Fuzzy Sets, Uncertainty and Information. Englewood Cliffs, NJ: Prentice-Hall, 1989. J.-L. Marichal, “Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral,” Eur. J. Oper. Res., vol. 155, no. 3, pp. 771–791, Jun. 2004. J.-L. Marichal, P. Meyer, and M. Roubens, “Sorting multiattribute alternatives : The TOMASO method,” Comput. Oper. Res., vol. 32, no. 4, pp. 861–877, 2005. R. Mesiar, “Generalizations of k-order additive discrete fuzzy measures,” Fuzzy Sets Syst., no. 102, pp. 423–428, 1999. P. Miranda, E. Combarro, and P. Gil, “Extreme points of some families of non-additive measures,” Eur. J. Oper. Res., vol. 33, no. 10, pp. 3046–3066, 2006. P. Miranda and M. Grabisch, “p-symmetric fuzzy measures,” in Proc. 9th Int. Conf. Inf. Process. Manage. Uncertain. Knowl.-Based Syst. (IPMU), Annecy, France, Jul. 2002, pp. 545–552. P. Miranda and M. Grabisch, “p-symmetric bi-capacities" Kybernetica, vol. 40, no. 4, pp. 421–440, 2004. P. Miranda, M. Grabisch, and P. Gil, “p-symmetric fuzzy measures" Int. J. Uncertain., Fuzz. Knowl.-Based Syst., vol. 10 (Suppl.), pp. 105–123, 2002. D. Radojevic, “The logical representation of the discrete Choquet integral" Belg. J. Oper. Res., Statist. Comput. Sci., vol. 38, no. 2–3, pp. 67–89, 1998. G. C. Rota, “On the foundations of combinatorial theory I. Theory of Möbius functions,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, no. 2, pp. 340–368, 1964. D. Schmeidler, “Integral representation without additivity,” Proc. Amer. Math. Soc., vol. 2, no. 97, pp. 255–261, 1986. M. Sugeno, “Theory of fuzzy integrals and its applications,” Ph.D. dissertation, Tokyo Inst. of Technol., Tokyo, Japan, 1974. M. Sugeno and T. Terano, “A model of learning based on fuzzy information" Kybernetes, no. 6, pp. 157–166, 1977. J. W. Z. Wang, K. Xu, and G. Klir, “Using genetic algorithms to determine nonnegative monotone set functions for information fusion in environments with random perturbation,” Int. J. Intell. Syst., vol. 14, pp. 949–962, 1999. |

Deposited On: | 07 Nov 2012 09:35 |

Last Modified: | 07 Feb 2014 09:40 |

Repository Staff Only: item control page