Combarro, Elías F. and Miranda Menéndez, Pedro
(2006)
*Identification of fuzzy measures from sample data with genetic algorithms.*
Computers and Operations Research, 33
(10).
pp. 3046-3066.
ISSN 0305-0548

PDF
Restricted to Repository staff only until 2020. 283kB |

Official URL: http://www.sciencedirect.com/science/article/pii/S0305054805000900

## Abstract

In this paper, we introduce a method for the identification of fuzzy measures from sample data. It is implemented using genetic algorithms and is flexible enough to allow the use of different subfamilies of fuzzy measures for the learning, as k-additive or p-symmetric measures. The experiments performed to test the algorithm suggest that it is robust in situations where there exists noise in the considered data. We also explore some possibilities for the choice of the initial population, which lead to the study of the extremes of some subfamilies of fuzzy measures, as well as the proposal of a method for random generation of fuzzy measures.

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

Uncontrolled Keywords: | Genetic algorithms; Fuzzy measures; k-Additivity; p-Symmetry |

Subjects: | Sciences > Mathematics > Operations research |

ID Code: | 17079 |

References: | Combarro EF, Miranda P. A genetic algorithm for the identification of fuzzy measures from sample data. In: Proceedings of international fuzzy systems association conference (IFSA’03). Istanbul, Turkey, 2003. p. 163–6. Sugeno M. Theory of fuzzy integrals and its applications. Ph.D. thesis, Tokyo Institute of Technology, 1974. Choquet G. Theory of capacities. Annales de l’Institut Fourier 1953;5:131–295. Denneberg D. Non-additive measures and integral. Dordrecht: Kluwer Academic; 1994. von Neumann J, Morgenstern O. Theory of games and economic behaviour. NJ, USA: Princeton University Press; 1944. Anscombe FJ, Aumann RJ. A definition of subjective probability. The Annals of Mathematical Statistics 1963;34: 199–205. Ellsberg D. Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics 1961;75:643–69. Allais M. Le comportement de l’homme rationnel devant le risque: critique des postulats de l’école américaine. Econometrica 1953;21:503–46 [in French]. Chateauneuf A. Modelling attitudes towards uncertainty and risk through the use of Choquet integral. Annals of Operations Research 1994;52:3–20. Schmeidler D. Integral representation without additivity. Proceedings of the American Mathematical Society 1986;97(2):255–61. Grabisch M. Alternative representations of discrete fuzzy measures for decision making. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 1997;5:587–607. Grabisch M. k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems 1997;92:167–89. Shapley LS.A value for n-person games. In: Kuhn HW, TuckerAW, editors. Contributions to the theory of games. Annals of mathematics studies, vol. II. Princeton, NJ: Princeton University Press; 1953. p. 307–17. Grabisch M. k-order additive discrete fuzzy measures. In: Proceedings of sixth international conference on information processing and management of uncertainty in knowledge-based systems (IPMU). Granada, Spain, 1996. p. 1345–50. Rota GC. On the foundations of combinatorial theory I. Theory of Möbius functions. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1964;2:340–68. Hammer PL, Holzman R. On approximations of pseudo-boolean functions. Zeitschrift für Operations Research. Mathematical Methods of Operations Research 1992;36:3–21. Dubois D, Prade H, Sabbadin R. Qualitative decision theory with Sugeno integrals. In: Grabisch M, Murofushi T, Sugeno M, editors. Fuzzy measures and integrals. Studies in fuzziness and soft computing, vol. 40. Physica-Verlag; 2000. p. 314–31. Wang Z, Klir G. Fuzzy measure theory. NewYork: Plenum Press; 1992. Miranda P, Grabisch M. p-symmetric fuzzy measures. In: Proceedings of ninth international conference of information processing and management of uncertainty in knowledge-based systems (IPMU). Annecy, France: July 2002. p. 545–52. |

Deposited On: | 13 Nov 2012 10:13 |

Last Modified: | 07 Feb 2014 09:41 |

Repository Staff Only: item control page