Miranda Menéndez, Pedro y Combarro, Elías F. y Gil, Pedro (2006) Extreme points of some families of non-additive measures. European journal of operational research, 174 (3). pp. 1865-1884. ISSN 0377-2217
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Non-additive measures are a valuable tool to model many different problems arising in real situations. However, two important difficulties appear in their practical use: the complexity of the measures and their identification from sample data. For the first problem, additional conditions are imposed, leading to different subfamilies of non-additive measures. Related to the second point, in this paper we study the set of vertices of some families of non-additive measures, namely k-additive measures and p-symmetric measures. These extreme points are necessary in order to properly apply a new method of identification of non-additive measures based on genetic algorithms, whose cross-over operator is the convex combination. We solve the problem through techniques of Linear Programming.
|Tipo de documento:||Artículo|
|Palabras clave:||Decision analysis; Genetic algorithms; Multiple criteria analysis; Linear programming; Non-additive measures; k-additivity; p-symmetry; Vertices|
|Materias:||Ciencias > Matemáticas > Investigación operativa|
M. Allais, Le comportement de l'homme rationnel devant le risque: critique des postulats de l'École américaine, Econometrica 21 (1953) 503–546 (in French).
F.J. Anscombe, R.J. Aumann, A definition of subjective probability, The Annals of Mathematical Statistics 34 (1963) 199–205.
M. Bazaraa, J. Jarvis, H. Sherali, Linear Programming and Network Flows, John Wiley and Sons, 1990.
C. Berge, Principles of Combinatorics, in: Mathematics in Science and Engineering, vol. 72, Academic Press, 1971.
A. Chateauneuf, Modelling attitudes towards uncertainty and risk through the use of Choquet integral, Annals of Operations Research 52 (1994) 3–20.
A. Chateauneuf, J.-Y. Jaffray, Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion, Mathematical Social Sciences 17 (1989) 263–283.
G. Choquet, Theory of capacities, Annales de l'Institut Fourier 5 (1953) 131–295.
E.F. Combarro, P. Miranda, Identification of fuzzy measures from sample data with genetic algorithms, Computers and Operations Research, in press.
D. Denneberg, Non-additive Measures and Integral, Kluwer Academic, 1994.
D. Dubois, H. Prade, A class of fuzzy measures based on triangular norms, International Journal of General Systems 8 (1982) 43–61.
D. Dubois, H. Prade, R. Sabbadin, Qualitative decision theory with Sugeno integrals, in: M. Grabisch, T. Murofushi, M. Sugeno (Eds.), Fuzzy Measures and Integrals, Studies in Fuzziness and Soft Computing, vol. 40, Physica-Verlag, Berlin, 2000, pp. 314–331.
C.A. Bana e Costa, J.-C. Vansnick, MACBETH––An interative path towards the construction of cardinal value function, International Transactions in Operational Research 1 (4) (1994) 489–500.
D. Ellsberg, Risk, ambiguity, and the Savage axioms, Quarterly Journal of Economics 75 (1961) 643–669.
D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, 1989.
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, k-Order additive discrete fuzzy measures, in: Proceedings of 6th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU), Granada, Spain, 1996, pp. 1345–1350.
M. Grabisch, Alternative representations of discrete fuzzy measures for decision making, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5 (1997) 587–607.
M. Grabisch, k-Order additive discrete fuzzy measures and their representation, Fuzzy Sets and Systems (92) (1997)167–189.
M. Grabisch, The interaction and Möbius representations of fuzzy measures on finite spaces, k-additive measures: A survey, in: M. Grabisch, T. Murofushi, M. Sugeno (Eds.), Fuzzy Measures and Integrals––theory and Applications, Studies in Fuzziness and Soft Computing, vol. 40, Physica-Verlag, 2000, pp. 70–93.
M. Grabisch, J.-M. Nicolas, Classification by fuzzy integral-performance and tests, Fuzzy Sets and Systems, Special Issue on Pattern Recognition 65 (1994) 255–271.
P.L. Hammer, R. Holzman, On approximations of pseudo-boolean functions, Zeitschrift für Operations Research, Mathematical Methods of Operations Research 36 (1992) 3–21.
J.H. Holland, Adaptation in Natural and Artificial Systems, The University of Michigan Press, Ann Arbor, 1975.
J.-L. Marichal, k-Intolerant capacities and Choquet integrals, in: Proceedings of Tenth International Conference of Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), Perugia, Italy, July 2004, pp. 601–608.
J.-L. Marichal, Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral, European Journal of operational Research 155 (3) (2004) 771–791.
J.-L. Marichal, P. Meyer, M. Roubens, Sorting multiattribute alternatives: The TOMASO method, Computer and Operations Research 32 (4) (2005) 861–877.
|Depositado:||13 Nov 2012 10:19|
|Última Modificación:||07 Feb 2014 09:41|
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