AGGREGATION IN FUZZY FAULT TREE QUANTIFICATION: COMPARISON OF MEANS AND EXPERTONS TECHNIQUES
Keywords:
Fuzzy Fault Tree Quantification, Aggregation, Arithmetic Mean, ExpertonAbstract
This paper presents a comparison of the two techniques: arithmetic means and expertons, used for aggregation of experts’ judgments relative to basic events of fault trees. Valuations as confidence intervals included in [0, 1] have been considered. First, bounds are numbers to one decimal; next, numbers belonging to [0, 1]. In this last case, R+_expertons concept is used, with a counter-expertise form proposed. The means technique is well known in practice, but as fault tree is a logical diagram built by "AND" and "OR" gates, i.e. nonlinear operators, its use leads to wrong results and expertons technique should be used.Downloads
References
- Bowls J.B. and Pelaez C.E., "Application of fuzzy logic to reliability engineering", Proceedings of the IEEE, Vol. 83, N°3, (1995).
- Chun M.H. and Ahn K., "Assessment of the potential applicability of fuzzy set theory to accident progression event trees with phenomenological uncertainties", Reliability engineering and system safety, Vol. 37, (1992), pp. 237-252.
- Dubois D. and Prade H., "Une approche ensembliste de la combinaison d’informations imprécises ou incertaines", Revue d’intelligence artificielle, Vol. 1, N°4, (1987).
- Gil Aluja J., "Investment in uncertainty", Kluwer Academic Publishers, (1998).
- Kaufmann A. and Gil Aluja J., "Tecnicas especiales para la gestion de expertos", Ed. Milladoiro, Santiago de compostela, (1993).
- Kaufmann A., "Les expertons", Ed. Hermès, Paris, (1987).
- Kaufmann A. and Gil Aluja J., "Las matematicas del azar y de la incertidumbre", Editorial Centro de Estudios Ramon Areces, Madrid, (1990).
- Lai F.S., Shenoi S. and Fan L.T., "Fuzzy fault tree analysis: theory and application", in: “Engineering risk and hazard Assessment”, Vol. I, CRC Press, Inc. Florida, (Eds) A. Kandel and E. Avni, (1988).
- Limnios N., "Arbre de défaillance" , Ed. Hermes, Paris, (1991).
- M.W. Merkhofer, "Quantifying judgmental uncertainty: methodology, experiences and insights", IEEE Trans. on systems, man, and cybernetics, Vol. SMC-17, N°5, September / October, (1987).
- Mullet E., Cuny X. et Richardson J., "L’agrégation des opinions d’experts en milieu industriel: l’exemple du contrôle de qualité", Le Travail humain, Vol. 47, N°4, (1984).
- Sandri S.A. and Dubois D., "Elicitation, assessment, and pooling of experts’ judgments using possibility theory", IEEE Trans. On fuzzy systems, Vol. 3, N°3, August (1995).
- Tanaka H., Fan L.T., Lai F.S., and Toguchi K., "Fault tree analysis by fuzzy probability", IEEE Trans. On reliability, Vol. R-32, N°5, pp. 453-457, December, (1983).
- Ventsel H., "Théorie des probabilités", Ed. Mir, Moscou, (1973).
- Zadeh L.A., "Fuzzy sets", Information and control, Vol. 8, (1965), pp. 338-353.
