Abstract
Experts take into account several criteria to assess the effectiveness of torrential flood protection systems. In practice, scoring each criterion is imperfect. Each system is assessed choosing a qualitative class of effectiveness among several such classes (high, medium, low, no). Evidential Reasoning for Multi-Criteria Decision-Analysis (ER-MCDA) approach can help formalize this Multi-Criteria Decision-Making (MCDM) problem but only provides a coarse ranking of all systems. The recent Belief Function-based Technique for Order Preference by Similarity to Ideal Solution (BF-TOPSIS) methods give a finer ranking but are limited to perfect scoring of criteria. Our objective is to provide a coarse and a finer ranking of systems according to their effectiveness given the imperfect scoring of criteria. Therefore we propose to couple the two methods using an intermediary decision and a quantification transformation step. Given an actual MCDM problem, we apply the ER-MCDA and its coupling with BF-TOPSIS, showing that the final fine ranking is consistent with a previous coarse ranking in this case.
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Notes
- 1.
For any BBAs x, y, z defined on \(2^\varTheta \), a true distance metric d(x, y) satisfies the properties of non-negativity (\(d(x,y) \ge 0\)), non-degeneracy (\(d(x,y) = 0 \Leftrightarrow x=y\)), symmetry (\(d(x,y)=d(y,x)\)), and triangle inequality (\(d(x,y)+d(y,z) \ge d(x,z)\)).
- 2.
with the PCR6 rule in this paper [8] (Vol. 3).
References
Carladous, S., Tacnet, J.-M., Dezert, J., Batton-Hubert, M.: Belief function theory based decision support methods: application to torrent protection work effectiveness and reliability assessment. In: 25th International Conference on ESREL, Zürich, Switzerland (2015)
Tacnet, J.-M., Dezert, J., Batton-Hubert, M.: AHP and uncertainty theories for decision making using the ER-MCDA methodology. In: 11th International Symposium on AHP, Sorrento, Italy (2011)
Dezert, J., Tacnet, J.-M.: Evidential reasoning for multi-criteria analysis based on DSmT-AHP. In: 11th International Symposium on AHP, Sorrento, Italy (2011)
Dezert, J., Han, D., Yin, H.: A new belief function based approach for multi-criteria decision-making support. In: 19th International Conference on Fusion, Heidelberg, Germany (2016)
Saaty, T.: The Analytic Hierarchy Process. McGraw Hill, New York (1980)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Smarandache, F., Dezert, J., Tacnet, J.-M.: Fusion of sources of evidence with different importances and reliabilities. In: 13th International Conference on Fusion, Edinburgh, UK (2010)
Smarandache, F., Dezert, J.: Advances and applications of DSmT for information fusion, vol. 1–4. ARP (2004–2015). http://www.onera.fr/fr/staff/jean-dezert
Dezert, J., Tchamova, A.: On the validity of Dempster’s fusion rule and its interpretation as a generalization of Bayesian fusion rule. Int. J. Intell. Syst. 29(3), 223–252 (2014)
Smets, P., Kennes, R.: The transferable belief model. Artif. Intell. 66, 191–234 (1994)
Cobb, B.R., Shenoy, P.P.: On the plausibility transformation method for translating belief function models to probability models. IJAR 41(3), 314–330 (2006)
Dezert, J., Han, D., Tacnet, J.-M., Carladous, S.: Decision-making with belief interval distance. In: 4th International Conference on Belief Functions, Prague, Czech Republic (2016)
Han, D., Dezert, J., Yang, Y.: New distance measures of evidence based on belief intervals. In: 3rd International Conference on Belief Functions, Oxford, UK (2014)
Irpino, A., Verde, R.: Dynamic clustering of interval data using a Wasserstein-based distance. Pattern Recogn. Lett. 29, 1648–1658 (2008)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Lai, Y.J., Liu, T.Y., Hwang, C.L.: TOPSIS for MODM. Eur. J. Oper. Res. 76(3), 486–500 (1994)
Acknowledgments
The authors extend their thanks to the French Ministry of Agriculture, Forest (MAAF), and Environment (MEEM), the Grant for State Key Program for Basic Research of China (973) (No. 2013CB329405), the National Natural Science Foundation (No. 61573275), and the Science and technology project of Shaanxi Province (No. 2013KJXX-46) for their support.
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Carladous, S., Tacnet, JM., Dezert, J., Han, D., Batton-Hubert, M. (2016). Applying ER-MCDA and BF-TOPSIS to Decide on Effectiveness of Torrent Protection. In: Vejnarová, J., Kratochvíl, V. (eds) Belief Functions: Theory and Applications. BELIEF 2016. Lecture Notes in Computer Science(), vol 9861. Springer, Cham. https://doi.org/10.1007/978-3-319-45559-4_6
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