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New Belief Function Based Methods for Multi-Criteria Decision-Making

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Decision Support Systems – Collaborative Models and Approaches in Real Environments (EWG-DSS 2011)

Part of the book series: Lecture Notes in Business Information Processing ((LNBIP,volume 121))

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Abstract

Any decision is closely linked to the quality and availability of information. Innovative methodologies dealing with imperfect information provided by more or less reliable and conflicting sources are proposed to help decision-makers. Our methods combine new uncertainty theories within Multi-Criteria Decision-Making methods. In our evidential reasoning based approach for multi-criteria decision analysis, we use the fuzzy sets, the possibility and belief function theories as conceptual analytical frameworks. In DSmT-AHP, we replace the initial AHP aggregation principles by a fusion process with the introduction of discounting factors able to discriminate importance and reliability of criteria. In our COWA-ER, we propose a cautious Ordered Weighted Averaging method for multi-criteria decision making under uncertainty. All these methods fit well in the domain of expert assessment for the context of natural hazards in mountains. We present a synthesis of the three aforementioned methods which are detailed in papers listed in the bibliography.

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References

  1. Beynon, M., Curry, B., Morgan, P.: The Dempster-Shafer theory of evidence:an alternative approach to multicriteria decision modelling. Omega 28(1), 37–50 (2000)

    Article  MathSciNet  Google Scholar 

  2. Beynon, M.: DS/AHP method: A mathematical analysis, including an understanding of uncertainty. Eur. J. of Oper. Research 140, 148–164 (2002)

    Article  MATH  Google Scholar 

  3. Beynon, M.: Understanding local ignorance and non-specificity within the DS/AHP method of multi-criteria decision making. Eur. J. of Oper. Research 163, 403–417 (2005)

    Article  MATH  Google Scholar 

  4. Beynon, M.: A method of aggregation in DS/AHP for group decision-making with non-equivalent importance of individuals in the group. Comp. and Oper. Research (32), 1881–1896 (2005)

    Article  MATH  Google Scholar 

  5. Bloch, I., Hunter, A., Appriou, A., Ayoun, A., Benferhat, S., Besnard, P., Cholvy, L., Cooke, R., Cuppens, F., Dubois, D., Fargier, H., Grabisch, M., Kruse, R., Lang, J., Moral, S., Prade, H., Saffiotti, A., Smets, P., Sossai, C.: Fusion: General concepts and characteristics. International Journal of Intelligent Systems 16(10), 1107–1134 (2001)

    Article  Google Scholar 

  6. Bouyssou, D.: Modelling inaccurate determination, uncertainty, imprecision using multiple criteria. LNEMS vol. 335, pp. 78–87 (1989)

    Google Scholar 

  7. Dezert, J., Smarandache, F.: Proportional Conflict Redistribution Rules for Information Fusion. In: Dezert, J., Smarandache, F. (eds.) Advances and Applications of DSmT for Information Fusion- Collected Works, vol. 2, pp. 3–68. American Research Press, Rehoboth (2006)

    Google Scholar 

  8. Dezert, J., Tacnet, J.-M., Batton-Hubert, M., Smarandache, F.: Multi-criteria decision making based on DSmT-AHP. In: Proc. of Belief 2010 Int. Workshop, Brest, France, April 1-2 (2010)

    Google Scholar 

  9. Dezert, J., Tacnet, J.-M.: Soft ELECTRE TRI outranking method based on belief functions. In: 14th International Conference on Information Fusion Proceedings, Singapore, July 9-12 (2012)

    Google Scholar 

  10. Dubois, D., Prade, H.: Possibility Theory:an approach to Computerized Processing of Uncertainty. Plenum Press, New York (1988)

    MATH  Google Scholar 

  11. Roy, B.: Main sources of inaccurate determination, uncertainty and imprecision in decision models. Mathematical and Computer Modelling 12(10-11), 1245–1254 (1989)

    Article  Google Scholar 

  12. Saaty, T.L.: The analytic hierarchy process. McGraw Hill, New York (1980)

    MATH  Google Scholar 

  13. Shafer, G.: A mathematical theory of evidence. Princeton University Press (1976)

    Google Scholar 

  14. Smarandache, F., Dezert, J. (eds.): Advances and Applications of DSmT for Information Fusion, pp. 1–3. American Research Press, Rehoboth (2004-2009), http://fs.gallup.unm.edu//DSmT.htm

    MATH  Google Scholar 

  15. Smarandache, F., Dezert, J., Tacnet, J.-M.: Fusion of sources of evidence with different importances and reliabilities. In: 13th International Conference on Information Fusion Proceedings, Edinburgh, UK, July 26-29 (2010)

    Google Scholar 

  16. Smets, P.: The Combination of Evidence in the Transferable Belief Model. IEEE Trans. PAMI 12, 447–458 (1990)

    Article  Google Scholar 

  17. Stewart, T.J.: Dealing with Uncertainties in MCDA. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis:state of the Art Surveys. International Series in Operations Research and Management Science, vol. 78, pp. 445–470. Springer, Heidelberg (2005)

    Google Scholar 

  18. Tacnet, J.-M.: Prise en compte de l’incertitude dans l’expertise des risques naturels en montagne par analyse multicritéres et fusion d’information. PhD thesis in Environmental Engineering Sciences, Ecole Nationale Supérieure des Mines, Saint-Etienne, France (2009)

    Google Scholar 

  19. Tacnet, J.-M., Batton-Hubert, M., Dezert, J.: Information fusion for natural hazards in mountains. In: Dezert, J., Smarandache, F. (eds.) Advances and Applications of DSmT for Information Fusion- Collected Works, vol. 3, pp. 565–659. American Research Press, Rehoboth (2009)

    Google Scholar 

  20. Tacnet, J.-M., Batton-Hubert, M., Dezert, J.: A two-step fusion process for multi-criteria decision applied to natural hazards in mountains. In: 1st International Worshop on Belief functions (Belief 2010) Proceedings, Brest, France (2010)

    Google Scholar 

  21. Tacnet, J.-M., Batton-Hubert, M., Dezert, J., Richard, D.: Applying new uncertainty related theories and multicriteria decision analysis methods to snow avalanche risk management. In: International Snow Science Workshop (ISSW) Proceedings, Squaw Valley, Colorado, USA, October 17-22 (2010)

    Google Scholar 

  22. Tacnet, J.-M., Dezert, J.: Cautious OWA and evidential reasoning for decision under uncertainty. In: 14th International Conference on Information Fusion Proceedings, Chicago, Illinois, USA, July 5-8, pp. 2074–2081 (2011)

    Google Scholar 

  23. Yager, R.: On ordered weighted averaging operators in multi-criteria decision making. EEE Trans. on SMC 18, 183–190 (1988)

    MathSciNet  MATH  Google Scholar 

  24. Yager, R.: Decision making under Dempster-Shafer uncertainties. STUDFUZZ, vol. 219, pp. 619–632 (2008)

    Google Scholar 

  25. Zadeh, L.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  26. Zadeh, L.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Irstea, UR ETGR Erosion Torrentielle Neige Avalanches, 2 rue de la Papeterie, BP 76, F-38402, St-Martin-d’Heres, France

    Jean-Marc Tacnet

  2. The French Aerospace Lab, F-91761, Palaiseau, France

    Jean Dezert

Authors
  1. Jean-Marc Tacnet
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  2. Jean Dezert
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Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Jorge E. Hernández

  2. Tolouse University, Toulouse, France

    Pascale Zarate

  3. SimTech Simulation Technology, Graz, Austria

    Fátima Dargam

  4. University of Belgrade, Belgrade, Serbia

    Boris Delibašić

  5. University of Plymouth, Plymouth, Devon, UK

    Shaofeng Liu

  6. UNINOVA – CA3, Lisbon, Portugal

    Rita Ribeiro

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© 2012 Springer-Verlag Berlin Heidelberg

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Tacnet, JM., Dezert, J. (2012). New Belief Function Based Methods for Multi-Criteria Decision-Making. In: Hernández, J.E., Zarate, P., Dargam, F., Delibašić, B., Liu, S., Ribeiro, R. (eds) Decision Support Systems – Collaborative Models and Approaches in Real Environments. EWG-DSS 2011. Lecture Notes in Business Information Processing, vol 121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32191-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-32191-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32190-0

  • Online ISBN: 978-3-642-32191-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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