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Choice, Ranking and Sorting in Fuzzy Multiple Criteria Decision Aid

In: Multiple Criteria Decision Analysis: State of the Art Surveys

Author

Listed:
  • Patrick Meyer

    (University of Liège)

  • Marc Roubens

    (University of Liège)

Abstract

In this chapter we survey several approaches to derive a recommendation from some preference models for multiple criteria decision aid. Depending on the specificities of the decision problem, the recommendation can be a selection of the best alternatives, a ranking of these alternatives or a sorting. We detail a sorting procedure for the assignment of alternatives to graded classes when the available information is given by interacting points of view and a subset of prototypic alternatives whose assignment is given beforehand. A software dedicated to that approach (TOMASO) is briefly presented. Finally we define the concepts of good and bad choices based on dominant and absorbant kernels in the valued digraph that corresponds to an ordinal valued outranking relation. Aggregation with fuzzy environment, fuzzy choice, ordinal ordered sorting, choquet integral, TOMASO.

Suggested Citation

  • Patrick Meyer & Marc Roubens, 2005. "Choice, Ranking and Sorting in Fuzzy Multiple Criteria Decision Aid," International Series in Operations Research & Management Science, in: Multiple Criteria Decision Analysis: State of the Art Surveys, chapter 0, pages 471-503, Springer.
    • Handle: RePEc:spr:isochp:978-0-387-23081-8_12
    DOI: 10.1007/0-387-23081-5_12
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    Citations

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    Cited by:

    1. Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," European Journal of Operational Research, Elsevier, vol. 186(2), pages 766-785, April.
    2. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 217-245, April.
    3. Ragona, Maddalena & Mazzocchi, Mario & Alldrick, A.J., 2012. "Multi-criteria analysis for the impact assessment of food safety policies: The case of EU regulation on dietary arsenic," 2012 First Congress, June 4-5, 2012, Trento, Italy 124122, Italian Association of Agricultural and Applied Economics (AIEAA).
    4. Fernandez, Eduardo & Navarro, Jorge & Bernal, Sergio, 2009. "Multicriteria sorting using a valued indifference relation under a preference disaggregation paradigm," European Journal of Operational Research, Elsevier, vol. 198(2), pages 602-609, October.
    5. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    6. Bottero, M. & Ferretti, V. & Figueira, J.R. & Greco, S. & Roy, B., 2018. "On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application," European Journal of Operational Research, Elsevier, vol. 271(1), pages 120-140.
    7. Michel Grabisch, 2008. "How to score alternatives when criteria are scored on an ordinal scale," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00340381, HAL.
    8. Jian-Zhang Wu & Feng-Feng Chen & Yan-Qing Li & Li Huang, 2020. "Capacity Random Forest for Correlative Multiple Criteria Decision Pattern Learning," Mathematics, MDPI, vol. 8(8), pages 1-15, August.
    9. Jun-Jie Dong & Jian-Zhang Wu & Endre Pap & Aniko Szakal, 2017. "A Choquet Capacity and Integral Based Method to Identify the Overall Importance of Engineering Characteristics in Quality Function Deployment," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(4), pages 297-314.
    10. Marcella De Filippo & Delio Colangelo & Luca Farnia, 2017. "Innovation and new business models in tourism," RIVISTA DI STUDI SULLA SOSTENIBILITA', FrancoAngeli Editore, vol. 0(1), pages 149-168.
    11. Lorenza Campagnolo & Carlo Carraro & Fabio Eboli & Luca Farnia & Ramiro Parrado & Roberta Pierfederici, 2018. "The Ex-Ante Evaluation of Achieving Sustainable Development Goals," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 136(1), pages 73-116, February.
    12. Siskos, Eleftherios & Burgherr, Peter, 2022. "Multicriteria decision support for the evaluation of electricity supply resilience: Exploration of interacting criteria," European Journal of Operational Research, Elsevier, vol. 298(2), pages 611-626.
    13. Ragona, Maddalena & Albertazzi, Sergio & Nicolli, Francesco & Mazzanti, Massimiliano & Montini, Anna & Vitali, Giuliano & Canavari, Maurizio, 2014. "Alternative subsidy scenarios for different agricultural practices: A sustainability assessment using fuzzy multi-criteria analysis," 2014 Third Congress, June 25-27, 2014, Alghero, Italy 173095, Italian Association of Agricultural and Applied Economics (AIEAA).
    14. Ragona, Maddalena & Mazzocchi, Mario & Rose, Martin, 2012. "Regulatory impact assessment of food safety policies: A preliminary study on alternative EU interventions on dioxins," 86th Annual Conference, April 16-18, 2012, Warwick University, Coventry, UK 135093, Agricultural Economics Society.
    15. Arcidiacono, Sally Giuseppe & Corrente, Salvatore & Greco, Salvatore, 2021. "Robust stochastic sorting with interacting criteria hierarchically structured," European Journal of Operational Research, Elsevier, vol. 292(2), pages 735-754.
    16. Luca Farnia, 2019. "On the Use of Spectral Value Decomposition for the Construction of Composite Indices," Working Papers 2019.08, Fondazione Eni Enrico Mattei.
    17. Jian-Zhang Wu & Yi-Ping Zhou & Li Huang & Jun-Jie Dong, 2019. "Multicriteria Correlation Preference Information (MCCPI)-Based Ordinary Capacity Identification Method," Mathematics, MDPI, vol. 7(3), pages 1-13, March.
    18. Maurizio Canavari & Nicola Cantore & Sergio Albertazzi & Chiara Marco Della & Giuliano Vitali & Claudio Signorotti & Guido Baldoni & Concetta Cardillo & Antonella Trisorio & Guido Maria Bazzani & Robe, 2013. "Sustainability in organic and conventional farm ing: toward s a multicriteria model based on simulated farm indicators," ECONOMICS AND POLICY OF ENERGY AND THE ENVIRONMENT, FrancoAngeli Editore, vol. 2013(1), pages 175-200.
    19. Campagnolo, Lorenza & Eboli, Fabio & Farnia, Luca & Carraro, Carlo, 2018. "Supporting the UN SDGs transition: Methodology for sustainability assessment and current worldwide ranking," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-19.
    20. Chin-Yi Chen & Jih-Jeng Huang, 2019. "Forming a Hierarchical Choquet Integral with a GA-Based Heuristic Least Square Method," Mathematics, MDPI, vol. 7(12), pages 1-16, December.
    21. Li Huang & Jian-Zhang Wu & Rui-Jie Xi, 2020. "Nonadditivity Index Based Quasi-Random Generation of Capacities and Its Application in Comprehensive Decision Aiding," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    22. Mazzocchi, Mario & Ragona, Maddalena & Zanoli, Agostina, 2013. "A fuzzy multi-criteria approach for the ex-ante impact assessment of food safety policies," Food Policy, Elsevier, vol. 38(C), pages 177-189.

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