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Dominance-based Rough Set Approach to decision under uncertainty and time preference

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  • Salvatore Greco
  • Benedetto Matarazzo
  • Roman Słowiński

Abstract

We consider a problem of decision under uncertainty with outcomes distributed over time. We propose a rough set model based on a combination of time dominance and stochastic dominance. For the sake of simplicity we consider the case of traditional additive probability distribution over the set of states of the world, however, we show that the model is rich enough to handle non-additive probability distributions, and even qualitative ordinal distributions. The rough set approach gives a representation of decision maker’s time-dependent preferences under uncertainty in terms of “if…, then…” decision rules induced from rough approximations of sets of exemplary decisions. Copyright Springer Science+Business Media, LLC 2010

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  • Salvatore Greco & Benedetto Matarazzo & Roman Słowiński, 2010. "Dominance-based Rough Set Approach to decision under uncertainty and time preference," Annals of Operations Research, Springer, vol. 176(1), pages 41-75, April.
    • Handle: RePEc:spr:annopr:v:176:y:2010:i:1:p:41-75:10.1007/s10479-009-0566-8
    DOI: 10.1007/s10479-009-0566-8
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    1. Wen-Min Lu & Qian Long Kweh & Chung-Wei Wang, 2021. "Integration and application of rough sets and data envelopment analysis for assessments of the investment trusts industry," Annals of Operations Research, Springer, vol. 296(1), pages 163-194, January.
    2. Kułakowski, Konrad, 2018. "Inconsistency in the ordinal pairwise comparisons method with and without ties," European Journal of Operational Research, Elsevier, vol. 270(1), pages 314-327.
    3. Salvatore Greco & Benedetto Matarazzo & Roman Słowiński, 2013. "Comments on: Multicriteria decision systems for financial problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 268-274, July.
    4. Luisa Sturiale & Alessandro Scuderi & Giuseppe Timpanaro & Benedetto Matarazzo, 2020. "Sustainable Use and Conservation of the Environmental Resources of the Etna Park (UNESCO Heritage): Evaluation Model Supporting Sustainable Local Development Strategies," Sustainability, MDPI, vol. 12(4), pages 1-16, February.
    5. Salvatore Corrente & Salvatore Greco & Benedetto Matarazzo & Roman Słowiński, 2016. "Robust ordinal regression for decision under risk and uncertainty," Journal of Business Economics, Springer, vol. 86(1), pages 55-83, January.
    6. Wu, Siqi & Wu, Meng & Dong, Yucheng & Liang, Haiming & Zhao, Sihai, 2020. "The 2-rank additive model with axiomatic design in multiple attribute decision making," European Journal of Operational Research, Elsevier, vol. 287(2), pages 536-545.
    7. Fan, Tuan-Fang & Liau, Churn-Jung & Liu, Duen-Ren, 2011. "A relational perspective of attribute reduction in rough set-based data analysis," European Journal of Operational Research, Elsevier, vol. 213(1), pages 270-278, August.
    8. Marko Bohanec & Nejc Trdin & Branko Kontić, 2017. "A qualitative multi-criteria modelling approach to the assessment of electric energy production technologies in Slovenia," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(3), pages 611-625, September.
    9. Barbati, Maria & Greco, Salvatore & Kadziński, Miłosz & Słowiński, Roman, 2018. "Optimization of multiple satisfaction levels in portfolio decision analysis," Omega, Elsevier, vol. 78(C), pages 192-204.
    10. Du, Wen Sheng & Hu, Bao Qing, 2017. "Dominance-based rough fuzzy set approach and its application to rule induction," European Journal of Operational Research, Elsevier, vol. 261(2), pages 690-703.
    11. Nejc Trdin & Marko Bohanec, 2018. "Extending the multi-criteria decision making method DEX with numeric attributes, value distributions and relational models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(1), pages 1-41, March.
    12. Luisa Sturiale & Alessandro Scuderi, 2018. "The Evaluation of Green Investments in Urban Areas: A Proposal of an eco-social-green Model of the City," Sustainability, MDPI, vol. 10(12), pages 1-22, December.
    13. Durbach, Ian N. & Stewart, Theodor J., 2012. "Modeling uncertainty in multi-criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 223(1), pages 1-14.
    14. Sarnataro, Michele & Barbati, Maria & Greco, Salvatore, 2021. "A portfolio approach for the selection and the timing of urban planning projects," Socio-Economic Planning Sciences, Elsevier, vol. 75(C).
    15. Barbati, Maria & Corrente, Salvatore & Greco, Salvatore, 2020. "A general space-time model for combinatorial optimization problems (and not only)," Omega, Elsevier, vol. 96(C).
    16. Salvatore Corrente & Michael Doumpos & Salvatore Greco & Roman Słowiński & Constantin Zopounidis, 2017. "Multiple criteria hierarchy process for sorting problems based on ordinal regression with additive value functions," Annals of Operations Research, Springer, vol. 251(1), pages 117-139, April.
    17. Liu, Jiapeng & Liao, Xiuwu & Yang, Jian-bo, 2015. "A group decision-making approach based on evidential reasoning for multiple criteria sorting problem with uncertainty," European Journal of Operational Research, Elsevier, vol. 246(3), pages 858-873.
    18. Fu-Ling Cai & Xiuwu Liao & Kan-Liang Wang, 2012. "An interactive sorting approach based on the assignment examples of multiple decision makers with different priorities," Annals of Operations Research, Springer, vol. 197(1), pages 87-108, August.
    19. Alessandro SCUDERI & Luisa STURIALE, 2016. "Multi-criteria evaluation model to face phytosanitary emergencies: The case of citrus fruits farming in Italy," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 62(5), pages 205-214.
    20. Siraj, Sajid & Mikhailov, Ludmil & Keane, John A., 2015. "Contribution of individual judgments toward inconsistency in pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 242(2), pages 557-567.
    21. Durbach, Ian N. & Stewart, Theodor J., 2011. "An experimental study of the effect of uncertainty representation on decision making," European Journal of Operational Research, Elsevier, vol. 214(2), pages 380-392, October.
    22. Siraj, S. & Mikhailov, L. & Keane, J.A., 2012. "Preference elicitation from inconsistent judgments using multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 220(2), pages 461-471.

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