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Aggregation of Stochastic Rankings in Group Decision Making

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Collective Decisions: Theory, Algorithms And Decision Support Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 392))

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Abstract

We propose a novel method for group decision making. It is applicable in the context of multiple criteria ranking problems, where alternatives need to be ordered from the best to the worst by multiple Decision Makers (DMs). In the first stage, incomplete preference information of each DM is analyzed within the framework of stochastic analysis. Specifically, the Monte Carlo simulation is applied for exploiting the space of preference model parameters compatible with each DM’s preferences. In this way, we estimate the values of stochastic acceptability indices that quantify the support given to the preference, indifference, and incomparability relations for each pair of alternatives. In the second stage, such stochastic rankings are aggregated into a group compromise recommendation that minimizes either an average or a maximal distance from each DM’s input. Apart from accounting for the utilitarian and egalitarian perspectives, the dedicated mathematical programming models deal with the processing and constructing of complete or partial rankings. The proposed method is coupled with the robust variants of PROMETHEE I and II methods, however, it can be combined with any method from the broad family of Stochastic Multicriteria Acceptability Analysis (SMAA) techniques. Its applicability for supporting real-world group decision making is demonstrated in an illustrative case study concerning the ranking of project proposals by a research funding agency.

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Acknowledgements

Miłosz Kadziński and Dariusz Grynia acknowledge support from the Polish National Science Center under the SONATA BIS project (grant no. DEC-2019/34/E/HS4/00045). Grzegorz Miebs acknowledges support from the Polish Ministry of Science and Higher Education under the Diamond Grant project (grant no. DI2018 004348).

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Authors and Affiliations

  1. Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965, Poznań, Poland

    Miłosz Kadziński, Grzegorz Miebs, Dariusz Grynia & Roman Słowiński

  2. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Roman Słowiński

Authors
  1. Miłosz Kadziński
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  2. Grzegorz Miebs
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  3. Dariusz Grynia
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  4. Roman Słowiński
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Correspondence to Miłosz Kadziński .

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Editors and Affiliations

  1. Collegium of Economic Analysis, SGH Warsaw School of Economics, Warszawa, Poland

    Tomasz Szapiro

  2. Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland

    Janusz Kacprzyk

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Kadziński, M., Miebs, G., Grynia, D., Słowiński, R. (2022). Aggregation of Stochastic Rankings in Group Decision Making. In: Szapiro, T., Kacprzyk, J. (eds) Collective Decisions: Theory, Algorithms And Decision Support Systems. Studies in Systems, Decision and Control, vol 392. Springer, Cham. https://doi.org/10.1007/978-3-030-84997-9_4

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