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Accounting for Uncertainty and Disagreement in Multi-criteria Decision Making Using Triangular Fuzzy Numbers and Monte Carlo Simulation: A Case Study About Selecting Measures for Remediation of Agricultural Land After Radioactive Contamination

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Real Life Applications of Multiple Criteria Decision Making Techniques in Fuzzy Domain

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 420))

Abstract

In many MCDM applications, linguistic evaluation scales are becoming used more often to replace quantitative inputs because words are more natural than numbers to represent the preferences of people (García-Lapresta and González del Pozo in Eur. J. Oper. Res. 279:159–167, 2019 [1]). Most real-world decision making takes place in a complex environment, and therefore, the use of these linguistic scorings can become a tool for dealing with vagueness, imprecision and uncertainty. Both criteria scores for the considered alternatives and criteria weights can be expressed using fuzzy set theory in fuzzy numbers. In addition, when the MCDM is conducted by a group of decision makers, the impact of disagreement among them can be further characterized using these fuzzy numbers. One way of accounting for the uncertainties, related to the fuzziness in the MCDM-inputs, is the substitution of the ordinal linguistic scores by triangular fuzzy numbers (TFN) followed by a set of Monte Carlo runs of the MCDM. In this paper, we report on a case study of which the goal is to select the most appropriate of five candidate countermeasures to remediate an agricultural parcel contaminated with the radionuclide Cs-137. The linguistic evaluation scales according to which two of the criteria and the criteria weights are scored were converted in TFN and then sampled using a Monte Carlo procedure to generate 10.000 rankings of the alternative countermeasures. We demonstrate that the ranking resulting from the deterministic approach is increasingly challenged when the uncertainties resulting from (1) the linguistic criteria scores, (2) the linguistic criteria weights and (3) the disagreement between decision makers are additively considered. The outcome is a fuzzy ranking of alternatives that should make decision makers think twice about the apparent superiority or inferiority of alternatives.

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Acknowledgements

This work was supported by a PhD grant for Floris Abrams from the Belgian Nuclear Research Centre (SCK CEN).

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Authors and Affiliations

  1. Belgian Nuclear Research Centre (SCK CEN), Boeretang 200, 2400, Mol, Belgium

    Floris Abrams, Lieve Sweeck & Johan Camps

  2. Division of Forest, Nature and Landscape, Faculty of Department of Earth and Environmental Sciences, University of Leuven (KULeuven), 3001, Leuven, Belgium

    Floris Abrams, Lucas Hendrickx & Jos Van Orshoven

  3. Center for Industrial Management, Traffic and Infrastructure, Department of Mechanical Engineering, University of Leuven (KU Leuven), 3001, Leuven, Belgium

    Dirk Cattrysse

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  1. Floris Abrams
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  2. Lucas Hendrickx
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  5. Dirk Cattrysse
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  6. Jos Van Orshoven
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Correspondence to Floris Abrams .

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Editors and Affiliations

  1. Department of Computer and Information Science, Raiganj University, Raiganj, West Bengal, India

    Laxminarayan Sahoo

  2. School of Mathematics and Statistics, Southwest University, Chongqing, China

    Tapan Senapati

  3. Iona College, Machine Intelligence Institute, New Rochelle, NY, USA

    Ronald R. Yager

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Abrams, F., Hendrickx, L., Sweeck, L., Camps, J., Cattrysse, D., Van Orshoven, J. (2023). Accounting for Uncertainty and Disagreement in Multi-criteria Decision Making Using Triangular Fuzzy Numbers and Monte Carlo Simulation: A Case Study About Selecting Measures for Remediation of Agricultural Land After Radioactive Contamination. In: Sahoo, L., Senapati, T., Yager, R.R. (eds) Real Life Applications of Multiple Criteria Decision Making Techniques in Fuzzy Domain. Studies in Fuzziness and Soft Computing, vol 420. Springer, Singapore. https://doi.org/10.1007/978-981-19-4929-6_6

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