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

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.