Extending the multi-criteria decision making method DEX with numeric attributes, value distributions and relational models

DEX is a qualitative multi-criteria decision analysis method. The method supports decision makers in making complex decisions based on multiple, possibly conflicting, attributes. The attributes in DEX have qualitative value scales and are structured hierarchically. The hierarchical topology allows for decomposition of the decision problem into simpler sub-problems. In DEX, alternatives are described with qualitative values, taken from the scales of corresponding input attributes in the hierarchy. The evaluation of alternatives is performed in a bottom-up way, utilizing aggregation functions, which are defined for every aggregated attribute in the form of decision rules. DEX has been used in numerous practical applications—from everyday decision problems to solving decision problems in the financial and ecological domains. Based on experience, we identified the need for three major methodological extensions to DEX: introducing numeric attributes, the probabilistic and fuzzy aggregation of values and relational models. These extensions were proposed by users of the existing method and by the new demands of complex decision problems, which require advanced decision making approaches. In this paper, we introduce these three extensions by describing the extensions formally, justifying their contributions to the decision making process and illustrating them on a didactic example, which is followed throughout the paper.