Fuzzy Measures and Experts’ Opinion Elicitation

Abstract

To over pass the limits inherent in liner models, suitable aggregation operators are required, taking into account interactions among the criteria. This becomes more and more crucial in Decision Theory, where all the information can be inferred by one or more Experts, using an ad hoc questionnaire. This is the case of the FEEM SI sustainability index, a composite geo-referenced index which aggregates several economic, social and environmental dimensions-structured in a decision tree- into a single number between zero (the worst sustainable country) and one (the best one). Fuzzy measure (non additive measures) are here proposed for the aggregation phase. To this purpose, each intermediate node of the structure combines the values of the sub-nodes using a model based on second-order non additive measure. To infer the value of the measure for each node, a suitable questionnaire has been fulfilled by a set of Experts, and the obtained answers were processed using an optimization algorithm. To guarantee the strict convexity of the algorithm, the questionnaire needs to be carefully designed. The individual measures are subsequently aggregated and the numerical results permitted to compare the sustainability of all the considered territorial units.