Fuzzy Inference System for Measuring Composite Indicators' Overall Quality

The quality of composite indicators has been examined from various perspectives. However, the literature does not provide sociologists, geographers, and other scientists with a general measure of the quality of composite indicators to indicate which methods are appropriate for use and which mathematical properties best fit the theoretical framework of multidimensional phenomena. This research develops a fuzzy inference system to assess the overall quality of composite indicators. Four quality parameters were included in the fuzzy inference rules. The stability parameter considers how much the composite indicator scores constructed by a method fluctuate compared to those constructed by other methods. The reliability parameter considers the ability of the composite indicator to capture the multidimensional phenomenon concept and the informational loss from the original sub-indicator aggregation. This research has four points of originality. The adaptation of the uncertainty analysis to evaluate the stability of the scores obtained by the different methods. The implementation of the average variance extracted to measure the loss of information of all methods. The presentation of an overall measure of the composite indicators' quality. A new method for analyzing the robustness of fuzzy inference systems. The results are illustrated by analyzing the quality of composite indicators constructed by six methods to represent social exclusion in eight Brazilian cities. The results reveal that the quality of the composite indicator constructed by a method varies according to the city, and that the fuzzy inference system helps scientists choose the most appropriate method for each specific context.