A Guide to Integrating Expert Opinion and Fuzzy AHP When Generating Weights for Composite Indices

Abstract

Composite indices are a great tool for researchers and policymakers alike as they provide a simplification of reality of complex phenomena, as well as their enabling ability for cross-country comparisons. A troublesome issue with constructing composite indices is the selection of the weighting system as it can greatly influence the results of the index developed. One of the most reliable weighting systems is the expert weighting system, where experts on the topic being studied are delegated the weight selection process, and the average of their responses are then transformed into weights. The limitation of this method, however, is the high subjectivity, uncertainty, and inconsistency of the expert responses. This paper seeks to address this limitation by providing a guide to researchers on how to improve the expert weights by subjecting them to the fuzzy analytic hierarchy process (FAHP) method for multicriteria decision making (MCDM) to compute the fuzzy weights, a more objective and reliable weights relative to expert weights. That said, and despite the benefits of the FAHP method, it can produce weights that can skew the composite index results. To address this limitation, the study introduces the interval weights, which are calculated by finding the midpoint between the expert weights and the fuzzy weights. The resulting interval weights exhibit the benefits of both principal component analysis (PCA) and the FAHP process, the difference being that PCA cannot be applied for noncompensatory indices.

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“…The methodology behind integrating the expert weighting system and the FAHP method is based on Al Fozaie and Wahid (2022), and it involves 1) Developing a weighting scale based on a scale of relative importance; 2) Selecting a panel of experts and delegate the weighting process; 3) Assigning alpha values to the experts based on their level of expertise; 4) Transforming the survey responses into expert weights; 5) Applying the FAHP method to the expert weights; 6) Normalizing the fuzzy weights to produce the interval weights which are midpoint between the fuzzy weights and the expert weights, and are the final weights to be applied to the BBI.…”