Estimating and predicting the human development index with uncertain data: a common weight fuzzy benefit-of-the-doubt machine learning approach

One of the most important composite indicators (CIs) to assess the development of countries or regions is the human development index (HDI) which is used by the United Nations (UN) to rank countries. HDI has three dimensions including healthy life, population education, and standard of living. A total of four different sub-indicators are defined for these three dimensions. The UN evaluates and ranks all countries using a simple arithmetic or geometric average of the sub-indicators and then categorizes the countries into four different groups based on their HDI scores. To measure the HDI, the benefit-of-the-doubt (BOD) model is used by researchers instead of the geometric mean. The conventional BOD model has some main drawbacks. The first is not accounting for data uncertainty, and the second is evaluating countries using different weights for the same sub-indicators. Furthermore, BOD model is not capable of predicting countries' future HDI scores. To overcome these deficiencies, this paper proposes a common weight fuzzy BOD (CWFBOD) model to measure the HDI scores. First, to take into account the uncertainty, data are considered fuzzy numbers, and a fuzzy BOD model (FBOD) is introduced. Then, to find a set of common weights for the three dimensions of HDI, the proposed FBOD model is transformed into a multiple-objective CWFBOD model. To convert and solve the multiple objective CWFBOD model to a single objective model, a fuzzy theory approach is used. In addition, of predicting the future HDI scores of countries, an artificial neural network (ANN) is designed and trained, where the original data on sub-indicators health, education, and income are considered as the features, and the HDI scores generated by CWBOD are assumed as the target of ANN. Finally, this study applies the fuzzy C-Means clustering technique to cluster all countries into four different clusters based on the HDI scores generated by FBOD and CWFBOD models. To illustrate the ability of the proposed methodology, the HDI scores of 190 countries during the period of 2015-2021 have been estimated and predicted. The results show that the proposed integrated methodology can be effectively used to estimate and predict the HDI scores as well as to cluster countries.