Raha Imanirad

This study measures the efficiency of airlines using a novel fuzzy common weight additive network data envelopment analysis (NDEA) with shared resources, negative data, and undesirable outputs. First, an appropriate two-stage network is designed for each airline so that stages 1 and 2 are called the Production and Service stages, respectively. The proposed model adopts a top-down approach and calculates the efficiency of the system first and then estimates the efficiency of stages 1 and 2. To evaluate and predict the airlines’ efficiency considering fuzzy data and the reliability of the information, the values of input/intermediate/output variables are predicted as the Z-number and the appropriate Z-number version of NDEA (ZNDEA) models is proposed. To develop the proposed ZNDEA models and find common weights for the variables, three multi-objective ZNDEA models for the system, stage 1 and stage 2 are presented. The multi-objective common weight ZNDEA models are solved using the min-max Chebyshev goal programming technique and the final efficiencies are calculated. To illustrate the capability of the proposed approach, real-life data from Iranian airlines in 2022 are collected, and the efficiencies are analyzed.

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.

• Common weight