Pythagorean Fuzzy Based AHP-VIKOR Integration to Assess Rail Transportation Systems in Turkey

Rail transit systems, one of the important public transportation (PT) systems, are widespread in large cities to satisfy passengers or commuters for their daily trips. However, rail transportation (RT) investments are costly, and the budgets are minimal. Thus assessing RT systems in big cities play a crucial role in deciding on the best RT investment. In this study, for the first time, a two-stage fuzzy set is used among the multi-criteria decision-making (MCDM) studies in the area of transportation. The proposed method is a unique technique integrating the Analytic Hierarchy Process (AHP) and Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) techniques with an extension of Pythagorean fuzzy sets. In this manner, datasets from the observations of three rail lines in Antalya, one of the largest cities in Turkey, are applied to the proposed method. Fuzzy Analytic Hierarchy Process (FAHP), a commonly used MCDM method, is used to weighting four main criteria and thirteen sub-factors. AHP is strengthened by interval-valued Pythagorean fuzzy numbers (IVPFNs). The Fuzzy VIKOR (FVIKOR) approach is then applied for the prioritization of three rail line alternatives. Results are achieved by analyzing not only real RT service observations, also actual RT expenditures or costs. Consequently, the uncertainty in results is thus minimized. Outcomes of the case study reveal the most serviceable RT line in the city evaluating the main criteria, namely economy, comfort, environment, and safety. Therefore, the proposed approach methodologically contributes to adopting a new insight into the integration of MCDM methods with fuzzy set.