Integrated decision support model for selection of industrial wastewater treatment technologies

In this paper, we introduce a novel decision support model based on cubic Fermatean fuzzy sets (CuFFSs), combining stepwise weight assessment ratio analysis (SWARA), vector similarity measures (VSM) and the extended Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR), named CuFF-SWARA-VSM-VIKOR method. The proposed method is applied to the selection of industrial wastewater treatment technologies (IWTTs), addressing multi-criteria decision-making (MCDM) problem under uncertainty. We first propose four vector similarity measures (i.e. Tanimoto, Sørensen, cosine and hybrid similarity measures) for CuFFSs and validate their effectiveness through theoretical proofs. Subsequently, the VIKOR method is extended to address the MCDM problem involving CuFFSs, with criteria weights derived from subjective weights via SWARA and objective weights based on proposed measures. Finally, a case study demonstrates the effectiveness of the proposed framework, providing decision-makers with a reliable ranking of alternatives. According to the results, among the six criteria considered, the most suitable alternatives to be selected as IWTTs are Reverse osmosis (0.0000), Membrane bioreactor (0.3372), Electrocoagulation (0.3969), Activated sludge process (0.7621) and Constructed wetlands (1.0000). Additionally, comparisons with existing methods are performed to verify the robustness of the proposed method.