Integrated VIKOR-TOPSIS strategy based on picture fuzzy knowledge and accuracy measures with application in waste-water treatment

In contrast to a fuzzy and intuitionistic fuzzy (AInF) set, a picture fuzzy (PIF) set may be taken as an effective tool to tackle decision-making problems. Fuzzy and intuitionistic fuzzy set theory can be extended to PIF-set theory. In light of the insufficiency of existing information and knowledge measures, this work proposes a knowledge measure for PIF-sets. The suggested knowledge measure efficacy and consistency are proven using numerical examples by comparing it to existing information andproper knowledge measures in the PIF-context. Aside from that, the proposed knowledge measure is used to develop an accuracy measure for PIF-sets. In pattern identification problems, the use of proposed accuracy measure is presented. Their effectiveness is demonstrated by using numerical examples. A modified version of the Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) approach based on the proposed accuracy measure is presented with the goal to address a multi-criteria decision-making (MCDM) difficulty in a picture fuzzy context. Finally, a case study on how to choose the most suitable method to treat wastewater is provided.