Picture fuzzy Choquet integral-based VIKOR for multicriteria group decision-making problems

Choquet integral operator has been proved more ideal than traditional aggregation operators in the modeling of interaction phenomena among the criteria in multicriteria group decision-making (MCGDM) problems. In this paper, we mention the limiting behavior of Choquet integral operator for intuitionistic fuzzy set (IFS) and propose Choquet integral for picture fuzzy set (PFS). This limitation is due to the incapability of IFS to model information that may be available in the form of refusal and abstain. We define Choquet averaging and Choquet geometric mean operators for PFS along with their few properties. We have also proposed picture fuzzy Choquet integral-based VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) for MCGDM problems. Proposed picture fuzzy Choquet integral-based VIKOR method includes benefits of PFS and addresses issue of interdependency among noncommensurable criteria in MCGDM problems. An example of supplier selection problem is included to show suitability and applicability of proposed picture fuzzy Choquet integral-based VIKOR method.