Application of Choquet integral in interval type‐2 Pythagorean fuzzy sustainable supply chain management under risk

The purpose of this study is to offer requisite models for unravelling the complex issues that arise in a supplier selection-order allocation problem by soothing the risk and disturbances. To do this, a new uncertain environment, interval type-2 Pythagorean fuzzy set (IT2PFS) is introduced to assist the experts for assuring secure and reliable outcomes in hesitant situations. The operational laws on IT2PFS under Dombi t-norm and t-conorm are defined, which are further utilized to develop geometric Bonferroni mean and Bonferroni mean operators based on Choquet integral (CI) under IT2PFS. The aggregation operators can ennoble the pliability of the information blending process through the adjustment of several parameters and can make good interactions among the criteria with their weights. Thereafter, to determine the weights of the criteria, an empirical method, namely the decision making trial and evaluation laboratory (DEMATEL) is amplified by conjoining CI and IT2PFS into it. A multicriteria decision making method, namely, the multiattribute border approximation area comparison (MABAC) and subsequently the CI based grey relational analysis method are then employed to classify the suppliers and derive their corresponding weights with reference to the sustainable criteria. Over and above, a new multiobjective optimization model is exhibited to uphold the purchasing managers for assembling suppliers keeping in mind the sustainability aspects and overall risk of suppliers by following Markowitz portfolio theory. A real-life supply chain management problem is demonstrated to elucidate the aptness and efficiency of the proposed work. Furthermore, the effectiveness and importance of the study are validated via the comparative analysis with existing approaches. The main contribution of the study is in handling the difficulty and confusion that arise during information gathering, information aggregation, suppliers evaluation and order allocation phases.