Interval-valued intuitionistic hesitant fuzzy set (IVIHFS) has a key role in multiple attribute decision making (MADM) problems due to its ability to represent the decision maker’s hesitant opinions using preferred and non-preferred intervals. In this paper, we develop an interactive decision-making approach to solve multi-attribute group decision making (MAGDM) problems with incomplete weight information using probabilistic interval-valued intuitionistic hesitant fuzzy set (P-IVIHFS), which is an extension of IVIHFS. The assessments provided by the decision makers for individual alternatives regarding different attributes are expressed using probabilistic interval-valued intuitionistic hesitant fuzzy elements (P-IVIHFEs). Linear programming (LP) is used to obtain the optimal weights of attributes from the partially known weight information. Moreover, we extend the technique for order preference by similarity to ideal solution (TOPSIS) method in the framework of P-IVIHFS for the ranking purpose. Finally, we have solved a numerical example for the supplier selection problem using the proposed method to illustrate the applicability of the proposed approach. The comparative study demonstrates the suitability of the proposed approach over the existing methods.
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