A Novel Multi-attribute Group Decision-Making Method Based on q-Rung Dual Hesitant Fuzzy Information and Extended Power Average Operators

Multi-attribute group decision-making (MAGDM) is one of the most active research fields in modern social cognition and decision science theory. An obvious challenge in MAGDM problems is that it is not easy to appropriately describe decision-makers’ (DMs’) cognitive information, which is because the cognition of DMs is usually diverse and contains a lot of uncertainties and fuzziness. The recently proposed q-rung dual hesitant fuzzy set (q-RDHFS), encompassing diverse cognition and providing wide information space, has been proved to be effective to depict DMs’ cognitive information in the MAGDM process. However, existing operations and aggregation operators of q-RDHFSs still have limitations, which result in the weakness of existing q-RDHFS-based MAGDM methods. Therefore, this paper aims at introducing new operational rules and aggregation operators to deal with q-rung dual hesitant fuzzy information. To this end, we first propose a wide range of generalized operations for q-rung dual hesitant fuzzy elements (q-RDHFEs) based on Archimedean t-norm and t-conorm. Second, we put forward some new aggregation operators by generalizing the recently invented extended power average (EPA) operator into q-RDHFSs. Existing literature has revealed the powerfulness and flexibility of the EPA operator over the classical power average operator. Finally, a new MAGDM approach based on the proposed operators is developed. Our proposed method can effectively handle MAGDM problems with q-rung dual hesitant fuzzy cognitive information. Some numerical examples are conducted to demonstrate the validity of the new MAGDM method. Further, we conduct parameter analysis and comparative analysis to prove the flexibility and superiority of our proposed MAGDM method, respectively. In a word, this paper contributes to a new q-rung dual hesitant fuzzy MAGDM method, which absorbs the advantages of EPA operator and Archimedean operations. This method can be applied to describe complex cognitive information and solving realistic MAGDM problems effectively.