A method to multi-attribute decision-making based on interval-valued q-rung dual hesitant linguistic Maclaurin symmetric mean operators

The aim of this paper is to propose a new multi-attribute decision-making (MADM) method to rank all feasible alternatives in complex decision-making scenarios and determine the optimal one. To this end, we first propose the notion of interval-valued q-rung dual hesitant linguistic sets (IVq-RDHLSs) by combining interval-valued q-rung dual hesitant fuzzy (IVq-RDHF) sets with linguistic terms set. The proposed IVq-RDHLSs utilize IVq-RDHF membership and non-membership degrees to assess linguistic terms, so that they can fully express decision-makers’ evaluation information. Additionally, some related concepts such as the operational rules, score and accuracy functions, and ranking method of IVq-RDHLSs are presented. Considering the good performance of the classical Maclaurin symmetric mean (MSM) in integrating fuzzy information, we further generalize MSM into IVq-RDHLSs to propose the interval-valued q-rung dual hesitant linguistic MSM operator, the interval-valued q-rung dual hesitant linguistic dual MSM operator, as well as their weighted forms. Afterwards, we study the applications of IVq-RDHLSs and their aggregation operators in decision-making and propose a new MADM method. Some real decision-making problems in daily life are employed to prove the rightness of the proposed method. We also attempt to demonstrate the advantages and superiorities of our proposed method through comparing with some other methods in this paper.