Admissible orders of typical hesitant fuzzy elements and their application in ordered information fusion in multi-criteria decision making

• Develop the total orders (called admissible orders) of HFEs for MCDM.
• Derive the distinct rankings of HFEs from different admissible orders.
• Redefine the hesitant fuzzy OWA operator based on the proposed total orders.
• Investigate a series of desirable properties of the operator.

Typical hesitant fuzzy elements (HFEs) are quite useful for multi-criteria decision making (MCDM) in hesitant fuzzy setting. To reach a decision, it is necessary to derive the orders of HFEs. However, all the existing orders presented for HFEs in the literature are partial orders. We may need total orders sometimes such as in the situations when aggregating information by the ordered weighted aggregation (OWA) operators. Thus, the first purpose of this paper is to develop the total orders (called admissible orders) of HFEs for MCDM. The admissible orders improve the existing partial orders of HFEs and can be generated by a set of special functions. We demonstrate that the distinct ranking of HFEs can be derived according to different admissible orders. Another purpose is to redefine the hesitant fuzzy OWA operator based on the proposed total orders. Some interesting properties of the operator are also discussed.