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This study develops an approach that incorporates power aggregation operators with the evaluation based on distance from average solution (EDAS) method under linguistic neutrosophic situations to solve fuzzy multi-criteria group decision-making problems. Firstly, the existing operational laws and comparison methods of linguistic neutrosophic numbers (LNNs) are analysed. Secondly, the distance measurement between two LNNs is defined. Thirdly, the power-weighted averaging operator and the power-weighted geometric operator with LNNs are developed to support the decision makers' evaluation information. The models to derive the criteria weights are also constructed based on the proposed distance measurements. Finally, the EDAS method is extended to resolve group decision-making problems in the linguistic neutrosophic environment. An illustrative example of the property management company selection is given to verify the effectiveness and practicality of the proposed approach. [ABSTRACT FROM AUTHOR]

Probabilistic interval‐valued hesitant fuzzy sets (PIV‐HFSs) are suitable for aggregating information from different groups because the probabilistic information of all the groups can be included by using interval values. Moreover, decision makers (DMs) prefer to use interval values to provide evaluation information. Furthermore, the traditional multi‐criteria group decision‐making (MCGDM) approach has some limitations, such as obtaining the DMs' weights with inappropriate methods and neglecting the interactions amongst the criteria and the psychological characteristics of DMs. Motivated by these research background, the main contents of this study are as follows. First, PIV‐HFSs are proposed, and the convex combination operation is extended into PIV‐HFSs. Second, a hybrid MCGDM approach with PIV‐HFSs is suggested that is based on the maximizing deviation method, fuzzy analytic network process (FANP) and TODIM (an acronym in Portuguese for interactive and multi‐criteria decision‐making model). Third, an evaluation case of health management centres based on the service‐specific failure mode and effect analysis (FMEA) is considered. The results show that the most crucial secondary factor is frequency (0.35775) and that the most serious failure mode is the inaccurate check‐in. The results demonstrate that the proposed model can evaluate service quality effectively and that it performs better than other methods. [ABSTRACT FROM AUTHOR]