Managing Consensus by Multi-Stage Optimization Models With Linguistic Preference Orderings and Double Hierarchy Linguistic Preferences

Abstract

Preference ordering structures are useful and popular tools to represent experts’ preferences in the decision making process. In the existing preference orderings, they lack the research on the precise relationship between any two adjacent alternatives in the preference orderings, and the decision making methods are unreasonable. To overcome these issues, this paper establishes a novel concept of linguistic preference ordering (LPO) in which the ordering of alternatives and the relationships between two adjacent alternatives should be fused well, and develops two transformation models to transform each LPO into the corresponding double hierarchy linguistic preference relation with complete consistency. Additionally, to fully respect the experts’ expression habits and provide more refined solutions to experts, this paper establishes a multi-stage consensus optimization model by considering the suggested preferences represented in both the continuous scale and the discrete scale, and develops a multi-stage interactive consensus reaching algorithm to deal with multi-expert decision making problem with LPOs. Furthermore, some numerical examples are presented to illustrate the developed methods and models. Finally, some comparative analyses between the proposed methods and models and some existing methods have been made to show the advantages of the proposed methods and models.

Double hierarchy linguistic term set and its extensions: The state‐of‐the‐art survey

“…Remark The proposed distance and similarity, and correlation measures of DHHFLTSs are the basic tool of some decision‐making methods, such as MULTIMOORA, 7 TOPSIS, 32 VIKOR, 48 and so forth, and are also the basic of the consistency measure, 17,49,50 consensus model, 13,16,51,52 and clustering methods 16,51 . However, up to now, only two measure methods have been researched.…”

“…In addition, considering that the consensus reaching process (CRP) is one of the important constituent parts in group decision‐making and large‐scale group decision‐making (LSGDM). Therefore, some scholars have also researched the CRP with LPOs, 13 DHLPRs, 16 and DHHFLPRs 49,80 …”

“…When experts evaluate all alternatives and provide their preference orderings, two forms of LPOs are very familiar. One is to rank all alternatives using an LPO in a continuous form directly, and the other one is to give the relationship between any two alternatives and then all these relationships make up a set of preference orderings in a decentralized form 13 . The descriptions of the above two LPOs are given in detail as follows:(a) The LPO in continuous form : Let be a DHLTS, and be a set of alternatives.…”

“…Furthermore, even though preference ordering structures 9–12 are useful and popular tools to represent experts’ preferences in decision‐making processes, they usually lack the research on the precise relationship between any two adjacent alternatives. Therefore, Gou et al 13 defined the concept of linguistic preference orderings (LPOs) in which the ordering of alternatives and the relationships between two adjacent alternatives are fused closely. Moreover, considering that the pairwise comparison methods are more accurate than nonpairwise methods because experts only need to focus exclusively on two alternatives at a time 14,15 .…”

Interval Consistency Repairing Method for Double Hierarchy Hesitant Fuzzy Linguistic Preference Relation and Application in the Diagnosis of Lung Cancer

“…In addition, considering that complex uncertain linguistic information is common in decision-making processes, to represent this kind of linguistic information, Gou et al (2017) extended the DHLTS to hesitant fuzzy environment and developed the concept of double hierarchy hesitant fuzzy linguistic term set (DHHFLTS). During the past several years, lots of research results about double hierarchy linguistic information have been developed such as linguistic preference ordering (Gou et al, 2020d), preference relations (Gou et al, 2018(Gou et al, , 2019(Gou et al, , 2020a(Gou et al, , 2020b(Gou et al, , 2020c, measure methodologies (Fu & Liao, 2019;Gou, Xu, et al, 2018) and decision-making methodologies (Krishankumar et al, 2019, Liu et al, 2019Montserrat-Adell et al, 2019;Wang et al, 2020), etc.…”