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.
Highlights
Multi-expert decision making (MEDM) can be regarded as a situation in which a group of experts are invited to provide their individual opinions by evaluating the given alternatives, and select the optimal alternative(s)
The main innovation points of this paper are highlighted as follows: (1) By combining the preference ordering and double hierarchy linguistic terms (DHLTs), we develop two novel concepts of linguistic preference ordering (LPO), which are in continuous form and in decentralized form, respectively
Transforming each LPO into the corresponding double hierarchy linguistic preference relation (DHLPR) with complete consistency equivalently is the preparation of the consensus reaching process
Summary
Multi-expert decision making (MEDM) (or Group decision making) can be regarded as a situation in which a group of experts are invited to provide their individual opinions by evaluating the given alternatives, and select the optimal alternative(s). Motivated by Wu, Huang and Xu (2019a) and to fully respect the experts’ expression habits, in this paper, we focus on establishing some consensus optimization models by considering the suggested preferences represented in both the continuous scale and the discrete scale. To provide more refined solutions to experts, this paper develops a multi-stage consensus optimization model which consists of three objectives including minimizing the deviations of the modification magnitudes, minimizing the cardinal number of modifications while keeping the value of the first objective constant, and minimizing the number of experts who need to change their evaluations. Motivation 2: Consensus model for LPOs (Section 1.4) The most important advantage of optimization models is that they can provide the adjusted preference solutions directly by setting goals and solving the established models.
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