Additive Consistency-Based Decision-Making with Incomplete Probabilistic Linguistic Preference Relations

Abstract

Probabilistic linguistic term set (PLTS), an efficient tool to describe decision information, can sufficiently express decision makers' hesitation and preference. Probabilistic linguistic preference relation (PLPR) is based on PLTSs to describe the preference information of experts for paired alternatives. However, in practice, due to the complexity of the problem, the incompleteness of information and the lack of professional knowledge, the incomplete PLPR (InPLPR) with missing information often appears. Therefore, this paper proposes a decision-making method under InPLPR. Firstly, in order to fully consider the specific situation of missing values, missing linguistic term-InPLTS (MLT-InPLTS) is subdivided into missing single linguistic term-InPLTS (MSLT-InPLTS) and missing multiple linguistic terms-InPLTS (MMLT-InPLTS). Then, a two-stage mathematical optimization model of missing information estimation based on additive consistency, fuzzy entropy and hesitation entropy is established. Subsequently, aiming at the unacceptable consistency of complete PLPR (CPLPR) after filling in the missing values, a consistency improvement method based on the idea of gradient descent is proposed. Afterward, probabilistic linguistic weighted averaging (PLWA) operator is used to rank alternatives. Finally, medical supplier selection is taken as an example to verify the effectiveness of the proposed decision-making method, and the robustness and advantages of this method are illustrated by sensitivity analysis and comparison with other methods.

Grey Relational Analysis Method for Probabilistic Double Hierarchy Linguistic Multiple Attribute Group Decision Making and Its Application to College Tennis Classroom Teaching Effect Evaluation

“…Furthermore, to check on the feasibility as well as availability of the new proposed method, useful comparative analysis is also designed. In the near future, we shall pay attention to the consensus reaching process [66][67][68][69][70][71], influence of DMs' psychological factors [72][73][74][75][76][77], and how to deal with the situations when criteria weights are incompletely known [78][79][80][81][82][83].…”