Managing Missing Preference Values Through Consistency and Consensus in Distributed Linguistic Preference Relations: A Two-stage Method Based on Personalized Individual Semantics

Linguistic distribution, as a flexible representation structure, is often used in linguistic decision-making. Several approaches have been proposed for managing the missing elements in incomplete preference relations when decision makers cannot provide all the linguistic comparisons between alternatives in preference relations. However, in linguistic decision-making, words can mean different things to different people, which implies the necessity of personalizing individual semantics. This study proposes a two-stage method, including a personalized individual semantics (PIS)-based consistency model and a PIS-based consensus model, to manage PIS and missing elements in incomplete distributed linguistic preference relations (DLPRs). The proposed method combines the characteristics of the personalization of linguistic expression and estimates the missing values, guaranteeing optimum consistency and consensus at the same time in group decision-making with incomplete DLPRs. Numerical and comparison analyses were performed to illustrate the use of the two-stage method, and demonstrates the various numerical meanings of words and the features of the obtained complete DLPRs from the proposed model.