Consistency and consensus-driven models to personalize individual semantics of linguistic terms for supporting group decision making with distribution linguistic preference relations

Distribution linguistic preference relations (DLPRs) that model linguistic expressions with the aid of probabilistic distributions of multiple linguistic terms provide an effective tool to accurately elicit the preferences of decision makers (DMs) in linguistic decisions. Meanwhile, numerical scale models have been suitable choices for DMs to handle computing with words when solving linguistic decision problems. This study focuses on improving the group decision making (GDM) with DLPRs via the help of numerical scale models by filling the following gap. It is obvious that words might exhibit different meanings for different people. DMs may have a varying understanding of a given linguistic term in real-world fuzzy linguistic GDM. Setting personalized semantics of the linguistic terms for each DM becomes a critical task in GDM with DLPRs. To do this, we first define an improved numerical scale model to facilitate the linkages between DLPRs and numerical fuzzy preference relations. Then an additive consistency and a multiplicative consistency of DLPRs are analyzed, and the corresponding consistency indices are provided to measure the consistency levels of DLPRs. Based on them, we develop two consistency-driven optimization models to personalize numerical scales for linguistic terms with individual DLPRs. Next, we develop an approach for addressing GDM with DLPRs. In the proposed approach, a dissimilarity-based consensus measure is designed. To determine a group numerical scale for the linguistic terms with the corresponding group DLPR, two consistency and consensus-driven optimization models are constructed. Finally, illustrative examples are analyzed using the proposed approach to demonstrate its applicability and validity.