Derivation of personalized numerical scales from distribution linguistic preference relations: an expected consistency-based goal programming approach

Due to the promising performance of distribution linguistic preference relations (DLPRs) in eliciting the comparison information coming from decision makers (DMs), linguistic decision problems of this type of preference relations have attracted considerable research interest in recent years. However, to our best knowledge, there is little research on the personalized individual semantics of linguistic terms when dealing with computing with words (CWW) in the process of solving linguistic decision problems with DLPRs. As is well known, one statement about CWW in linguistic decisions is that words might exhibit different meanings for different people. Words need to be individually quantified when dealing with CWW. Hence, the objective of this study is to fill this gap by applying the idea of personalizing numerical scales of linguistic terms for different DMs in linguistic decision with DLPRs to manage the statement about CWW. First, this study connects DLPRs to fuzzy preference relations and multiplicative preference relations by using different types of numerical scales. Then, definitions of expected consistency for DLPRs are presented. On the basis of expected consistency, some goal programming models are built to derive personalized numerical scales for linguistic terms from DLPRs. Finally, a numerical study concerning football player evaluation is analyzed by using the proposed method to demonstrate its applicability in practical decision scenarios. A discussion and a comparative study highlight the validity of the proposed method in this paper.