Multiplicative consistency analysis of linguistic preference relation with self‐confidence level and self‐doubting level and its application in a group decision making

This article focuses on a group decision-making (GDM) approach based on the multiplicative consistency of linguistic preference relation (LPR) with experts' self-confidence and self-doubting (SC&SD) levels. To give their preferences, the experts use their knowledge of the experience according to their degree of SC&SD levels. First, we propose the concepts of multiplicative consistent LPR-SC&SD using the experts' general minimum self-confidence level and the maximum self-doubting level. We suggest then a consensus-building iterative process, that is, a consensus reaching process (CRP) algorithm to achieve multiplicative consistency of LPR-SC&SD according to identification and adjustment rules. A theorem is given for convergence of the CRP algorithm. In a GDM problem, social network analysis is studied for the experts to obtain their weight according to the degree of SC&SD. When we achieve the acceptable preferences of all the experts using the CRP algorithm of the multiplicative consistent LPR-SC&SD, then we aggregate all the preferences by the experts' weights. The aggregation of all preferences is also an LPR-SC&SD, known as the weight collective LPR-SC&SD. Finally, a case-by-case example and several comparative analyses are done with the current GDM processes to demonstrate the viability and applicability of the proposed GDM system.