Group prioritisation with unknown expert weights in incomplete linguistic context

Abstract

ABSTRACTIn this paper, we study a group prioritisation problem in situations when the expert weights are completely unknown and their judgement preferences are linguistic and incomplete. Starting from the theory of relative entropy (RE) and multiplicative consistency, an optimisation model is provided for deriving an individual priority vector without estimating the missing value(s) of an incomplete linguistic preference relation. In order to address the unknown expert weights in the group aggregating process, we define two new kinds of expert weight indicators based on RE: proximity entropy weight and similarity entropy weight. Furthermore, a dynamic-adjusting algorithm (DAA) is proposed to obtain an objective expert weight vector and capture the dynamic properties involved in it. Unlike the extant literature of group prioritisation, the proposed RE approach does not require pre-allocation of expert weights and can solve incomplete preference relations. An interesting finding is that once all the experts express their preference relations, the final expert weight vector derived from the DAA is fixed irrespective of the initial settings of expert weights. Finally, an application example is conducted to validate the effectiveness and robustness of the RE approach.