A novel probabilistic linguistic decision-making method with consistency improvement algorithm and DEA cross-efficiency

Abstract

Probabilistic linguistic term set (PLTS) is highly useful for decision-makers (DMs) to describe qualitative and uncertain information in the decision-making process. This paper proposes a novel probabilistic linguistic decision-making method with consistency improvement algorithm and data envelopment analysis (DEA) cross-efficiency. Firstly, we put forward the concept of order consistency of probabilistic linguistic preference relation (PLPR). The order consistency is helpful for DMs to make quick and efficient decision in certain situations. Then, based on the defined multiplicative consistency of PLPR, we develop a consistency improvement algorithm to transform the unacceptable multiplicative consistent PLPRs into the acceptable ones. Furthermore, a DEA model is established to derive the priority weight vector of alternatives from the acceptable multiplicative consistent PLPR. Meanwhile, for the alternatives that have equal priority weights, we use a DEA cross-efficiency model to further differentiate and obtain the final ranking of alternatives. Finally, a numerical example of emergency logistics distribution selection is given to illustrate the effectiveness and applicability of the proposed method.