2-tuple linguistic decision-making with consistency adjustment strategy and data envelopment analysis

2-tuple linguistic preference relations (2-TLPRs) are useful tools for addressing decision-making issues where the decision makers (DMs) are inclined to apply linguistic variables to express evaluation information. To retain the DM's initial preference information as much as possible, this paper provides a 2-tuple linguistic decision-making method that incorporates a consistency adjustment algorithm and a 2-tuple linguistic data envelopment analysis (DEA) model. As two important aspects of decision-making, it is worthy to further study the improvements in consistency and weight generation for alternatives with 2-TLPRs. In this paper, in order to adjust the consistency of an original 2-TLPR to a predetermined level, a convergent consistency-improving algorithm is first presented, and we employ a minimum adjustment strategy to preserve the DM's initial evaluation information. A 2-tuple linguistic DEA model is then developed to generate a vector of weights for the alternatives and we can derive reliable decision-making results. Finally, we provide a numerical example that can identify the most influential factor in Fog-haze weather to indicate the applicability of the 2-tuple linguistic decision-making method. The comparative analysis highlights the advantages and effectiveness of the 2-tuple linguistic decision-making method.