A minimum deviation approach for improving the consistency of uncertain 2-tuple linguistic preference relations

This paper proposes a novel approach for improving the consistency of uncertain 2-tuple linguistic preference relations (U2TLPRs). In particular, we introduce a new definition of consistency for U2TLPRs and show that the degree of consistency of a given U2TLPR can be measured explicitly by minimizing its deviation from a consistent U2TLPR. Based on this finding, we provide an iterative algorithm for repeatedly adjusting the consistency of a U2TLPR to a desired level while taking into account the initial preferences of decision makers. In addition, by analyzing the structural properties of the algorithm, we further present an improved version of the procedure for directly obtaining an acceptable U2TLPR without any iteration. Numerical results indicate that the proposed method is not only simple and efficient in calculation but also effective in preserving the original preference information provided by decision makers.