Additive consistency-based approach for group decision making with hesitant 2-tuple linguistic preference relations

This paper develops an hesitant 2-tuple linguistic preference relation (H2TLPR) in which the pairwise comparisons are represented by hesitant 2-tuple linguistic sets (H2TLSs) and then, uses the additive consistency concept for linguistic fuzzy preference relations to give an additive consistency definition for H2TLPRs. Two iterative optimization methods, namely, feedback optimization method (FOM) and automatic optimization method (AOM) are proposed to obtain a solution with a desired consistency index of H2TLPR. In the FOM, the decision makers (DMs) are suggested to give their new preference values in a specific range. If the DMs/experts are unwilling to offer their updated preferences, the AOM is proposed to carry out the consistency improvement process. A score H2TLPR is proposed, and then introduced hesitant 2-tuple linguistic weighted averaging (H2TLWA) operator for the aggregation of H2TLPRs. Furthermore, the quantifier-guided dominance degrees are used to obtain hesitant 2-tuple linguistic ordered weighted averaging (H2TLOWA) operator weights. Finally, a case study is carried out, showing the potentials of the methodology by using the H2TLPRs and the optimization methods, and evaluating the selection of a best investment company that's interested in the construction of one of the main infrastructure project of China Pakistan Economic Corridor (CPEC).