Some consistency measures of extended hesitant fuzzy linguistic preference relations

Linguistic preference relations (LPRs) enable decision makers to express preferences by pair-wise comparisons in qualitative setting. The fundamental aspect of LPRs is to measure the degrees of consistency when applying them in decision making. Extended hesitant fuzzy linguistic term sets (EHFLTSs) are a powerful tool for modeling uncertain linguistic information in group decision making. Based on which we first present the concept of extended hesitant fuzzy linguistic preference relations (EHFLPRs), and then develop the additive consistency measure and the weak consistency measure respectively. Furthermore, in order to solve the consistency problem by the perspective of graphs, two algorithms are proposed based on two kinds of predefined graphs, i.e., the hesitant preference graphs and the symmetric hesitant preference graph. The selective algorithm selects the arcs with the highest additive consistency level from the symmetric hesitant preference graph and constructs a LPR. While the broken circle algorithm removes the arcs from circular triads of the hesitant preference graph, it makes the EHFLPR with weak consistency and divides the EHFLPR into several possible LPRs satisfying weak consistency. This paper therefore explores a visible interpretation of consistency measures. The rationality of the proposed algorithms is verified by several examples, and some related issues are also discussed.