Multi-stage optimization model for hesitant qualitative decision making with hesitant fuzzy linguistic preference relations

Hesitant fuzzy linguistic preference relation (HFLPR) as a new preference relation is introduced to express the decision makers’ (DMs’) hesitant preference information for each pairwise comparison between different alternatives or criteria. In this paper, the priority vector and consistency of HFLPR are discussed based on a two-stage optimization and multiplicative consistency. Based on the original hesitant preference information, the multiplicative consistency index of an HFLPR is defined to measure the consistency level of the HFLPR. For an unacceptable multiplicative consistent HFLPR, a goal programming model, which is an integer optimization model, is developed to derive an acceptable, multiplicative, consistent HFLPR. According to probability sampling, a linguistic preference relation (LPR) with the best consistency level and an LPR with the worst consistency level with regard to an HFLPR are defined. Combining the two LPRs, a two-stage optimization framework is constructed to obtain the HFLPR’s priority vector, which considers the DM’s risk preference. A multi-stage optimization approach is proposed to solve decision-making problems by integrating the goal programming model and the two-stage optimization framework. Two real life problems are analyzed to show the feasibility of the proposed approach.