Extended VIKOR method for multiple criteria decision-making with linguistic hesitant fuzzy information

•An order relationship of LHFSs is defined considering position weights of membership.•Some distance measures of LHFSs are defined by considering the position weights.•The criteria weights are estimated by two new optimization programming models.•A LHF-VIKOR method is proposed for MCDM with LHFSs.

Linguistic hesitant fuzzy set (LHFS), a special hesitant fuzzy set (HFS) defined on linguistic term set (LTS), not only can express decision makers' (DMs') qualitative preferences, but can reflect their uncertainty and hesitancy. This paper develops a new LHF-VIKOR (linguistic hesitant fuzzy Vlsekriterijumska Optimizacija I Kompromisno Resenje) method for solving multiple criteria decision-making (MCDM) problems with LHFSs. Firstly, a new order relationship is proposed to rank LHFS by sufficiently considering the weights of membership degrees. Subsequently, a series of new distance measures of LHFS are defined including generalized distance, generalized Hausdorff distance, hybrid generalized distance, hybrid Hamming distance, and hybrid Euclidean distance. Some desirable properties of the defined distance measures are discussed in detail. Then, according to the maximizing deviation method, two optimization models are constructed to derive the criteria weights objectively for the case of completely unknown weight information and the case of incomplete weight information, respectively. Finally, by extending VIKOR method into LHF environment, a new LHF-VIKOR method is proposed to rank alternatives. An intelligent transportation system (ITS) evaluation example is analyzed to demonstrate the effectiveness and feasibility of the proposed method.