New Operations on Generalized Hesitant Fuzzy Linguistic Term Sets for Linguistic Decision Making

Hesitant fuzzy linguistic term set is defined in hesitant fuzzy linguistic decision frameworks in which all decision makers are agreed on the primary linguistic scale and its membership functions; however, this situation does not always happen, because words mean different things to different people or there are some linguistic term sets with different semantics for different people. Hence, normalization of linguistic information is necessary. Inspired by normalizing linguistic information based on 2-tuple linguistic model, in this paper, the concept of generalized hesitant fuzzy linguistic term set is proposed when decision makers are not agreed on the primary linguistic scale and its membership functions, which is an extension of hesitant fuzzy linguistic term set. Then, t-norms and t-conorms are utilized to define new operations on generalized hesitant fuzzy linguistic term sets and their properties are discussed. Based on these new operations, the likelihood-based comparison relation of generalized hesitant fuzzy linguistic term sets is presented, which is an extension of the likelihood-based comparison relation of hesitant fuzzy linguistic term sets. Accordingly, the generalized hesitant fuzzy linguistic weighted average operator, generalized hesitant fuzzy linguistic weighted geometric operator, generalized hesitant fuzzy linguistic ordered weighted average operator and generalized hesitant fuzzy linguistic ordered weighted geometric operator are provided to fuse generalized hesitant fuzzy linguistic term sets in linguistic decision making. A case study is used to illustrate the practicality of the method based on generalized hesitant fuzzy linguistic term sets and compare with Lee and Chen's method, Rodriguez's method and Wei's method. It seems that the method based on generalized hesitant fuzzy linguistic term sets is flexible and useful method for hesitant fuzzy linguistic decision making.