Hesitant Fuzzy Linguistic Term Set with Granularity Level

According to the literature review of HFLTSs in Chap. 1 , although the existing linguistic model can allow decision makers to use multiple linguistic terms to express evaluation information in the decision-making process, there are still some defects in the use of hesitant fuzzy linguistic model. For example, different people have different understandings when they use the same set of HFLEs; The original HFLEs cannot present flexible semantics; Some semantics given by decision makers may change in the process of traditional consistency improvement methods, resulting in that the original evaluation opinion of decision makers may change. Therefore, it is necessary to develop a new form of linguistic term set based on the original hesitant fuzzy linguistic model to embody the flexibility, fuzziness and personality of semantics. Inspired by the idea of granular computing, this chapter proposes a new hesitant fuzzy linguistic representation method, namely, Hesitant Fuzzy Linguistic Term Set with Granularity level (G-HFLTS), which allows decision makers to provide flexible, hesitant and uncertain evaluation information in the decision-making process. This linguistic model stipulates that the representation structure of decision-making information should be granular rather than purely numerical, which brings some flexibility and personality to the structure of hesitant fuzzy linguistic representation information, and also provides a new way to represent linguistic information. According to the two different situations if the evaluation information is complete or not, this chapter mainly introduces two corresponding term sets, namely, the complete G-HFLTS and the incomplete G-HFLTS, and presents the consistency index of HFLPR and the consistency improvement algorithm, respectively.