A new method for multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets

This paper presents a new method for multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets. The context-free grammar is used to produce the linguistic assessments of alternatives with respect to criteria. The linguistic expressions are transformed into hesitant fuzzy linguistic term sets by means of a transformation function. The fuzzy sets in each hesitant fuzzy linguistic term set are combined into a fuzzy set. The system performs the α-cut operations to these aggregated fuzzy sets to get intervals, respectively, where α ∈ (0,1]. For each alternative, the system performs the minimum operations among the intervals obtained by the a-cuts of the aggregated fuzzy sets to get a derived interval of each alternative, where α ∈ (0,1]. Finally, for each alternative, the system calculates the likelihood p(X ≥ [0, 1]) of X ≥ [0,1], where X is a derived interval of the alternative. The larger the likelihood value of the alternative, the better the preference order of the alternative. The proposed method is simpler than the existing method for multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets.