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In this paper, we present a new fuzzy decision-making method, which is based on likelihood-based comparison relations. First, we introduce the concepts of likelihood-based comparison relations for intervals. Then, we propose the concept of likelihood-based comparison relations for type-1 fuzzy sets and interval type-2 fuzzy sets. Then, we present a new method to rank fuzzy sets by using fuzzy targets based on the proposed likelihood-based comparison relations for fuzzy sets. Finally, we present a new fuzzy decision-making method based on the proposed likelihood-based comparison relations for fuzzy sets and the proposed fuzzy ranking method. The proposed fuzzy decision-making method has the advantage that the evaluated values can either be represented by crisp values, intervals, type-1 fuzzy sets or interval type-2 fuzzy sets. It can overcome the drawbacks of Huynh et al.'s method due to the fact that Huynh et al.'s method cannot deal with the ranking of interval type-2 fuzzy sets for fuzzy decision-making and cannot distinguish the ranking order between the alternatives in some situations.