EDAS (Evaluation Based on Distance from Average Solution) is based on the distances of each alternative from the average solution. It is similar to other distance based multi-attribute decision-making methods such as TOPSIS and VIKOR. Hesitant fuzzy sets are an extension of ordinary fuzzy sets where the hesitation arises in the assignment of membership degrees of the elements to a fuzzy set. In this paper, we extend classical EDAS method to its hesitant fuzzy version in order to capture decision makers' hesitancies. The proposed Hesitant Fuzzy Evaluation Based on Distance from Average Solution (HF-EDAS) is based on different aggregation operators with defuzzification and without-defuzzification processes, which is presented by four HF-EDAS versions. The proposed method has been applied to a multi-criteria and multi-expert hospital selection problem for organ transplantation. Additionally, we present a comparative analysis with hesitant fuzzy TOPSIS (HF-TOPSIS). The results show that HF-EDAS selects the same best alternative as HF-TOPSIS. However, the proposed versions of HF-EDAS indicated some slight changes in the ranking of alternatives.