A novel cross-efficiency evaluation method under hesitant fuzzy environment

In the cross-efficiency model, when the decision making unit (DMU) self-evaluation efficiency value is optimal, the sets of input and output weights exhibit non-uniqueness, and the choice among alternative optimal solutions results in different peer- evaluation values, consequently leading to different cross-efficiency scores and rankings. In addition, the interval value constitutes the cross-efficiency value, which increases the uncertainty of the decision- making due to the information fuzziness. To solve this problem, a group decision-making method for cross-efficiency is proposed on the basis of hesitant fuzzy sets (HFSs). This method selects five optimal solutions. Moreover, given that the attitudes of decision-makers range from pessimistic to optimistic, this method introduces HFSs to the cross-efficiency matrix, and obtains the multi-objective optimization method to rank the alternatives based on the relative closeness degree. Finally, a classical numerical example is provided to illustrate the potential applications of the proposed method and its effectiveness in ranking DMUs.