The Group Evaluating Method For Cross-efficiency Based On Hesitant Fuzzy Sets

In the production of social activities,often need to evaluate or sort the similar decision making units.Because the decision involves more than one property,so it is hard to make decisions.Cross efficiency evaluation method is means of linear programming.The combination of cross efficiency model is self-evaluation and peer-evaluation.However,based on the existence of the non-uniqueness of self-evaluation in cross-efficiency evaluation,the choice among alternative optimal solutions makes different peer-evaluation,which consequently causes different cross-efficiency scores and rankings.On the other side,the rapid development of fuzzy set theory has provided a new way to solve the problem of multiple optimal solutions in cross-efficiency evaluation.Considering the multiple optimal solutions,we propose a new method for cross-efficiency based on hesitant fuzzy sets.The key issue of the study is how to construct the group cross efficiency matrix by hesitant fuzzy set and sort the decision-making units.The main work is as follows:1.This paper studies the sorting problem of decision unit under the cross efficiency matrix composed of hesitant fuzzy sets.Method ? is based on overall-coordination.This method selects five optimal solutions as decision makers from pessimism to optimism,introduces hesitant fuzzy sets to the cross efficiency matrix,obtains the multi-objective optimization method and rank the alternatives based on the relative closeness degree.2.In order to reflect the comprehensive efficiency of the decision-making unit intuitively,we propose Method ? based on decision makers' risk attitudes.It is an improvement to the previous method.In the proposed approach,we introduce the interval hesitant fuzzy set and decision makers' risk attitudes.To aggregate the efficiency values,we use the ordered weighted averaging(OWA)operator determined by the latent information(LI)function.3.Empirical analysis.Through the methods mentioned above,study the regional innovation efficiency of the six provinces in the central region.Then analyze the efficiency from two periods.In this paper,we introduce hesitant fuzzy set into the cross efficiency matrix and propose two solutions based on the hesitant fuzzy set.We also analysis the regional innovation efficiency by the method proposed.There will be a new direction for the research of cross efficiency evaluation.