Determining the Degree of Preference Liking and Effectiveness of DMUs over a Long Period of Time by Means of a New Approach based on the Cross Efficiency Value Chain in Harmony with Fuzzy Arithmetic

In this paper, an alternative approach is presented for the evaluation of the likeability preference and effectiveness of DMUs, based on the DEA and fuzzy DEA models. In the magnitudes of variable values according to input-output levels, over the time period, some have not completely clear (fuzzy) values obtained from perceptions and surveys. For a more realistic assessment of effectiveness and determination of the degree of preference liking, to avoid accidental fluctuation values, and to get as close as possible to the trend of the process's progress, dynamic analysis of smoothing of the time series is applied to the input-output value levels. This is done according to a k-order moving average, determining the new levels of the input-output values. The approach is applied in two phases. In the first phase, the efficiency value chain matrix is determined, applying conventional DEA models with constant and variable returns to scale, evaluation of super efficiencies, fuzzy efficiency, and cross-efficiency. The data and the comparison of the models are analyzed, focusing in particular on the cross-efficiency value chain. In the second phase, fuzzy triangular numbers are composed of of the chain of cross-efficiency values for each DMU. Then based on fuzzy arithmetic as well as the concept given by the geometric probability model is determined and the transition matrix of the degree of preference liking, the evaluation of the ranking is obtained according to the degree of preference liking of each DMU in relation to other DMUs. In the paper, the contributions of the approach to the evaluation of the effectiveness and the degree of preference liking with the relevant conclusions are highlighted.