The Abnormal Phenomena of Entropy Weighting Method in the Dynamic Evaluation of Agricultural Water Conservation

Through a simple and intuitive example of the agricultural water conservation assessment in 3 provinces, China, the abnormal phenomena of the entropy weighting method (EWM) in the dynamic evaluation are revealed. The results show the following. (i) The irrigation water efficiency percentages (IWEPs) of these 3 provinces are improved from 53%, 53%, and 55% to 55%, 56%, and 56%, respectively. And their water-saving irrigation projects percentages (WSIPPs) are improved from 40%, 41%, and 41% to 42%, 42%, and 42%, respectively. However, their comprehensive agricultural conservation indices deteriorate from 52.11, 52.45, and 56.1 to 46.07, 46.74, and 48.57, respectively. (ii) EWM leads to the following paradox in the dynamic evaluation. All the indicators show improving trends, but the comprehensive evaluation results show a deteriorating trend. (iii) These abnormal phenomena of EWM are induced by that though all the indicators are improved, the discrimination of the worse indicators becomes larger while the discrimination of the better indicators becomes smaller. (iv) The abnormal phenomena of EWM in dynamic evaluation can be avoided by the trend analysis of the observation data and entropy values. When all the indicators have improvement trends, but the entropies of the better indicators are increasing and the entropies of the worse indicators are decreasing, EWM should not be used for assigning weights.