**Changming Ji 1, Xiaoqing Liang 1,2, Yang Peng 1, Yanke Zhang 1,\*, Xiaoran Yan <sup>1</sup> and Jiajie Wu <sup>1</sup>**


Received: 15 January 2020; Accepted: 28 February 2020; Published: 3 March 2020

**Abstract:** In decision-making with interval numbers, there are problems such as how to reduce the loss of decision information to improve decision accuracy and the difficulty of using interval numbers for sorting. On the basis of fully considering the subjective and objective weights of indexes, the grey entropy method (GEM) is improved by taking advantage of the Mahalanobis-Taguchi System (MTS) in which the orthogonal design has few tests but much obtained information, and the Mahalanobis distance can reflect the correlation between indexes. Then, the signal-to-noise ratio is integrated with the improved degree of balance and approach, and a multi-dimensional interval number decision model based on MTS and GEM is put forth. This model is applied to selecting the optimal scheme of controlling the Pankou reservoir's water level in flood season. Compared with the decision results of other methods, the optimal scheme selected by the proposed model can achieve greater benefits within an acceptable risk range and thus better coordinate the balance between risk and benefit, which verifies the feasibility and validity of the model.

**Keywords:** Mahalanobis-Taguchi System; grey entropy method; signal-to-noise ratio; degree of balance and approach; interval number
