Aiming at the triangular fuzzy (TF) multi-attribute decision making (MADM) problem with a preference for the distribution density of attribute (DDA), a decision making method with TF number two-dimensional density (TFTD) operator is proposed based on the density operator theory for the decision maker (DM). Firstly, a simple TF vector clustering method is proposed, which considers the feature of TF number and the geometric distance of vectors. Secondly, the least deviation sum of squares method is used in the program model to obtain the density weight vector. Then, two TFTD operators are defined, and the MADM method based on the TFTD operator is proposed. Finally, a numerical example is given to illustrate the superiority of this method, which can not only solve the TF MADM problem with a preference for the DDA but also help the DM make an overall comparison.

For chemical processes, dynamic optimization is employed for process transition. On the basis of the multilayer control structure, the employment of dynamic optimization is affected by the regulatory control system. To avoid the adjustment of the regulatory control system, set-point optimization is proposed. For comparison, two types of optimization models, namely direct optimization and set-point optimization, are formulated. The superiority of set-point optimization is rigorously proven. By simulating the commercial process of a throughput-fluctuating ethylene column, the integrated absolute error and maximum deviation of product quality are reduced by more than 150% with set-point optimization. The results indicate that the approach to process transition via regulatory controllers not only avoids the insecurity caused by the switching of set-point controllers but also improves the optimization performance. In conclusion, the proposed optimization structure, namely set-point optimization, is operable and stable for commercial chemical process transitions.