## 3 Applications
### Development of DRSFO-EES Model  
Minimizing the system cost is the objective of DRSFO-EES, which includes costs for coke processing, heat processing, input for coal-based power, oil refining, input for natural gas-based power, imported electricity, first-stage of electricity generation, second-stage of electricity generation,  
Figure 1: Schematic overview of this study. electricity expansion, energy production, subsidy for solar power generation, subsidy for wind power generation, EVs charging piles, EVs charging stations, pollutants treatment, and risk recourse for the stochastic and fuzzy uncertainties. The proposed DRSFO-EES can be solved by Lingo 11.0 software. The schematic diagram of DRAOM-EWNS model is presented in Figure 2.  
In the DRSFO-EES, \(t\) denotes the planning periods, period 1 (2020), period 2 (2025), and period 3 (2030); \(i\) denotes the primary energy production type, \(i=1\) is coal, \(i=2\) is natural gas, and \(i=3\) is crude oil; \(k\) denotes the electric conversion technology, \(k=1\) is coal-based power, \(k=2\) is natural gas-based power, \(k=3\) is solar power, and \(k=4\) is wind power; \(h\) expresses the electricity demand-level, \(h=1\)  
Figure 2: The schematic diagram of dual robust stochastic fuzzy optimization—energy and environmental systems (DRSFO-EES). (low demand level), \(h=2\) (medium demand level), \(h=3\) (high demand level), \(\sum\limits_{h=1}^{3}p_{h}=1\); \(g\) are the vehicles types, \(g=1\) is HDVs, \(g=2\) is LDVs, \(g=3\) is TDTs, \(g=4\) is HDTs, and \(g=5\) is others. The proposed DRSFO-EES is formulated as follows:  
Objective:  
\[ \begin{array}{ll}\text{Min }\widetilde{f}&=\overline{f}+\lambda_{1}(f_{\text{ max}}-\overline{f})+\lambda_{2}(\overline{f}-f_{\text{min}})+VF_{t}\\ &=f_{1}\ +\ f_{2}\ +\ f_{3}\ +\ f_{4}\ +\ f_{5}\ +\ f_{6}\ +\ f_{7}\\ &+\ f_{8}\ +\ f_{9}\ +\ f_{10}\ -\ f_{11}-f_{12}+f_{13}\ +\ f_{14}\\ &+\ f_{15}+\ f_{16}\end{array}  \tag{22}\]  
where \(\widetilde{f}\) represents the system cost; \(\widetilde{f}_{1}\) denotes the heat processing cost; \(\widetilde{f}_{2}\) denotes oil refining cost; \(\widetilde{f}_{3}\) denotes coke processing cost; \(\widetilde{f}_{4}\) denotes the cost of coal inputs for coal-based power; \(\widetilde{f}_{5}\) denotes the cost of natural gas inputs for natural gas-based power; \(\widetilde{f}_{6}\) denotes importing electricity cost; \(\widetilde{f}_{7}\) denotes the cost of first-stage electricity generation; \(\widetilde{f}_{8}\) denotes the cost of second-stage electricity generation; \(\widetilde{f}_{9}\) denotes electricity expansion cost; \(\widetilde{f}_{10}\) denotes the energy production cost; \(\widetilde{f}_{11}\) denotes the subsidy for solar power; \(\widetilde{f}_{12}\) denotes the subsidy for wind power; \(\widetilde{f}_{13}\) denotes the cost of charging pile; \(\widetilde{f}_{14}\) denotes the cost of changing station; \(\widetilde{f}_{15}\) denotes air-pollutants removal cost; \(\widetilde{f}_{16}\) denotes the risk recourse costs of stochastic and fuzzy uncertainties. \(VF_{t}\) represents the positive deviation between maximum values and worst value of fuzzy parameters. \(\lambda_{1}\) and \(\lambda_{2}\) represent their respective weight coefficients, where it is assumed \(\lambda_{1}\) and \(\lambda_{2}\) are fixed (i.e., \(\lambda_{1}=\lambda_{2}=1\)). (1) Cost of heat processing. This cost is used for heat processing, and it is calculated based on the unit-price and amount of heat processing. \[ \begin{array}{ll}\widetilde{f}_{1}=\sum\limits_{t=1}^{3}\left[0.25(HPP_{t} {}^{1}+2 HPP_{t}{}^{2}+HPP_{t}{}^{3})\cdot HGA_{t}\right.\\ +\left.\lambda_{1}\cdot\sum\limits_{t=1}^{3}\left[HPP_{t}{}^{3}-0.25(HPP_{t} {}^{1}+2 HPP_{t}{}^{2}+HPP_{t}{}^{3})\right]\right.HGA_{t}\\ +\left.\lambda_{2}\cdot\sum\limits_{t=1}^{3}\left[0.25(HPP_{t}{}^{1}+2 HPP_{t }{}^{2}+HPP_{t}{}^{3})-HPP_{t}{}^{1}\right]\right.HGA_{t}\end{array}