## 3 Applications
### Development of DRSFO-EES Model
\[\widetilde{f}_{15}=\ \widetilde{f}_{15s}+\widetilde{f}_{15N}+\widetilde{f}_{15 PM} \tag{37}\]  
where \(\widetilde{f}_{15s}\) is the cost of desulfurization; \(SO2K_{t}\) is the SO\({}_{2}\) emissions from coking processing; \(SO2 CE_{t}\) is the SO\({}_{2}\) emissions from coal-based power; \(SO2 NE_{t}\) is the SO\({}_{2}\) emissions from natural gas-based power; \(SO2H_{t}\) is the SO\({}_{2}\) emissions from heating processing; \(SO2O_{t}\) is the SO\({}_{2}\) emissions from oil refining; \(T\widetilde{PS}_{t}(TPS_{t}{}^{1},TPS_{t}{}^{2},TPS_{t}{}^{3})\) is the desulfurization cost of per unit of SO\({}_{2}\) emission; \(\eta_{s}\) is the desulfurization efficiency. (15a) Costs for SO\({}_{2}\) emissions reduction. The cost is calculated in terms of the total SO\({}_{2}\) emissions, the desulfurization cost per unit of SO\({}_{2}\) emission, and the desulfurization efficiency. \[\begin{array}{l}\widetilde{f}_{155}=\ \{\sum\limits_{t=1}^{3}\left(SO2K_{t}+SO2 CE_{t }+\ SO2 NE_{t}+SO2H_{t}+\ SO2O_{t}\right)\\ \ \ \ \ \ \ \ \ \  
\(T\widetilde{PPM}_{t}(TPPM_{t},^{1}TPPM_{t},^{2},TPPM_{t}\)\({}^{3})\) is the treatment cost per unit of PM emission; \(\eta_{PM}\) is the PM removal efficiency.  
(16) Costs for risk recourse of stochastic and fuzzy uncertainties.  
\[\widetilde{f}_{16}=V\widetilde{T}S+V\widetilde{T}F=\rho_{1}{\cdot}\sum_{i=1}^{ l}\sum_{t=1}^{T}\sum_{h=1}^{H}p_{th}(V_{ith}+VC_{ith})+\rho_{2}{\cdot}\sum_{t=1}^{ 3}VF_{t} \tag{41}\]  
where \(V\widetilde{T}S\) denotes the risk recourse cost for stochastic uncertainties; \(V\widetilde{T}F\) denotes the risk recourse cost of fuzzy uncertainties, with capturing the difference between the extreme values of fuzzy parameters. The nonnegative factors \(\rho_{1}\) and \(\rho_{2}\) represent robust levels (its range from 0 to 1), which can help managers make trade-offs between system economy and reliability. Constraints:  
The constraints of the proposed DRSFO-EES model include traffic sector, heat processing, coke processing, oil refining, electricity generation, energy production, air-pollutants treatment, and risk recourse cost for stochastic uncertainties and risk recourse for fuzzy uncertainties. (1) Constraints for traffic sector. This constraint represents that the optimized vehicles population must be not less than the lower bounds of vehicle population. \(Cr\{M\widetilde{AL}_{gt}\big{|}MA_{gt}\geq M\widetilde{AL}_{gt}\big{\}}\geq\alpha\) means the credibility of the \(MA_{gt}\geq M\widetilde{AL}_{gt}\) is higher than or equal to confidence-level \(\alpha\). \[Cr\{M\widetilde{AL}_{gt}\big{|}MA_{gt}\geq M\widetilde{AL}_{gt}\big{\}}\geq\alpha \tag{42}\]  
where \(MA_{gt}\) is the optimized solutions of vehicles population; \(M\widetilde{AL}_{gt}(MAL_{gt}\)\({}^{1},\ MAL_{gt}\)\({}^{2},\ MAL_{gt}\)\({}^{3})\) is the lower bounds of vehicle population, which is expressed as a triangular fuzzy number. Constraints for vehicle-emissions, including CO, NOx, HC, and PM emissions. These constraints represent that the vehicle-emissions are calculated in terms of the annual average mileage, the proportion of electric vehicles and the emission factors of CO, NOx, HC and PM emissions.