## 3 Applications
### Development of DRSFO-EES Model
 \tag{23}\]  
where \(H\widetilde{P}P_{t}(HPP_{t}{}^{1},HPP_{t}{}^{2},HPP_{t}{}^{3})\) is the cost for unit of heat processing, which is expressed as a triangular fuzzy number; \(HGA_{t}\) is the heat processing amount. (2) Cost for oil refining. This cost is calculated in terms of the unit-price and the amount of oil refining. \[ \begin{array}{ll}\widetilde{f}_{2}=\sum\limits_{t=1}^{3}\left[0.25(PVO_{t}{ }^{1}+2 PVO_{t}{}^{2}+PVO_{t}{}^{3})\cdot OFOIL_{t}\right.\\ +\left.\lambda_{1}\cdot\sum\limits_{t=1}^{3}\left[PVO_{t}{}^{3}-0.25(PVO_{t}{ }^{1}+2 PVO_{t}{}^{2}+PVO_{t}{}^{3})\right]OFOIL_{t}\\ +\left.\lambda_{2}\cdot\sum\limits_{t=1}^{3}\left[0.25(PVO_{t}{}^{1}+2 PVO_{t}{ }^{2}+PVO_{t}{}^{3})\ -PVO_{t}{}^{1}\right]OFOIL_{t}\end{array}  \tag{24}\]  
where \(P\widetilde{V}O_{t}\)\((PVO_{t}{}^{1},PVO_{t}{}^{2},PVO_{t}{}^{3})\) is the cost for unit of oil refining; \(OFOIL_{t}\) is the crude oil consumption of oil refining. (3) Cost for coke processing. This cost is calculated in terms of the unit-price and the amount of coke processing. \[ \begin{array}{ll}\widetilde{f}_{3}=\sum\limits_{t=1}^{3}\left[0.25(PWO_{t}{ }^{1}+2 PWO_{t}{}^{2}+PWO_{t}{}^{3})\cdot CKPA_{t}\right.\\ +\left.\sum\limits_{t=1}^{3}\left[PWO_{t}{}^{3}-0.25(PWO_{t}{}^{1}+2 PWO_{t}{ }^{2}+PWO_{t}{}^{3})\right]\right.CKPA_{t}\\ +\left.\sum\limits_{t=1}^{3}\left[0.25(PWO_{t}{}^{1}+2 PWO_{t}{}^{2}+PWO_{t}{ }^{3})\ -PWO_{t}{}^{1}\right]CKPA_{t}\end{array}  \tag{25}\]where \(P\widetilde{WO}_{t}(PWO_{t}{}^{1},PWO_{t}{}^{2},PWO_{t}{}^{3})\) is the cost for unit of coke processing; and \(CKPA_{t}\) is the coke processing amount. (4) Cost for purchasing coal resources. This cost is used for purchasing coal resources, and it is calculated based on the unit-price and the amount of coal resource. \[\begin{split}&\widetilde{f}_{4}=\sum\limits_{t=1}^{3}\left[0.25(NSC _{t}{}^{1}+2 NSC_{t}{}^{2}+NSC_{t}{}^{3})\right]\cdot ECOALM_{t}\\ &+\lambda_{1}\cdot\sum\limits_{t=1}^{3}\left[NSC_{t}{}^{3}-0.25( NSC_{t}{}^{1}+2 NSC_{t}{}^{2}+NSC_{t}{}^{3})\right]ECOALM_{t}\\ &+\lambda_{2}\cdot\sum\limits_{t=1}^{3}\left[0.25(NSC_{t}{}^{1}+ 2 NSC_{t}{}^{2}+NSC_{t}{}^{3})\right.\right.\right.\right.\right.\right. \tag{26}\]  
where \(N\widetilde{SC}_{t}(NSC_{t}{}^{1},NSC_{t}{}^{2},NSC_{t}{}^{3})\) is the price for unit of coal resource; and \(ECOALM_{t}\) is the coal consumption of coal-based power. (5) Cost for purchasing natural gas resources. This cost is used for purchasing natural gas resources, and it is calculated based on the unit-price and the amount of natural gas resource. \[ \begin{split}&\widetilde{f}_{5}=\sum\limits_{t=1}^{3}\left[0.25( NSN_{t}{}^{1}+2 NSN_{t}{}^{2}+NSN_{t}{}^{3})\right]\cdot ENGM_{t}\\ &+\lambda_{1}\cdot\sum\limits_{t=1}^{3}\left[NSN_{t}{}^{3}-0.25( NSN_{t}{}^{1}+2 NSN_{t}{}^{2}+NSN_{t}{}^{3})\right]ENGM_{t}\\ &+\lambda_{2}\cdot\sum\limits_{t=1}^{3}\left[0.25(NSN_{t}{}^{1}+ 2 NSN_{t}{}^{2}+NSN_{t}{}^{3})\right.\right.\left.-NSN_{t}{}^{1}\right]ENGM_{t} \end{split}  \tag{27}\]  
where \(N\widetilde{S}N_{t}(NSN_{t}{}^{1},\ NSN_{t}{}^{2},\ NSN_{t}{}^{3})\) is the price for unit of natural gas resource; and \(ENGM_{t}\) is the natural gas consumption of natural gas-based power. (6) Cost for importing electricity. This cost is calculated in terms of the unit-price and the amount of importing electricity. \[ \begin{split}&\widetilde{f}_{6}=\sum\limits_{t=1}^{3}\sum \limits_{t=1}^{3}\left[0.25(NE_{t}{}^{1}+2 NE_{t}{}^{2}+NE_{t}{}^{3})\cdot ED_{ th}\right.\\ &+\lambda_{1}\cdot\sum\limits_{t=1}^{3}\sum\limits_{t=1}^{3}[NE_{ t}{}^{3}-0.25(NE_{t}{}^{1}+2 NE_{t}{}^{2}+NE_{t}{}^{3})]ED_{th}\\ &+\lambda_{2}\cdot\sum\limits_{t=1}^{3}\sum\limits_{t=1}^{3}[0.25( NE_{t}{}^{1}+2 NE_{t}{}^{2}+NE_{t}{}^{3})\right.\left.-NE_{t}{}^{1}\right]ED_{ th}\end{split}  \tag{28}\]  
where \(N\widetilde{E}_{t}(NE_{t}{}^{1},\ NE_{t}{}^{2},\ NE_{t}{}^{3})\) is the price for unit of imported electricity; \(ED_{th}\) is the amount of imported electricity. (7) Operation cost for first-stage electricity generation.