Introduction
Literature search
Multiple criteria decision making
Goal programming (GP)
Linguistic variables | Triangle Fuzzy numbers |
---|---|
Very low (VL) | (0%, 5%, 10%) |
Low (L) | (5%, 10%, 25%) |
Medium–low (ML) | (20%, 32.5%, 45%) |
Medium (M) | (40%, 50%, 60%) |
Medium–high (MH) | (55%, 67.5%, 80%) |
High (H) | (75%, 85%, 95%) |
Very high (VH) | (90%, 100%, 100%) |
1st Decision maker | 2nd Decision maker | 3rd Decision maker | |
---|---|---|---|
Installed capacity increased | MH | M | L |
Energy generation increased | H | VH | M |
Power plants increased | M | H | ML |
Power consumption increased | VH | H | L |
CO\(_{2}\) emission decreased | M | VH | VH |
1st Decision maker (moderate) (a) | 2nd Decision maker (optimistic) (b) | 3rd Decision maker (pessimistic) (c) | |
---|---|---|---|
Installed capacity increased | 0.55,67.5,80 | 40,50,60 | 5,15,25 |
Energy generation increased | 75,85,95 | 90,100,100 | 40,50,60 |
Power plants increased | 40,50,60 | 75,85,95 | 20,32.5,45 |
Power consumption increased | 90,100,100 | 75,85,95 | 5,15,25 |
Installed capacity increased | 0.55,67.5,80 | 40,50,60 | 5,15,25 |
Energy generation increased | 75,85,95 | 90,100,100 | 40,50,60 |
Power plants increased | 40,50,60 | 75,85,95 | 20,32.5,45 |
Power consumption increased | 90,100,100 | 75,85,95 | 5,15,25 |
\(\hbox {CO}_{2}\) emission decreased | 40,50,60 | 90,100,100 | 90,100,100 |
Analytic Hierarchy Process (AHP)
Fuzzy Analytic Hierarchy Process (Fuzzy AHP)
Linguistic variable | Fuzzy values | Reciprocal values |
---|---|---|
Equally important | (1, 1, 1) | (1/1, 1/1, 1/1/) |
Weakly important | (1, 3, 5) | (1/5, 1/3, 1) |
Essentially important | (3, 5, 7) | (1/7, 1/5, 1/3) |
Very strongly important | (5, 7, 9) | (1/9, 1/7, 1/5) |
Absolutely important | (7, 9, 11) | (1/11, 1/9, 1/7) |
Application
The Preemptive Goal Programming application
Power plants | The number of current power plants | Installed capacity/the number of current power plants | Energy generation/the number of current power plants | Energy demand/the number of current power plants | Greenhouse gas emission/the number of current power plants |
---|---|---|---|---|---|
Coal | 38 | 0.423 | 2282.6 | 1.2 | 1.4 |
Natural gas | 213 | 0.109 | 672.6 | 0.109 | 0.419 |
Hydro | 562 | 0.047 | 124.7 | 0.106 | 0.0026 |
Wind | 130 | 0.035 | 93.4 | 0.010 | 0.00066 |
Geothermal | 22 | 0.029 | 158 | 0.0025 | 0.004 |
Solar | 113 | 0.0036 | 5.28 | 0.067 | – |
Biomass | 68 | 0.0049 | 23.69 | 0.012 | 0.00058 |
Variable | Value | Variable | Value |
---|---|---|---|
\(x_{1}\)
| 71,00000 |
\(d_{11}\)
| 0,000000 |
\(x_{2}\)
| 340,0000 |
\(d_{12}\)
| 7,088600 |
\(x_{3}\)
| 766,0000 |
\(d_{21}\)
| 0,000000 |
\(x_{4}\)
| 572,0000 |
\(d_{22}\)
| 133184,0 |
\(x_{5}\)
| 22,00000 |
\(d_{31}\)
| 47,92500 |
\(x_{6}\)
| 834,0000 |
\(d_{32}\)
| 0,000000 |
\(x_{7}\)
| 68,00000 |
\(d_{41}\)
| 0,000000 |
\(d_{42}\)
| 525,0000 | ||
\(d_{51}\)
| 0,000000 | ||
\(d_{52}\)
| 4,356560 |
Criteria | ED | IC | SR | PE | VP |
---|---|---|---|---|---|
Environmental damage (ED) | (1, 1, 1) | (1/5, 1/3, 1) | (5, 7, 9) | (3, 5, 7) | (1, 3, 5) |
Investment cost (IC) | (1, 3, 5) | (1, 1, 1) | (7, 9, 11) | (3, 5, 7) | (3, 5, 7) |
Space requirement (SR) | (1/9, 1/7, 1/5) | (1/11, 1/9, 1/7) | (1, 1, 1) | (1, 3, 5) | (1/5, 1/3, 1) |
Provided employment (PE) | (1/7, 1/5, 1/3) | (1/7, 1/5, 1/3) | (1/5, 1/3, 1) | (1, 1, 1) | (3, 5, 7) |
Visual pollution (VP) | (1/5, 1/3, 1) | (1/7, 1/5, 1/3) | (1, 3, 5) | (1/7, 1/5, 1/3) | (1, 1, 1) |
Fuzzy AHP application
-
\(\mathrm{S}_{1}\): Hydro
-
\(\mathrm{S}_{2}\): Wind
-
\(\mathrm{S}_{3}\): Geothermal
-
\(\mathrm{S}_{4}\): Solar
-
\(\mathrm{S}_{5}\): Biomass
Criteria | l | m | u |
---|---|---|---|
SED | 0.117 | 0.295 | 0.665 |
SIC | 0.190 | 0.420 | 0.890 |
SSR | 0.030 | 0.080 | 0.210 |
SPE | 0.060 | 0.120 | 0.280 |
SVP | 0.030 | 0.090 | 0.220 |
V | SED | SIC | SSR | SPE | SVP |
---|---|---|---|---|---|
SED | – | 0.79 | 1 | 1 | 1 |
SIC | 1 | – | 1 | 1 | 1 |
SSR | 0.3 | 0.06 | – | 0.79 | 0.95 |
SPE | 0.48 | 0.23 | 1 | – | 1 |
SVP | 0.33 | 0.08 | 1 | 0.84 | – |
Criteria | ED | IC | SR | PE | VP |
---|---|---|---|---|---|
Hydro | 0.244 | 0.311 | 0.423 | 0 | 0 |
Wind | 0.381 | 0.338 | 0.017 | 0.104 | 0.581 |
Geothermal | 0.068 | 0.017 | 0.309 | 0.313 | 0 |
Solar | 0.091 | 0.196 | 0.237 | 0.336 | 0.419 |
Biomass | 0.213 | 0.135 | 0.012 | 0.245 | 0 |
Criteria Weights | 0.365 | 0.463 | 0.027 | 0.106 | 0.037 |
Total superiority weights of alternatives | |
---|---|
Hydro | 0.244 |
Wind | 0.327 |
Geothermal | 0.072 |
Solar | 0.179 |
Biomass | 0.167 |