Читать книгу Renewable Energy for Sustainable Growth Assessment - Группа авторов - Страница 63

To address the uncertainties associated with qualitative data fuzzy-TOPSIS is used for ranking. Table 2.3 will be the input decision matrix for fuzzy-TOPSIS. Since indicator’s ratings are not in the form of fuzzy linguistic variables, normalization in the range of [0, 1] is done using equations (2.18) and (2.19), and presented as Table 2.5.

 (i) For the beneficial indicators:(2.18)

 (ii) For the non-beneficial indicators:(2.19)

In the next step, decision matrix with a fuzzy linguistic variable has to be established using triangular membership functions defined as shown in Figure 2.2.

Table 2.5 is now transformed to Table 2.6 as described with an example. If the numeric rating of an indicator value is 0.50, the equivalent fuzzy linguistic value then will be “Medium”. Table 2.6 now is converted to Table 2.7 the fuzzy decision matrix using Figure 2.2. Table 2.7 presents the fuzzy decision matrix. As per step (e) of Section 2.4, V+ and V- are defined as Vj⁺ = (0,0,0) and Vj^- = (1,1,1) for beneficial indicators and Vj^- = (0, 0, 0) and Vj⁺ = (1, 1, 1) for non-beneficial indicators respectively. Table 2.8 presents the resulting fuzzy weighted decision matrix with their values ranges from the closed interval [0,1] and final ranking obtained following steps (f)-(h).

Table 2.4 The TOPSIS result.

RE technology	I1	I2	I3	I4	I5	I6	I7	I8	I9	I10	Si+	Si-	Ri	Ranking
Large hydropower	0.0611	0.0822	0.0472	0.0379	0.0682	0.0179	0.0020	0.0115	0.0722	0.0674	0.0952	0.1589	0.6253	2
Small hydropower	0.0611	0.0164	0.0472	0.0483	0.0477	0.0001	0.0001	0.0344	0.0433	0.0405	0.0857	0.1587	0.6494	1
Solar PV	0.0114	0.0164	0.0189	0.0500	0.0341	0.0022	0.0022	0.0574	0.0144	0.0270	0.1030	0.1603	0.6088	4
Onshore wind power	0.0267	0.0164	0.0262	0.0403	0.0341	0.0109	0.0110	0.0574	0.0289	0.0135	0.0938	0.1505	0.6162	3
Bioenergy	0.0412	0.0493	0.0671	0.0459	0.0273	0.0978	0.0993	0.0459	0.0433	0.0539	0.1588	0.0807	0.3369	5
Vj+	0.0611	0.0822	0.0671	0.0379	0.0682	0.0001	0.0001	0.0574	0.0144	0.0135
Vj-	0.0114	0.0164	0.0189	0.0500	0.0273	0.0978	0.0993	0.0115	0.0722	0.0674

Table 2.5 Normalized decision matrix for fuzzy-TOPSIS.

RE technology	I1	I2	I3	I4	I5	I6	I7	I8	I9	I10
Large hydropower	1.00	1.00	0.59	1.00	1.00	0.82	0.94	0.00	0.00	0.00
Small hydropower	1.00	0.00	0.59	0.13	0.50	1.00	1.00	0.50	0.50	0.50
Solar PV	0.00	0.00	0.00	0.00	0.17	0.98	0.81	1.00	1.00	0.75
Onshore wind power	0.31	0.00	0.15	0.80	0.17	0.89	0.97	1.00	0.75	1.00
Bioenergy	0.54	0.50	1.00	0.33	0.00	0.00	0.00	0.75	0.50	0.25
Wj	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10

Figure 2.2 Fuzzy triangular membership function [88].