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What Is The Normalize Weight Variable?

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V(Ŝi ≥ Ŝj) = (16) Where Ŝi= (li,mi.ui) and Ŝj= (lj,mj.uj) In order to compare, Ŝi and Ŝj, both the value of V(Ŝi ≥ Ŝj) and V(Ŝj ≥ Ŝi) were computed Step 3: The basic principles in Step 2 were then extended to calculate the degree of possibility of, Ŝi, of one criterion, being greater than all the other (n- 1) convex fuzzy numbers, Ŝj, of other criteria. This can be defined as follows, V(Ŝi ≥ Ŝj| j=1,……,n; ji) (17) By taking the minimum values in the degree of possibility sets created from Equation 17, it was possible to determine a weight vector, w, as follows, w = (d*(A1), d*(A2),…, d*(An))T, where d*(Ai) = min V(Ŝi ≥ Ŝj| j=1,……,n; ji) (18) Step 4: The normalized weight vectors for each fuzzy comparison matrix, Ã, at each …show more content…

Table 22: The TFN pairwise comparison matrix of G ← F1−F3. G F1 F2 F3 W F1 (1,1,1) (1.0,3.0,5.0) (3.0,5.0,7.0) 0.573454 F2 (0.20,0.333,1) (1,1,1) (1.0,3.0,5.0) 0.375408 F3 (0.143,0.2,0.333) (0.20,0.333,1) (1,1,1) 0.051138 FCR = 0.011927035, G = Rainwater harvesting site suitability, F1 = Environmental factors, F2 = Hydrological factors, F3 = Socio-Economic factors and W is the weight of F1, F2 and F3 to G. V (SF1 ≥ SF2, SF3) = 1; V (SF2 ≥ SF1, SF3) = 0.654643557; V (SF3 ≥ SF1, SF2) = 0.089175 Table 23: The TFN pairwise comparison matrix of F1← L1−L4. F1 L1 L2 L3 L4 W L1 (1,1,1) (1.0,3.0,5.0) (3.0,5.0,7.0) (5.0,7.0,9.0) 0.475603 L2 (0.2,0.333,1) (1,1,1) (1.0,3.0,5.0) (3.0,5.0,7.0) 0.337951 L3 (0.143,0.2,0.333) (0.2,0.333,1) (1,1,1) (1.0,3.0,5.0) 0.150307 L4 (0.111,0.143,0.2) (0.143,0.2,0.333) (0.2,0.333,1) (1,1,1) 0.036139 FCR = 0.016, F1 = Environmental factors, L1 = Topography, L2 = Geology, L3 = Soil, L4 = LU/LC, W is the weight of L1, L2, L3, L4 to F1. V (SL1 > SL2, SL3, SL4) = 1;V(SL2 > SL1, SL3, SL4) = 0.710573; V (SL3> SL1 , SL2, SL4) = 0.316035; V(SL4 > SL1 , SL2, SL3)= 0.075987 Table 24: The TFN pairwise comparison matrix of F2 ← L5−L6. F2 L5 L6 W L5 (1,1,1) (1.0,3.0,5.0) 0.700023 L6 (0.2,0.333,1.0) (1,1,1) 0.299977 FCR = 0.000, F2 = Hydrological factors, L5 = Runoff, L6 = Drainage density, W is the weight of L5, L6 to F2 V (SL5 ≥ SL6 =1; V (SL6 ≥ SL5) = 0.428525512 Table 25: The TFN pairwise comparison matrix

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