A hybrid approach using AHP–TOPSIS–entropy methods for sustainable ranking of structural materials

Figures & data

Figure 1 System hierarchical structure.

Figure 2 Dimensions of the sustainable MADM problem.

Figure 3 Model procedure chart.

Table 1 Calculation of sustainable factors weights.

	SF1	SF2	SF3	SF4	SF5	SF6	SF7	SF8	SF9	SF10
Pairwise comparison matrix
SF1	1.000	1.250	0.952	1.300	1.200	1.050	1.450	1.500	1.550	1.350
SF2	0.800	1.000	0.769	1.050	0.952	0.833	1.200	1.250	1.300	1.100
SF3	1.050	1.300	1.000	1.350	1.250	1.100	1.500	1.550	1.600	1.400
SF4	0.769	0.952	0.741	1.000	0.909	0.800	1.150	1.200	1.250	1.050
SF5	0.833	1.050	0.800	1.100	1.000	0.870	1.250	1.300	1.350	1.150
SF6	0.952	1.200	0.909	1.250	1.150	1.000	1.400	1.450	1.500	1.300
SF7	0.690	0.833	0.667	0.870	0.800	0.714	1.000	1.050	1.100	0.909
SF8	0.667	0.800	0.645	0.833	0.769	0.690	0.952	1.000	1.050	0.870
SF9	0.645	0.769	0.625	0.800	0.741	0.667	0.909	0.952	1.000	0.833
SF10	0.741	0.909	0.714	0.952	0.870	0.769	1.100	1.150	1.200	1.000
Sustainable factors weights
Weights (%)	12.27	9.95	12.76	9.53	10.39	11.78	8.39	8.05	7.74	9.13
Note: SF, sustainable factor.

Table 2 Calculation of sustainable scores for TOPSIS matrix.

	SF1	SF2	SF3	SF4	SF5	SF6	SF7	SF8	SF9	SF10
Percentage score of sustainable factors per unit of material
RC	93	91	95	77	97	6	50	88	50	50
Steel	31	36	32	38	61	49	50	88	50	63
Glulam	74	38	59	75	00	00	50	88	50	100
Final percentage score of sustainable factors for the designed structural element
RC	93	91	95	77	97	6	50	88	50	50
Steel	85	86	85	86	91	49	50	88	50	63
Glulam	94	86	91	94	77	0	50	88	50	100

Table 3 Alternatives' rank by TOPSIS.

	S^+	S^−	R^+				Rank
Phase	I		I	II	III	Overall	I	II	III	Overall
RC	0.11626	0.20099	0.54	0.58	0.72	0.54	2	3	3	2
Steel	0.06218	0.18606	0.69	0.65	0.79	0.69	1	1	1	1
Glulam	0.12507	0.20191	0.53	0.62	0.74	0.52	3	2	2	3
Phases weights by entropy
	Phase I		Phase II				Phase III
Weights (%)	81		10				9