Comparison of Fuzzy AHP and Fuzzy TOPSIS for Road Pavement Maintenance Prioritization: Methodological Exposition and Case Study

Table 3

(a) Fuzzy linguistic variables and corresponding fuzzy numbers. (b) Fuzzy number memberships of pairwise comparisons [8].

(a)

Linguistic variable	Fuzzy number	Membership function	Definition
Equally important		(1, 1, 2)	Practical knowledge and experience imply that factor is equally important when compared to factor .
Moderately important		(2, 3, 4)	Practical knowledge and experience imply that factor is moderately more important when compared to factor .
More important		(4, 5, 6)	Practical knowledge and experience imply that factor is more important when compared to factor .
Strongly important		(6, 7, 8)	Practical knowledge and experience imply that factor is strongly important when compared to factor .
Extremely important		(8, 9, 9)	Practical knowledge and experience imply that factor   is extremely important when compared to factor and totally outweighs it.

(b)

	Fuzzy number		Fuzzy number
1	(1, 1, 2)	0.50	(0.33, 0.5, 1)
2	(1, 2, 3)	0.33	(0.25, 0.33, 0.5)
3	(2, 3, 4)	0.25	(0.2, 0.25, 0.33)
4	(3, 4, 5)	0.20	(0.17, 0.2, 0.25)
5	(4, 5, 6)	0.17	(0.14, 0.17, 0.2)
6	(5, 6, 7)	0.14	(0.13, 0.14, 0.17)
7	(6, 7, 8)	0.13	(0.11, 0.13, 0.14)
8	(7, 8, 9)	0.11	(0.11, 0.11, 0.13)
9	(8, 9, 9)	Diagonal elements	(1, 1, 1)