Table 1. The fuzzy spectrum equivalent to nine-degree scale of Saati in AHP technique.

Verbal statement of status of comparison of i in relation to j	Fuzzy equivalent	Inverse fuzzy Equivalent
EquallyPreferred	(1, 1, 1 )	(1, 1, 1)
In between	(1, 2, 3)	$$\left(\frac{1}{3},\frac{1}{2},1\right)$$
moderatelyPreferred	(2, 3, 4 )	$$\left(\frac{1}{4},\frac{1}{3},\frac{1}{2}\right)$$
In between	(3, 4, 5 )	$$\left(\frac{1}{5},\frac{1}{4},\frac{1}{3}\right)$$
StronglyPreferred	(4, 5, 6 )	$$\left(\frac{1}{6},\frac{1}{5},\frac{1}{4}\right)$$
In between	(5, 6, 7 )	$$\left(\frac{1}{7},\frac{1}{6},\frac{1}{5}\right)$$
very strongly Preferred	(6, 7, 8 )	$$\left(\frac{1}{8},\frac{1}{7},\frac{1}{6}\right)$$
In between	(7, 8, 9 )	$$\left(\frac{1}{9},\frac{1}{8},\frac{1}{7}\right)$$
Extremely Preferred	(9, 9, 9 )	$$\left(\frac{1}{9},\frac{1}{9},\frac{1}{9}\right)$$