Table 7 FAHP equations

1-Sum of a fuzzy number ⊕ 

ñA ⊕ ñB = (\(a\) A + \(a\) B, \(b\) A + \(b\) B, \(c\) A + \({ }c\) B)

(1)

2-Multiplication of a fuzzy number ⊗ 

ñA ⊗ ñB = (\(a\) AX \(a\) B, \(b\) AX \(b\) B, \(c\) AX \(c\) B)

(2)

3-Division of a fuzzy number ∅

ñA ∅ ñB = (\(a\) A/\(a\) B, \(b\) A/\(b\) B, \(c\) A/\(c\) B)

(3)

4-Subtraction of a fuzzy number ϴ

ñA ϴ ñB = (\(a\) A–\(a\) B, \(b\) A − \(b\) B, \(c\) A–\({ }c\) B)

(4)

5-Reciprocal of a fuzzy number

Xñ a − 1 = (\(a,{ }b,{ }c)\) − 1 = (1/\(c\), 1/\(b\), 1/\(a\))

(5)

6-In this research, the geometric mean technique was employed to perform the data analysis to compute the fuzzy values (Coffey and Claudio 2021)

Ƒ = (ñi,1 ⊗ ñi,2 ⊗ … ñi,n) 1/n

 = ((\(a\) i, 1X \(a\) i, 2 X \(a\) i, 3 … X \(a\) i, n) 1/n,

(\(b\) i, 1X \({ }b\) i, 2 X \(b\), i3 … X \({ }b\) i, n) 1/n,

(\(c\) i, 1 X \(c\) i, 2 X \(c\) i, 3 … X \(c\) i, n) 1/n)

(6)

7-wi = fuzzy weight of the \(i\)th event

(7)

8-Ƒi = geometric mean of the ith row

DF Wi = \(\frac{{\left[ {\left( {ci - ai} \right) + \left( {bi - ai} \right)} \right]}}{3 + ai}\)

(8)

9-Difuzzified (DF) mean of the weights

Then Wi = \(\frac{{DF\;{\text{W}}i}}{{\sum DF{\text{W}}i}}\) (A9)

(9)