Algorithm 2: General type-2 fuzzy Sugeno integral algorithm

Input:n represents the sources number, D(xi) denotes the information and M(xi) the FD in the domain (0,1).

Output: General type-2 Sugeno integral h.

1: Estimate the M(xi) and D(xi) using the function $$\tilde{\mu }\left(x,u\right)=trigausstype2\left(x,u,\left[a_1,b_1,c_1,a_2,b_2,c_2,\rho \right]\right)$$

2: Determine the alpha cuts (αi) for D(xi) and M(xi) $$\mu (M_{iL{\alpha }_i}\left(x_i\right)),\mu (M_{iR{\alpha }_i}\left(x_i\right))$$ $$\mu (D_{L{\alpha }_i}\left(x_i\right)),\mu (D_{R{\alpha }_i}\left(x_i\right))$$

3: Calculate λ and the αi cuts for ${\mathsf{\lambda }}_L$ and ${\mathsf{\lambda }}_R$ using Equations (14) and (15).

4: Determine the FM ${\mu }_{L{\alpha }_i}\left(B_i\right)$ and ${\mu }_{R{\alpha }_i}\left(B_i\right)$ applying Equations (16)–(19).

5: Calculate the Sugeno integral $h\left({\tilde{\sigma }}_{{\alpha }_i}\right)$, for all the αi with Equation (20).

6: Finally, calculate the GT2SI