Algorithm 1 Forward cloud generator

Input: $\left\{E\mathrm{x},E\mathrm{n},He\right\}$;

Output: $\left\{Drop\left(x_i,u_i\right),i=1,2,\dots ,n\right\}$

Generate normal random numbers $E{\mathrm{n}}_i{}^{\prime }~N$($E\mathrm{n},H{e}^2$); Generate normal random numbers $x_i{}^{\prime }~N$($E\mathrm{n},E{\mathrm{n}}_i{}^{\prime }$); Find the cloud drops $u\left(x_i\right)=\exp (-\frac{{\left(x_i-E\mathrm{x}\right)}^2}{2{\left(E{\mathrm{n}}_i{}^{\prime }\right)}^2})$; $u\left(x_i\right)$ is the degree of determination and $x_i$ is 1 cloud drop in the number field; Repeat steps 1–4 until N cloud drops are generated. Let the left boundary of each rating interval of the evaluation index be $I_{min}$ and the right boundary be $I_{max}$ Cloud parameters $\left(E\mathrm{x},E\mathrm{n},He\right)$ are determined by $I_{min}$ and $I_{max}$:

$$\{\begin{array}{c}\begin{array}{c}E\mathrm{x}=\left( I_{max}+I_{min}\right)/2\\ E\mathrm{n}=\left( I_{max}-I_{min}\right)/6\\ He=k\end{array}\end{array}$$ (8)

where $E\mathrm{x}$ is the sample cloud expectation, $E\mathrm{n}$ is the cloud entropy value, $He$ is the cloud super-entropy, $E{\mathrm{n}}_i{}^{\prime }$ is the cloud entropy value of the index after the next iteration, and k reflects the randomness and linguistic fuzziness of each evaluation index and is a constant and should not be too large; here, k is 0.02.