**Appendix A**

When applied to the case study, the FILP model can be formulated as follows: Objective functions Maximize its membership function:

$$\text{Max}\lambda^{\pm} \tag{A1}$$

Constraints Maximize the economic benefit:

$$\sum\_{i=1}^{4} \sum\_{j=1}^{16} \sum\_{k=1}^{4} e\_{jk}^{\pm} a\_{ijk} x\_{ijk}^{\pm} \ge f\_1^- + \lambda^{\pm} (f\_1^+ - f\_1^-) \tag{A2}$$

Maximize the overall satisfaction of water users:

$$\sum\_{j=1}^{16} \sum\_{k=1}^{4} \frac{a\_{ijk} \boldsymbol{\chi}\_{ijk}^{\pm}}{G\_{jk}^{\pm}} \boldsymbol{a}\_{jk}^{\pm} \ge f\_2^{-} + \lambda^{\pm} (f\_2^{+} - f\_2^{-}) \tag{A3}$$

Minimize the chemical oxygen demand (COD) discharge of major pollutants in the region:

$$\sum\_{i=1}^{4} \sum\_{j=1}^{16} \sum\_{k=1}^{4} d\_{jk}^{\pm} x\_{ijk}^{\pm} \le f\_3^+ - \lambda^{\pm} (f\_3^+ - f\_3^-) \tag{A4}$$

Water supply constraint:

$$\sum\_{j=1}^{16} \sum\_{k=1}^{4} \varkappa\_{ijk}^{\pm} \le S\_i^{\pm} \tag{A5}$$

Water demand constraint:

$$D\_{jk}^{\\\pm} \le \sum\_{i=1}^{4} a\_{ijk} x\_{ijk}^{\\\\\pm} \le G\_{jk}^{\\\\\pm} \tag{A6}$$

Water transporting capacity constraint:

$$\sum\_{k=1}^{4} \varkappa\_{ijk}^{\pm} \le \mathcal{Q}\_{ij}^{\pm} \tag{A7}$$

The COD emission constraint:

$$\sum\_{i=1}^{4} \sum\_{k=1}^{4} d\_{jk}^{\pm} \mathbf{x}\_{ijk}^{\pm} \le F\_j^{\pm} \tag{A8}$$

Nonnegative constrains:

$$\mathfrak{x}\_{ijk}^{\pm} \ge 0 \tag{A9}$$

1 ≥ *λ* <sup>±</sup> ≥ 0 (A10)
