An integrated regional water quality assessment method considering interrelationships among monitoring indicators

Abstract

To monitor and manage water environments, China developed a centralized multi-level administrative system where governments and agencies at each level are responsible for water quality within their regions. In this case, regional water quality assessment has become a critical issue. However, as a complex multi-criteria decision making (MCDM) problem, it faces many challenges such as diverse implement indicator framework, complicated indicator interrelations, and lack of reliable assessment methods. Therefore, this paper constructs a novel multistage decision support framework for regional water quality assessment. In phase I, we determine indicator framework strictly according to the national standards, involving PH, dissolved oxygen (DO), chemical oxygen demand (COD), etc., totally 21 water quality indicators where the temperature indicator is excluded due to its lack of assessment standard. In addition, considering the matching between the characteristic of water quality data and the probabilistic linguistic term set (PLTS) technique, we employ PLTS theory to process massive monitoring data. In phase II, relative weight considering indicators’ interrelationship is produced by the proposed regression-based decision-making trial and evaluation laboratory (DEMATEL) method, and further forms combined weight by balancing single-factor weight. In phase III, we present a new PLTS measure and extend the fuzzy technique for order performance by similarity to ideal solution (FTOPSIS) method to generate assessment results. Then, we investigate water quality status of 16 administrative districts in Shanghai, China, with the proposed method. The collected data are derived from 26 water quality monitoring sites and covers the period during September 2018 to February 2019. The results confirm a hypothesis that the statistically significant interrelationship does exist among indicators, and point out that Huang Pu District remains the best water quality with highest values of $CC_{i}$ in the range of (0.79–0.85) over the 6 months. Moreover, the parameter analysis and comparative analysis are further given that verifies the robustness and reliability of the model in details.

Appendices

Appendix 1

Table 9 PLDM information of September, 2018

Appendix 2

Property: The proposed distance measure should satisfy the basic principles:

• 1. $0 \le d(L_{1} (p),L_{2} (p)) \le 1$

• 2. $d(L_{1} (p),L_{2} (p)) = 0$, if and only if $L_{1} (p) = L_{2} (p)$

• 3. $d(L_{1} (p),L_{2} (p)) = d(L_{2} (p),L_{1} (p))$

• 4. $d(L_{1} (p),L_{2} (p)) = 1,$ if and only if $L_{1} (p) = \{ s_{\tau } (1)\}$ and $L_{2} (p) = \{ s_{0} (1)\}$.

Proof: Since $0 \le \psi (L(p)) \le \alpha^{L} \le \tau$ and $\zeta^{L} = \sum\nolimits_{\alpha = 0}^{L} {p^{L} \le 1}$, then $0\leq\vert\psi\left(L_1\left(p\right)\right)-\psi\left(L_2\left(p\right)\right)\vert$  $\le \tau$ and $\max (\min (\zeta_{1}^{L} ,\zeta_{2}^{L} )) \le 1$. Therefore, $0 \le d(L_{1} (p),L_{2} (p)) \le \int\limits_{0}^{1} 1 = 1$. If $L_{1} (p) = L_{2} (p),$, then $\psi (L_{1} (p)) = \psi (L_{2} (p))$, and thus, $d(L_{1} (p),L_{2} (p)) = 0$; If $\zeta^{l} > 0,$, then $\left| {\alpha_{1}^{l} - \alpha_{2}^{l} } \right| = 0$ when $d(L_{1} (p),L_{2} (p)) = 0$; thus, $L_{1} (p) = L_{2} (p)$. It is obvious that $d(L_{1} (p),L_{2} (p)) = d(L_{2} (p),L_{1} (p))$ and $d(L_{1} (p),L_{2} (p)) = 1$ when $L_{1} (p) = \{ s_{\tau } (1)\}$ and $L_{2} (p) = \{ s_{0} (1)\}$. If $L_{1} (p) \ne \{ s_{\tau } (1)\}$ or $L_{2} (p) \ne \{ s_{0} (1)\}$, there is at least on $\zeta$ that satisfies $\left| {\psi (L_{1} (p)) - \psi (L_{2} (p))} \right| < \tau$, therefore $d(L_{1} (p),L_{2} (p)) \ne 1$. The proof is finished.