# Quality Evaluation of Wasteless Mining in Dongguashan Based on Intuitionistic Fuzzy Set and VIKOR
## 4 Case Study
### Evaluation of Wasteless Mining in Dongguashan Based on Intuitionistic Fuzzy Set and VIKOR
They are calculated as follows:  
\[x_{ij}^{*}=y_{l}^{*}+\frac{x_{ij}-y_{l}}{y_{k}-y_{l}}(y_{k}^{*}-y_{l}^{*}) \tag{10}\]  
where \(x_{ij}^{*}\) is the affiliation degree of wassteless mining quality indicators; \(x_{\bar{\imath}i}\) is the actual affiliation degree of wassteless mining quality indicators; \(y_{l}\), \(y_{l}^{*}\) are lower limit values of \(x_{\bar{\imath}i}\) in the interval of evaluation criteria and their affiliation degree; \(y_{k}\), \(y_{k}^{*}\) are the upper limits of \(x_{ij}\) in the interval of evaluation criteria and their affiliation degree. The wastewater, waste gas and soil quality can be qualitatively obtained from the actual index data of the mine to get the corresponding grading, their affiliation and non-affiliation degrees. Combining the actual production of Dongguashan in Section 4.1 with its evaluation index levels in Table 9, it can be concluded that: the quantitative indicators, such as waste rock utilization, tailing sand utilization resource recovery and other indicators can be directly transformed into the affiliation degree after standard normalization. For the resource recovery rate, the mining loss rate and the beneficiation recovery rate are only considered, therefore, a hesitation degree of 0.05 is used. The qualitative indicators, such as wastewater, waste gas and soil pollution are classified as Class I, according to the actual monitoring results of the mine, with affiliation degrees between 0.8 and 1.0. Considering that the mine production still causes certain impacts on the water bodies, air and soil, these indicators are calculated with the lowest affiliation degree of their level, and a hesitation degree of 0.05 is also used. Table 10 shows the affiliation and non-affiliation degrees of the six evaluation indicators of Dongguashan Copper Mine after the calculation. The affiliation and non-affiliation degrees of the parameters are expressed in the form of an intuitionistic fuzzy set decision matrix:  
\(F=(<0.9352,0.0648><0.8436,0.1564><0.8,0.2><0.8,0.2><0.8,0.2><0.731,0.269>)\)  
A set of intuitive fuzzy number matrices for the evaluation of Dongguashan Copper Mine can be obtained according to the affiliation degree assignment of the index classification and the affiliation and non-affiliation degrees of the six evaluation indexes of Dongguashan Copper Mine, as follows:  
\[F*=\left[ \begin{array}{l}<1.00,0.00><1.00,0.00><1.00,0.00><1.00,0.00><1.00,0 0.00><1.00,0.00>\\ <0.80,0.20><0.80,0.20><0.80,0.20><0.80,0.20><0.80,0.20><0.80,0.20>\\ <0.60,0.40><0.60,0.40><0.60,0.40><0.60,0.40><0.60,0.40><0.60,0.40>\\ <0.40,0.60><0.40,6.00><0.40,0.60><0.40,0.60><0.40,0.60><0.40,0.60>\\ <0.00,1.00><0.00,1.00><0.00,1.00><0.00,1.00><0.00,1.00><0.00,1.00>\\ <0.94,0.06><0.84,0.16><0.80,0.15><0.80,0.15><0.80,0.15><0.73,0.22>\end{array} \right]\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Waste Rock** & **Tailings** & **Wastewater** & **Exceeds the** & **Exhaust** & **Quality of** & **Recovery of** \\  & **Utilization** & **Utilization** & **Standard** & **Gas** & **Soil** & **Resource** \\ \hline Affiliation & 0.9352 & 0.8436 & 0.8000 & 0.8000 & 0.8000 & 0.7310 \\ Non-affiliation & 0.0648 & 0.1564 & 0.1500 & 0.1500 & 0.1500 & 0.2190 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Affiliation and non-affiliation degrees of six indicators. (2) Determination of weighting factors  
In the evaluation of the green mine, the AHP, binomial coefficient method, principal component analysis method, deviation and mean square deviation method are used to determine the weight of the evaluation index. Referring to the research results of the index weight in the literature on wasteless mining and the green mine evaluation system, the intuitionistic fuzzy set VIKOR method is used to calculate the index weight in this study [34; 35].