## 4 Case Study
### Calculate combined weights
#### 4.2.3 Comprehensive Evaluation  
(1) Determination of classical and nodal domains  
In order to make an evaluation of the advantages and disadvantages of the performance of the intelligent lubrication system of off-highway mining mechanically driven dump trucks, three evaluation levels are set up, namely qualified, good, and excellent, and both the knuckle domain and the evaluation model set up have 15 features which are \(C_{1}\), \(C_{2}\), \(C_{3}\),... \(C_{15}\). For the classical domain of each index and the knuckle domain, we have:  
\[R_{1}= \begin{pmatrix}N_{1}&C_{1}&(0.0.8)\\ &C_{2}&(0,0.8)\\ &\vdots&\vdots\\ &\dot{C}_{i}&(0.0.8)\\ &\vdots&\vdots\\ &C_{15}&(0.0.8)\\ \end{pmatrix} R_{2}= \begin{pmatrix}N_{2}&C_{1}&(0.8,0.9)\\ &C_{2}&(0.8,0.9)\\ &\vdots&\vdots\\ &\dot{C}_{i}&(0.8,0.9)\\ &C_{15}&(0.8,0.9)\\ \end{pmatrix} \]  
\[R_{3}= \begin{pmatrix}N_{3}&C_{1}&0.9,1\\ &C_{2}&0.9,1\\ &\vdots&\vdots\\ &\dot{C}_{i}&0.9,1\\ &\vdots&\vdots\\ &C_{15}&0.9,1\\ \end{pmatrix} R_{\text{P}}= \begin{pmatrix}N_{\text{P}}&C_{1}&(0,1)\\ &C_{2}&(0,1)\\ &\vdots&\vdots\\ &\dot{C}_{i}&(0,1)\\ &\vdots&\vdots\\ &C_{15}&(0,1)\\ \end{pmatrix} \]  
(2) Determine the material element to be evaluated \(R_{\text{q}}\)  
The data for each indicator are based on the data in Table 8, and the data for 2021 are used as a proxy to create the matrix of elements to be evaluated, \(R_{\text{q}}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name of the Indicator** & **Subjective** & **Objective** & **Combined** \\  & **Weights** & **Weights** & **Weights** \\ \hline Equipment load & 0.0578 & 0.0888 & 0.0733 \\ Operating temperature & 0.2056 & 0.0490 & 0.1273 \\ Viscosity of the lubricant & 0.1188 & 0.0886 & 0.1037 \\ Anti-wear properties of lubricants & 0.0521 & 0.0671 & 0.0596 \\ Thickness of oil film & 0.1042 & 0.0399 & 0.0721 \\ Failure rate & 0.1397 & 0.0521 & 0.0959 \\ MTBF & 0.0533 & 0.0772 & 0.0653 \\ MTTR & 0.0396 & 0.0672 & 0.0534 \\ Lubricant replacement intervals & 0.0690 & 0.0810 & 0.0750 \\ Lubricant consumption & 0.0196 & 0.0578 & 0.0387 \\ Electricity consumption & 0.0133 & 0.0795 & 0.0464 \\ Selection of friction sub-materials & 0.0568 & 0.0700 & 0.0634 \\ Selection of lubricants & 0.0431 & 0.0736 & 0.0584 \\ Payback period & 0.0136 & 0.0462 & 0.0299 \\ Profitability & 0.0135 & 0.0655 & 0.0395 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Combined weights. \[R_{\text{q}}= \begin{bmatrix}\text{q}&C_{1}&0.91\\ &C_{2}&0.89\\ &C_{3}&0.93\\ &C_{4}&0.98\\ &C_{5}&0.90\\ &C_{6}&0.83\\ &C_{7}&0.79\\ &C_{8}&0.80\\ &C_{9}&0.81\\ &C_{10}&0.99\\ &C_{11}&0.90\\ &C_{12}&0.85\\ &C_{13}&0.79\\ &C_{14}&0.94\\ &C_{15}&0.87\end{bmatrix}  \tag{3}\]  
Calculating relevance and determining evaluation ratings  
When calculating the degree of correlation, it is necessary to continually calculate the distance between the values of each indicator and each grade in order to determine the value of the correlation function that determines the evaluation grade. The computations are large and cumbersome; thus, MATLAB and EXCEL interactive localization methods are used to compute the correlation degree, correlation function, and evaluation grade. The correlation and integrated correlation and evaluation score results are shown in Table 11 below. The results of the calculations lead to the following conclusions:  
Looking at the evaluation ratings as a whole, the maximum correlation for 2021 is \(-0.0460\), with a rating of good. This indicates that the smart lubrication system operated well in 2021 and performance was not affected. From the evaluation scores of the metrics in Table 11, the performance of the smart lubrication system in 2021 was good overall, specifically, mostly excellent and good, but there are individual metrics that qualify. For example, the average trouble-free time, lubricant selection, etc., indicate that the performance of intelligent lubrication systems needs to be further improved.