## 4 Case Study
### Calculation of Criteria Weights Integrating Rough BWM and Entropy Weight Method  
#### 4.2.1 Calculation of Subjective Weights of CV and Economic Criteria for Warehouse Logistics System  
Step 1. Consistent with previous studies [53], four experts were invited to determine the best and worst criteria. The selected experts possess skills and experience in the design and development of warehouse logistics PSSs, and they include one forklift designer, one service engineer, one manufacturing engineer, and one PSS researcher. The best and worst CV criteria were P1 and P5, while the best and worst economic criteria were E7 and E8, respectively. Step 2. The four DMs were asked to compare each criterion to \(c_{B}\) and \(c_{W}\) on a 9-point scale. Then, the best-to-others vector and the others-to-worst vector were obtained through comparison between criteria, as shown in Equations (19) and (20). Among them, \(h^{k}_{WW}=1\) and \(h^{k}_{BB}=1\). \[\begin{array}{ccccccccc}\text{PSS criteria: 1}&2&3&4&5&6&7&8&9&10\\ \text{DM}_{1}&\left[ \begin{array}{ccccccccccccc}1&2&6&6&9&6&8&4&2&4\\ \text{DM}_{2}&1&3&3&6&9&5&5&6&2&6\\ \text{DM}_{3}&1&2&2&7&9&2&5&2&5&6\\ \text{DM}_{4}&1&2&3&6&9&5&3&3&5&3\\ \end{array} \right],&H^{p}_{W}=\left[ \begin{array}{ccccccccccccc}1&2&3&4&5&6&7&8 &9&10\\ \text{9}&6&6&3&1&4&4&3&7&3\\ \text{9}&6&6&3&1&7&4&7&4&3\\ \text{9}&4&7&6&1&6&3&5&4&3\\ \text{9}&6&6&3&1&4&6&6&4&6\\ \end{array} \right]\\ \text{Economic criteria: 1}&2&3&4&5&6&7&8\\ H^{E}_{B}= \begin{array}{ccccccccc}\text{DM}_{1}&\left[\begin{array}{ccccccccccccc}3&4&1&4&3&4&1&9\\ \text{DM}_{2}&3&1&2&5&2&8&1&9\\ \text{DM}_{3}&1&5&1&3&3&4&1&9\\ \text{DM}_{4}&1&4&2&2&4&2&1&9\\ \end{array}\right],&H^{E}_{W}=\left[\begin{array}{ccccccccccccc}6&9&7&4&7&1&9 &1\\ \text{8}&4&8&6&6&5&9&1\\ \text{7}&4&6&3&6&9&9&1\\ \text{9}&5&7&7&5&7&9&1\\ \end{array}\right]\end{array}  \tag{20}\]  
Step 3. The rough comparison vector for the CV and economic objectives were calculated by Equations (1) and (2). Taking the results of the best criterion P1 to P2 as an example, the result was {2,3,2,2}, \(RN(h^{p}{}_{\text{B2}})=\) {[[2,2.75], [2.33,3.5], [2,2.75], [2.75,4]], and the average rough set was \(\overline{RN}(h^{p}{}_{\text{B2}})=\) {[(2+2.333+2+2.75)/4, (2.75+3.5+2.75+4)/4] = [2.271,3.250]. Then, the rough sets of other evaluation criteria were integrated to construct the rough comparison vector, as shown in Table 7. \begin{table}
\begin{tabular}{c c c} \hline
**Label** & **Criterion** & **Description** & **Category** \\ \hline E1 & Rated lifting capacity & The maximum mass allowed for forklift loads when the center of \\  & & gravity is within the standard load center distance of the forklift truck \\ E2 & Maximum driving speed & The maximum steady speed of the forklift truck when the fork carries \\  & & the rated load at maximum speed \\ E3 & Maximum lifting height & The height that the forklift can lift when it is on level ground and the \\  & & fork carries the rated lifting weight \\ E4 & Motor power & The maximum power that the motor can run normally when the \\  & & forklift is on the level ground and running stably after starting \\ E5 & Production cost & The total cost of the forklift after design, processing and assembly, \\  & & including materials, supplies, research and development, etc \\ E6 & Maintenance costs & The expenses for regular inspection, maintenance and replacement of \\  & & vulnerable parts of the forklift \\ E7 & Safety & The reliability of forklift design and the ability to protect the driver \\  & & and cargo during operation and operation \\ E8 & Forklift weight & The total weight of all parts of a forklift truck when it is not loaded \\ \hline \end{tabular}
\end{table} 
Table 6: Description of evaluation criteria in the economic objective of warehouse logistics system. Step 4. By constructing the rough comparison vector, a programming problem was constructed according to Equations (6) and (7).