*4.2. Result of Single Target Production Quality Verification*

The median of the experimental results was used for comparative analysis. The median of the tool wear was 4.38 μm−2, as shown in Table 15. The median of the cutting noise was 82.83 dB, as shown in Table 16. According to the median and the comparative analysis of the two production qualities, the data obtained in this research was better than the median, which showed that the innovative strategies of both production qualities were optimized, as shown in Table 17.

**Table 15.** Median values of tool wear.



**Table 16.** Median values of cutting noise.



#### *4.3. Multi-Quality Optimal Strategy*

### 4.3.1. Establish Initial Payoff Matrix Z2

Four preferred groups of the strategy were chosen through the experimental combination and fuzzy quantified. The output values were input into matrix Z2, as shown in Table 18. The parameters of the matrix were defined as follows.


**Table 18.** Multi-quality payoff matrix Z2.

Player (target)

A: Tool wear

B: Cutting noise

Strategy planning

A-1: Cutting speed is "low", cutting depth is "high", and feed rate is "high". (Rule9) A-2: Cutting speed is "medium", cutting depth is "medium", and feed rate is "low". (Rule13) A-3: Cutting speed is "medium", cutting depth is "high", and feed rate is "low". (Rule16) A-4: Cutting speed is "medium", cutting depth is "high", and feed rate is "high". (Rule18) B-1: Cutting speed is "low", cutting depth is "high", and feed rate is "high". (Rule9) B-2: Cutting speed is "medium", cutting depth is "medium", and feed rate is "low". (Rule13) B-3: Cutting speed is "medium", cutting depth is "high", and feed rate is "low". (Rule16) B-4: Cutting speed is "medium", cutting depth is "high", and feed rate is "high". (Rule18)

#### 4.3.2. Mixed Strategy as the Problem Solver

Since the initial payoff matrix Z2 cannot obtain the equilibrium solution or the approximate equilibrium solution, the cycle repeated continuously in some strategy combinations and a mixed strategy was needed for problem solving. As shown in the simplified payoff matrix Z3 (Table 19), two strategies remained, respectively, in both production quality A and B. However, the values of the strategies were output after fuzzy quantification, the differences of the values couldn't be distinguished clearly. To solve the problem, the strategy values were restored to the corresponding experimental values, as shown in Table 20. The optimal strategy combination was A1 and B1, as shown in Table 20. The optimal strategy of the two production qualities and its adoption probability are shown in Table 21.




4.3.3. Analysis of the Results of Multi-Quality Optimization

The conflict between production qualities and control parameters was aimed to be solved through the game matrix with the green production issue, which was internationally concerned and was selected as the research target. Multi-quality optimization was obtained through game theory. The optimal strategies of tool wear and cutting noise were, respectively, increasing the cutting depth and decreasing the cutting speed. The optimization obtained was further compared to the median commonly used in the industry, as shown in Table 22. The results of the comparison show that the improvement of the multi-quality cutting problem can indeed be achieved even without the operation of the equipment, and further develop a set of universal green innovative production optimization mechanism, which can provide technical personnel with a set of all-purpose economic prospective parameter analysis methods to stimulate alternative, innovative considerations of the industry.

**Table 22.** Comparison of multi-quality optimization and median data.


#### **5. Conclusions**

Nowadays, the industrial production design is getting more and more complicated, and with the increasingly demanding machining requirements, the setting of cutting parameters must be extremely strict to prevent changes to some parameters that could influence other production qualities. The most difficult breakthrough of CNC turning was the difficulty in setting the turning parameter. Due to the considerations of cost and time, the quality characteristics were judged by expert experience with a trial and error method, which might cause the doubts of improper use of quality measurement indicators.

Coupled with the environmental awareness and international regulation in recent years, reducing environmental harm in the product design stage avoids being labeled as a high pollution industry and prevents being forced to move or even close down factories. It is necessary for the automated CNC turning industry to use an easy-to-use quality-improving analysis program. In view of the inability of the operators to optimize the turning quality, fuzzy theory was used in the research to define the semantic rule of the relationship between control parameters and production qualities for fuzzy quantification. The output value after quantification was input into game theory to resolve the conflict between control parameters and production qualities for carrying out the game of multi-quality. With the statistic of the strategy probability, the strategy with the highest sum of probability was selected to obtain the multi-quality and multi-strategy optimization.

The results show that, within the parameter combination of multi-quality optimization, compared with the parameter combination recommended in the cutting manual, the tool wear reduced by 23% and the cutting noise reduced by 1%. The cutting problem of multi-quality is indeed improved by the research. In order to enhance the international competitiveness of the automated CNC cutting industry, the method used in the research can further be promoted and applied to the process or other industries. **Author Contributions:** Conceptualization, T.-S.L.; Formal Analysis, K.-C.C., T.-S.L., L.-P.Z. and X.-J.D.; Investigation, L.-P.Z., Y.-M.C. and X.-J.D.; Methodology, K.-C.C. and T.-S.L.; Project administration, K.-C.C.; Software, K.-C.C., L.-P.Z. and Y.-M.C.; Validation, K.-C.C. and X.-J.D.; Visualization, Y.-M.C.; Writing-Original Draft, T.-S.L., L.-P.Z. and X.-J.D; Writing-Review & Editing, K.-C.C. and Y.-M.C.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors would like to thank for the comments from many reviewers to improve this work.

**Conflicts of Interest:** The authors declare no conflicts of interest.
