3.4.1. Establishment of the Game Model

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1. Player (target)
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Tool wear and cutting noise were set as players. The experimental data of the qualities are shown in Tables 8 and 9. Player A is referred to as the tool wear (the smaller, the better) and player B as the cutting noise (the smaller, the better) in the following.


**Table 8.** Test data of tool wear.



2. Strategic planning (control parameter)

(1) Cutting speed

(2) Depth of cut

(3) Feed rate

(4) Tool nose runoff

#### 3.4.2. Target of Bargaining Games

The overall optimal improvement strategy was prioritized to obtain important control parameters considered preferentially by each production quality and was used to improve the turning process to obtain the best multi-quality and multi-strategy optimization. In order to take both the production qualities into account to develop a multi-quality and multi-strategy optimization, the numbers of the appearance of each strategy of the production qualities were counted. Four main strategies were selected, and the output values of their corresponding semantic rules after quantification were imported into game theory. The initial payoff matrix (Z1) was constructed under consideration of the strategies of the two production qualities, as shown in Table 10.


#### 3.4.3. Mixed Strategies Game

In the initial payoff matrix initially established, the payoff value of all strategic combinations were filled in the corresponding spaces, resulting in the two-player multi-strategy game payoff matrix Z2, as shown in Table 11. Matrix Z2 was analyzed to establish whether the dominant strategy (one player's strategies are always better than the other player's strategies) existed. If positive, the matrix must first be simplified, as shown in Table 12. Finally, the probability values generated by all the games were statistically analyzed with their strategy probability, and the strategy with the highest probability sum was chosen to be the optimal strategy of that production quality. The optimal strategy of each production quality and its adoption probability are listed in Table 13 to obtain the optimal multi-quality and multi-strategy strategies.


**Table 11.** Payoff matrix Z2.

Pa: the payoff value of quality A under different situation; Pb: the payoff value of quality B under different situation.


**Table 12.** Simplified payoff matrix Z3.

**Table 13.** Optimal multi-quality and multi-strategy strategies.


#### **4. Experimental Verification**
