*3.3. Combination of Rules and Fuzzy Operation*

According to the level range (low, medium, and high), the corresponding membership functions were the highest point of each fuzzy area, and the membership functions of input targets were determined by way of the intersection. The fuzzy operations of each target-preset result are shown below.

1. When the fuzzy region denotes "minimal" tool wear:

*Average value* <sup>=</sup> <sup>1</sup> <sup>×</sup> 0.84 <sup>+</sup> <sup>2</sup> <sup>×</sup> 0.68 <sup>+</sup> <sup>3</sup> <sup>×</sup> 0.52 <sup>+</sup> <sup>4</sup> <sup>×</sup> 0.36 <sup>+</sup> <sup>5</sup> <sup>×</sup> 0.2 <sup>+</sup> <sup>6</sup> <sup>×</sup> 0.04 <sup>1</sup> <sup>+</sup> 0.84 <sup>+</sup> 0.68 <sup>+</sup> 0.52 <sup>+</sup> 0.36 <sup>+</sup> 0.2 <sup>+</sup> 0.04 <sup>=</sup> 1.1769

2. When the fuzzy region denotes "small" tool wear:

```
Average value
= 5×0.04+6×0.2+7×0.36+8×0.52+9×0.84+10×1+11×0.68+12×0.52+13×0.36+14×0.2+15×0.04
                  0.04+0.2+0.36+0.52+0.84+1+0.68+0.52+0.36+0.2+0.04
= 9.966
```
3. When the fuzzy region denotes "moderate" tool wear:

*Average value*

```
= 14×0.04+15×0.2+16×0.36+17×0.52+18×0.68+19×0.84+20×1+21×0.84+22×0.68+23×0.52+24×0.36+25×0.2+26×0.04
                       0.04+0.2+0.36+0.52+0.68+0.84+1+0.84+0.68+0.52+0.36+0.2+0.04
= 20
```
4. When the fuzzy region denotes "large" tool wear:

*Average value*

```
= 26×0.04+27×0.2+28×0.36+29×0.52+30×0.68+31×0.84+32×1+33×0.84+34×0.68+35×0.52+36×0.36+37×0.2+38×0.04
                       0.04+0.2+0.36+0.52+0.68+0.84+1+0.84+0.68+0.52+0.36+0.2+0.04
= 32
```
5. When the fuzzy region denotes "greatest" tool wear

$$\begin{array}{l} \text{Average value} \\ l = \frac{34 \times 0.04 + 35 \times 0.2 + 36 \times 0.36 + 37 \times 0.52 + 38 \times 0.68 + 39 \times 0.84 + 40 \times 1}{0.04 + 0.2 + 0.36 + 0.52 + 0.68 + 0.84 + 1} \\ l = 38.23 \end{array}$$

### *3.4. Optimal Strategies of Games*

A bargaining game for the two production qualities that are often considered in precision machining of cutting, tool wear, and cutting noise was conducted, and an innovative optimal mechanism was development afterward. The conflict among two production qualities and four control parameters was resolved through the perfect Bayesian equilibrium of game theory with one production quality as one individual player. The main strategy was chosen according to different production qualities. The probability value of strategies generated by the game was calculated to select the one with the highest sum of probability as the optimal strategy of each production quality. The optimal strategy chosen was also used to obtain the optimal plan of multi-quality and multi-strategy.
