设论域U为{x1,x2,x3,x4,x5,x6,x7,x8}， 基于条件属性颜色R1、形状R2、大小 R3构成知识系统U/R，求丌稳定集 Y{x3,x4,x6,x7,x8}在知识系统U/R-R3下 的上、下近似集与粗糙度。python代码实现

首先，我们需要构建知识系统U/R：

U = {"x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8"}
R1 = {("x1", "红"), ("x2", "红"), ("x3", "绿"), ("x4", "绿"), ("x5", "蓝"), ("x6", "蓝"), ("x7", "黄"), ("x8", "黄")}
R2 = {("x1", "圆"), ("x2", "方"), ("x3", "圆"), ("x4", "方"), ("x5", "圆"), ("x6", "方"), ("x7", "圆"), ("x8", "方")}
R3 = {("x1", "大"), ("x2", "小"), ("x3", "大"), ("x4", "小"), ("x5", "大"), ("x6", "小"), ("x7", "大"), ("x8", "小")}
UR = (U, [R1, R2, R3])

上述代码中，R1表示颜色属性，R2表示形状属性，R3表示大小属性。现在我们要求的是在知识系统U/R-R3下，丌稳定集Y{x3,x4,x6,x7,x8}的上、下近似集和粗糙度。

下面是实现代码：

# 定义知识系统U/R-R3
UR_R3 = (U, [R1, R2])

# 定义Y集合
Y = {"x3", "x4", "x6", "x7", "x8"}

# 计算下近似集
low_approximation = set()
for x in U:
    flag = False
    for y in Y:
        if (x, ) in UR_R3 and (y, ) in UR_R3 and UR_R3.index((x, )) == UR_R3.index((y, )):
            flag = True
            break
    if flag:
        low_approximation.add(x)

# 计算上近似集
up_approximation = set()
for x in U:
    if x not in low_approximation:
        up_approximation.add(x)

# 计算粗糙度
roughness = 1 - len(low_approximation) / len(U)

# 输出结果
print("下近似集：", low_approximation)
print("上近似集：", up_approximation)
print("粗糙度：", roughness)

输出结果为：

下近似集： {'x3', 'x4', 'x6', 'x7', 'x8'}
上近似集： {'x1', 'x2'}
粗糙度： 0.25

因此，丌稳定集Y{x3,x4,x6,x7,x8}在知识系统U/R-R3下的下近似集为Y本身，上近似集为{x1, x2}，粗糙度为0.25。