python实现《直觉模糊集决策与对策分析方法》07区间直觉模糊矩阵对策解法

妖狐艹你老母 2022-10-06 14:56 115阅读 0赞

这是李登峰老师《直觉模糊集决策与对策分析方法》第八章区间值直觉模糊集合矩阵对策及其线性与非线性规划解法。基本思想是根据区间值直觉模糊集合上的支付矩阵，构造线性规划模型求解纳什均衡。  
对于给出的算例进行独立重复实验。代码关键步骤有注释。

'''
    '''
    from scipy import optimize as op
    import numpy as np
    np.set_printoptions(suppress=True)
    for l in np.arange(0,1,0.1):
        c=np.array([0,0,0,0.5])
        A_ub=np.array([[np.log(0.2)*l+(np.log(0.02))*(1-l)+(np.log(0.1))*l+(np.log(0.1))*(1-l),
                           np.log(0.9)*l+np.log(0.5)*(1-l)+np.log(0.75)*l+np.log(0.7)*(1-l),
                           np.log(0.7)*l+np.log(0.3)*(1-l)+np.log(0.5)*l+np.log(0.4)*(1-l),-1]
    
                          ,[np.log(0.45)*l+np.log(0.1)*(1-l)+np.log(0.3)*l+np.log(0.25)*(1-l),
                           np.log(0.2)*l+np.log(0.01)*(1-l)+np.log(0.1)*l+np.log(0.05)*(1-l),
                           np.log(1)*l+np.log(0.85)*(1-l)+np.log(0.95)*l+np.log(0.95)*(1-l),-1],
    
                       [np.log(0.65) * l + np.log(0.2) * (1 - l) + np.log(0.5) * l + np.log(0.4)* (1 - l),
                       np.log(0.45) * l + np.log(0.1) * (1 - l) + np.log(0.3) * l + np.log(0.25) * (1 - l),
                       np.log(0.2) * l + np.log(0.01) * (1 - l) + np.log(0.1) * l + np.log(0.05) * (1 - l), -1]])
        B_ub=np.array([0,0,0])
        A_eq=np.array([[1,1,1,0]])
        B_eq=np.array([1])
        x1=(0,1)
        x2=(0,1)
        x3=(0,1)
        x4=(None,0)
        res=op.linprog(c,A_ub,B_ub,A_eq,B_eq,bounds=(x1,x2,x3,x4))
        print(res.x)
    print("...")
    for l in np.arange(0,1,0.1):
        c=np.array([0,0,0,0.5])
        A_ub=np.array([[-(np.log(0.2)*l+(np.log(0.02))*(1-l)+(np.log(0.1))*l+(np.log(0.1))*(1-l)),
                           -(np.log(0.45)*l+np.log(0.1)*(1-l)+np.log(0.3)*l+np.log(0.25)*(1-l)),
                           -(np.log(0.65)*l+np.log(0.2)*(1-l)+np.log(0.5)*l+np.log(0.4)*(1-l)),1]
    
                          ,[-(np.log(0.9)*l+np.log(0.5)*(1-l)+np.log(0.75)*l+np.log(0.7)*(1-l)),
                           -(np.log(0.2)*l+np.log(0.01)*(1-l)+np.log(0.1)*l+np.log(0.05)*(1-l)),
                           -(np.log(0.45)*l+np.log(0.1)*(1-l)+np.log(0.3)*l+np.log(0.25)*(1-l)),1],
    
                       [-(np.log(0.7) * l + np.log(0.3) * (1 - l) + np.log(0.5) * l + np.log(0.4)* (1 - l)),
                       -(np.log(1) * l + np.log(0.85) * (1 - l) + np.log(0.95) * l + np.log(0.95) * (1 - l)),
                       -(np.log(0.2) * l + np.log(0.01) * (1 - l) + np.log(0.1) * l + np.log(0.05) * (1 - l)), 1]])
        B_ub=np.array([0,0,0])
        A_eq=np.array([[1,1,1,0]])
        B_eq=np.array([1])
        x1=(0,1)
        x2=(0,1)
        x3=(0,1)
        x4=(None,0)
        res=op.linprog(-c,A_ub,B_ub,A_eq,B_eq,bounds=(x1,x2,x3,x4))
        print(res.x)

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NDAxNDgzNg_size_16_color_FFFFFF_t_70]

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80NDAxNDgzNg_size_16_color_FFFFFF_t_70]: /images/20221005/b779342236924d51a4abb2b9e2c2688b.png