game-class             package:kappalab             R Documentation

_C_l_a_s_s "_g_a_m_e"

_D_e_s_c_r_i_p_t_i_o_n:

     Class representing a game, i.e. a set function vanishing at the
     empty set (also called _non monotonic fuzzy measure_).

_O_b_j_e_c_t_s _f_r_o_m _t_h_e _C_l_a_s_s:

     Objects can be created by calls to the function 'game'.

_S_l_o_t_s:


     '_n': Object of class 'numeric' of length 1 equal to the number of
          elements of the set on which the game is defined.

     '_s_u_b_s_e_t_s': Object of class 'numeric' of length '2^n' containing
          the power set of the underlying set in "natural" order. The
          subsets are coded as integers.

     '_d_a_t_a': Object of class 'numeric' of length '2^n' containing the
          coefficients of the game in binary order.  We necessarily
          have 'data[1] = 0'.


_E_x_t_e_n_d_s:

     Class 'set.func', directly. Class 'superclass.set.func', by class
     'set.func'.

_M_e_t_h_o_d_s:


     _a_s._c_a_r_d._g_a_m_e 'signature(object = "game")'

     _C_h_o_q_u_e_t._i_n_t_e_g_r_a_l 'signature(object = "game", f = "numeric")'

     _M_o_b_i_u_s 'signature(object = "game")'

     _S_i_p_o_s._i_n_t_e_g_r_a_l 'signature(object = "game", f = "numeric")'

     _S_u_g_e_n_o._i_n_t_e_g_r_a_l 'signature(object = "game", f = "numeric")'

     _p_d_f._C_h_o_q_u_e_t._u_n_i_f 'signature(object = "game", f = "numeric")'

     _c_d_f._C_h_o_q_u_e_t._u_n_i_f 'signature(object = "game", f = "numeric")'

     _e_x_p_e_c_t._C_h_o_q_u_e_t._u_n_i_f 'signature(object = "game")'

     _s_d._C_h_o_q_u_e_t._u_n_i_f 'signature(object = "game")'

     _e_x_p_e_c_t._C_h_o_q_u_e_t._n_o_r_m 'signature(object = "game")'

     _s_d._C_h_o_q_u_e_t._n_o_r_m 'signature(object = "game")'

_S_e_e _A_l_s_o:

     'game', 
      'as.card.game-methods', 
      'Choquet.integral-methods',  
      'Mobius-methods', 
      'Sipos.integral-methods',  
      'Sugeno.integral-methods', 
      'pdf.Choquet.unif-methods',  
      'cdf.Choquet.unif-methods', 
      'expect.Choquet.unif-methods',  
      'sd.Choquet.unif-methods', 
      'expect.Choquet.norm-methods',  
      'sd.Choquet.norm-methods'.

_E_x_a_m_p_l_e_s:

     ## a game (which is a capacity)
     mu <- game(c(0,rep(1,15)))

     ## the attributes of the object
     mu@n
     mu@data
     mu@subsets

     ## a conversion
     as.card.game(mu)

     ## a transformation
     Mobius(mu)
     ## let us check ...
     zeta(Mobius(mu))

     ## integral calculations 
     f <- c(0.2,0.3,0.1,0.7)
     Choquet.integral(mu,f)
     Sugeno.integral(mu,f)
     f <- c(0.2,-0.3,0.1,-0.7)
     Sipos.integral(mu,f)

