capacity-class           package:kappalab           R Documentation

_C_l_a_s_s "_c_a_p_a_c_i_t_y"

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

     Class representing a capacity, i.e. a monotone set function
     vanishing at the empty set (also called _fuzzy measure_,
     _non-additive measure_, _monotone measure_).

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

     Objects can be mainly created by calls to the functions 'capacity'
     and 'entropy.capa.ident'.

_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 capacity 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 capacity in binary order. We necessarily
          have 'data[1] = 0' plus some additional monotonicity
          constraints.


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

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

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


     _a_s._c_a_r_d._c_a_p_a_c_i_t_y 'signature(object = "capacity")'

     _c_o_n_j_u_g_a_t_e 'signature(object = "capacity")'

     _e_n_t_r_o_p_y 'signature(object = "capacity")'

     _f_a_v_o_r 'signature(object = "capacity")'

     _i_s._n_o_r_m_a_l_i_z_e_d 'signature(object = "capacity")'

     _n_o_r_m_a_l_i_z_e 'signature(object = "capacity")'

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

     _o_r_n_e_s_s 'signature(object = "capacity")'

     _v_a_r_i_a_n_c_e 'signature(object = "capacity")'

     _v_e_t_o 'signature(object = "capacity")'

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

     'capacity', 
      'entropy.capa.ident', 
      'as.card.capacity-methods', 
      'conjugate-methods',  
      'entropy-methods', 
      'favor-methods',  
      'is.normalized-methods', 
      'normalize-methods', 
      'Mobius-methods',  
      'orness-methods', 
      'variance-methods',  
      'veto-methods'.

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

     ## a capacity
     mu <- capacity(c(0:13,13,13)/13)

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

     ## a test
     is.normalized(mu)
     normalize(mu)

     ## a conversion that should not work
     ## as.card.capacity(mu)

     ## some transformations
     conjugate(mu)
     Mobius(mu)
     ## let us check ...
     zeta(Mobius(mu))

     ## some summary indices
     orness(mu)
     veto(mu)
     favor(mu)
     variance(mu)
     entropy(mu)
     ## the same
     summary(mu)

