entropy-methods       package:kappalab       R Documentation(latin1)

_N_o_r_m_a_l_i_z_e_d _e_n_t_r_o_p_y _o_f _a _c_a_p_a_c_i_t_y

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

     Computes the normalized entropy of a capacity. The capacity can be
     given either under the form of an object of class 'capacity',
     'card.capacity' or 'Mobius.capacity'.

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



     _o_b_j_e_c_t = "_M_o_b_i_u_s._c_a_p_a_c_i_t_y"  The normalized entropy is computed
          from the Mobius transform of a capacity.

     _o_b_j_e_c_t = "_c_a_p_a_c_i_t_y"  The normalized entropy is computed directly
          from a capacity.

     _o_b_j_e_c_t = "_c_a_r_d._c_a_p_a_c_i_t_y"  The normalized entropy is computed from
          a cardinal capacity.


_R_e_f_e_r_e_n_c_e_s:

     J-L. Marichal (2002), _Entropy of discrete Choquet capacities_,
     European Journal of Operational Research, 3:137, 2002, pages
     612-624.

     I. Kojadinovic, J-L. Marichal and M. Roubens (2005), _An axiomatic
     approach to the definition of the entropy of a discrete Choquet
     capacity_, Information Sciences 172, pages 131-153.

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

     'capacity-class', 
      'Mobius.capacity-class', 
      'card.capacity-class', 
      'Mobius-methods'.

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

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

     ## its Mobius transform
     a <- Mobius(mu)

     ## their normalized entropy
     entropy(mu)
     entropy(a)

     ## similar examples with card.capacity objects
     mu <- lower.capacity(4)
     entropy(mu)
     mu <- uniform.capacity(4)
     entropy(mu)

