orness-methods       package:kappalab       R Documentation(latin1)

_O_r_n_e_s_s _d_e_g_r_e_e

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

     Computes the orness degree of a Choquet integral from the
     underlying *normalized* 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 orness degree is computed from the
          Mobius transform of a capacity.

     _o_b_j_e_c_t = "_c_a_p_a_c_i_t_y"  The orness degree 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 orness degree is computed from a
          cardinal capacity.

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

     J.-L. Marichal (2000), _Behavioral analysis of aggregation in
     multicriteria decision aid_, in Preferences and Decisions under
     Incomplete Knowledge, J. Fodor and B. De Baets and P. Perny Eds,
     Physica-Verlag, pages 153-178, 2000.

_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:

     ## the upper capacity
     mu <- capacity(c(0,rep(1,15)))

     ## the Choquet integral w.r.t mu behaves like the maximum operator
     f <- c(0.1,0.1,0,0.9)
     Choquet.integral(mu,f)

     ## its orness is 1
     orness(mu)

     ## the same example with a Mobius.capacity object
     a <- Mobius(mu)
     Choquet.integral(a,f)
     orness(a)

     ## the same example with a card.capacity object
     mu <- upper.capacity(4)
     Choquet.integral(mu,f)
     orness(mu)

