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12 changes: 6 additions & 6 deletions python/doc/source/reference/functions.metrics.rst
Original file line number Diff line number Diff line change
Expand Up @@ -106,13 +106,13 @@ is defined as :cite:p:`ZitThiLauFon2003:tec`
.. math::
epsilon(A,R) = \max_{r \in R} \min_{a \in A} \max_{1 \leq i \leq m} epsilon(a_i, r_i)

where :math:`a` and :math:`b` are objective vectors of length :math:`m`.
where :math:`a` and :math:`r` are objective vectors of length :math:`m`.

In the case of minimization of objective :math:`i`, :math:`epsilon(a_i,b_i)` is
computed as :math:`a_i/b_i` for the multiplicative variant (respectively,
:math:`a_i - b_i` for the additive variant), whereas in the case of
maximization of objective :math:`i`, :math:`epsilon(a_i,b_i) = b_i/a_i` for the
multiplicative variant (respectively, :math:`b_i - a_i` for the additive
In the case of minimization of objective :math:`i`, :math:`epsilon(a_i,r_i)` is
computed as :math:`a_i/r_i` for the multiplicative variant (respectively,
:math:`a_i - r_i` for the additive variant), whereas in the case of
maximization of objective :math:`i`, :math:`epsilon(a_i,r_i) = r_i/a_i` for the
multiplicative variant (respectively, :math:`r_i - a_i` for the additive
variant). This allows computing a single value for problems where some
objectives are to be maximized while others are to be minimized. Moreover, a
lower value corresponds to a better approximation set, independently of the
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10 changes: 5 additions & 5 deletions r/R/epsilon.R
Original file line number Diff line number Diff line change
Expand Up @@ -22,11 +22,11 @@
#'
#' where \eqn{a} and \eqn{b} are objective vectors of length \eqn{m}.
#'
#' In the case of minimization of objective \eqn{i}, \eqn{epsilon(a_i,b_i)} is
#' computed as \eqn{a_i/b_i} for the multiplicative variant (respectively,
#' \eqn{a_i - b_i} for the additive variant), whereas in the case of
#' maximization of objective \eqn{i}, \eqn{epsilon(a_i,b_i) = b_i/a_i} for the
#' multiplicative variant (respectively, \eqn{b_i - a_i} for the additive
#' In the case of minimization of objective \eqn{i}, \eqn{epsilon(a_i,r_i)} is
#' computed as \eqn{a_i/r_i} for the multiplicative variant (respectively,
#' \eqn{a_i - r_i} for the additive variant), whereas in the case of
#' maximization of objective \eqn{i}, \eqn{epsilon(a_i,r_i) = r_i/a_i} for the
#' multiplicative variant (respectively, \eqn{b_i - r_i} for the additive
#' variant). This allows computing a single value for problems where some
#' objectives are to be maximized while others are to be minimized. Moreover, a
#' lower value corresponds to a better approximation set, independently of the
Expand Down
12 changes: 6 additions & 6 deletions r/man/epsilon.Rd

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