  Fuzzy optimization deals with the problem of determining 'optimal'solutions
of an optimization problem when some of the elements that appear in the problem
are not precise. In real situations it is usual to have information, in systems
under consideration, that is not exact. Thisimprecision can be modeled in a
fuzzy environment. Zadeh (1965) analyzed systems of logic that permit truth
values between zero and one instead of the classical binary true-false logic.
In this framework, satisfying a certain condition means to evaluate how close
are the elements involved to the complete satisfaction. Then, each element in a
'fuzzy set' is coupled with a value in [0,1] that represents the membership
level to the set.
  In linear programming some or all the elements that describe a problem may be
considered fuzzy: objective function, right-hand side vector or constraint
matrix, the notion of optimality (ordering over the feasible solutions), the
level of satisfaction of the constraints, etc. Moreover, in integer programs,
the integrality constraints may be seen as fuzzy constraints.
  Here, we present new complexity results about linear integer programming
where some of its elements are considered fuzzy using previous results on short
generating functions for solving multiobjective integer programs.
