This paper addresses a multicriteria problem of Boolean linear
programming with parametric optimality. Parameterizations are introduced by dividing a
set of objectives into a family of disjoint subsets, within each Pareto optimality is used to
establish dominance between alternatives. The introduction of this principle allows us to
connect such classical optimality sets as Pareto and extreme. The parameter space of
admissible perturbations in such a problem is formed by a set of additive matrices, with
arbitrary Hölder’s norms specified in the solution and criterion spaces. The lower and
upper bounds for the radius of strong stability are obtained with some important
properties of attainability as corollaries.