Many practical optimization problems are characterized by some
flexibility in the problem constraints, where this flexibility can
be exploited for additional trade-off between improving the
objective function and satisfying the constraints. Especially in
decision making, this type of flexibility could lead to workable
solutions, where the goals and the constraints specified by
different parties involved in the decision making are traded off
against one another and satisfied to various degrees. Fuzzy sets
have proven to be a suitable representation for modeling this type
of soft constraints. Conventionally, the fuzzy optimization
problem in such a setting is defined as the simultaneous
satisfaction of the constraints and the goals. No additional
distinction is assumed to exist amongst the constraints and the
goals. This report proposes an extension of this model for
satisfying the problem constraints and the goals, where preference
for different constraints and goals can be specified by the
decision-maker. The difference in the preference for the
constraints is represented by a set of associated weight factors,
which influence the nature of trade-off between improving the
optimization objectives and satisfying various constraints.
Simultaneous weighted satisfaction of various criteria is modeled
by using the recently proposed weighted extensions of
(Archimed