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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 (Archimedean) fuzzy t-norms. The weighted
satisfaction of the problem constraints and goals are demonstrated by using a simple general,
and it can also be applied to fuzzy mathematical programming problems and multi-objective
fuzzy optimization
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