Optimization is a very old and classical area which is of high concern to many disciplines.  Engineering as well as Management, Politics as well as Medicine, Artificial Intelligence as well as Operations Research  and many other fields are in one way or another concerned with optimization of designs, decisions, structures, procedures or information processes. In a deterministic environment using a single well-defined criterion for evaluating potential alternatives, the optimal decision can be obtained through user friendly Mathematical programming software. Optimization procedure is , in this case , a batch-type process assuming a closed model in which all information is available and in which the Decision Maker could provide and process all information simultaneously. In a more turbulent environment involving intrinsic or informational imprecision, the optimization process is not that simple. Although probabilistic theories claim to model decision making under imprecision, there are qu

alitatively different facets of undeterminacy which are not covered by probabilistic apparatus. This has led to the development of  tools like Fuzzy sets, Possibility measures, Necessity measures, Credibility measures…, which do not substitute probabilities but complement them in the modelling of various kinds of imprecision. In this paper, we discuss impact of Fuzzy sets theory  in representation and processing of  vagueness in an optimization framework. First and foremost, we briefly discuss basic notions and principles of Fuzzy sets theory. Secondly we present an approach based on Fuzzy sets theory   for handling situations where some leeways are admitted in the objective and constraints satisfaction. In the third part, we consider Mathematical programming problems with fuzzy parameters. Here pivotal questions regarding the meaning and the interpretation of objective and constraints with fuzzy coefficients are addressed. The fourth part is devoted to extensions to Multiobjective pro

gramming problems and to Fuzzy Stochastic Optimization.