Abstarct: Given that there are collections that are not definite, and they are bad-definition, and ambiguous, and usually contain words such as about, approximately, almost, and ..., the use of fuzzy concepts is necessary to advance the goals of the decision making. Also learning interval computations, despite being complex because they are more precise and discussing the stability of systems, are unavoidable. In this thesis, the basic concepts of fuzzy analysis and methods for solving fuzzy optimization problems, which include symmetric and asymmetric problems are introduced. Then, by introducing fuzzy multi-objective problems, we discuss two-step methods for solving these problems and an ideal linear programming method in a fuzzy environment. In the following, we present The Karush-Kuhn-Tucker (KKT) optimality conditions for interval multi-objective problems by introducing the concepts of the LU and LS resolvent and proving that the LU concept is more general using the concept of generalized derivative. Using the generalized derivative concept instead of the derivative concept is more general and universal because there are issues that are not derivable but have generalized derivatives. Then, we will review the duality-theorems, including duality of Woolf and Mund-weir, in the form of data problems is irreducible.