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Abstract Decision making is an integral part of our daily lives. It ranges in scope from the individual to the largest groups and societies, including nations and, ultimately, organization at the global level. It considers situations ranging in complexity from the simple to the most complex one involving multiple objectives. The multicriteria decision making problems are classified into three approaches: 1. Vector optimization approach. 2. Goal programming approach. 3. Interactive approach. In this work, we study in details the third approach. An unified interactive procedure IS presented to identify the best compromise solution for multiobjective programming problems. This procedure is based mainly upon the branch-and-bound method and together with the STEM procedure. A fuzzy interactive approach is suggested to identify the best compromise solution for multiobjective programming problems. Also, some new concepts about the fuzzy ideal, degree of ideality and degree of efficiency are introduced. This approach is applied to solve two applicable problems, an environmental/economic power dispatch problem and an air defense allocation problem. The first problem is a bi-objective quadratic programming problem. One of its objectives is to minimize the cost of the fuel and the other is to minimize the emission of the NO, for the generators of a power system. The second problem is a multiobjective allocation problem of certain types of air defend-e weapons to defend vital targets. Some stability notions such as the solvability set and the stability set of the first kind (SSK I) are defined and characterized for multiobjective quadratic programming problems with fuzzy parameters (FMOQP) Also, an algorithm is proposed for the determination of the set (SSK1) for the (FMOQP) problems after introducing the so called a-level set of tile fuzzy numbers The thesis end with the conclusions and the recommendations for further researches in the field of interactive approaches for treating multicriteria decision-making problems. |