الفهرس 
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Abstract
The multiobjective nonlinear programming problems are the most complex and developing problems of optimization problems. Many thesis, books and research discussed these problems form theoretical perspective, the solution methods, and formulation forms. This thesis discussed the multiobjective nonlinear programming problems under uncertainty since they are the most recent problems needed due to scientific development. It describes problems resulting from the presence of the rough data. The nonlinear optimization problems in a rough environment are called Rough Nonlinear Optimization Problems (RNLOP) and can be classified to three classes according to roughness which may exist in objective function and/or constraints. There are two solution sets of the RNLOP: surely optimal solution set and possibly optimal solution set.
The multiobjective nonlinear optimization problems in a rough environment are called Multiobjective Rough Nonlinear Optimization Problems (MRNLOP) and can be classified to three classes according to roughness which may exist in objective functions and/or constraints. There are two solution sets of the MRNLOP: surely Pareto optimal solution set and possibly Pareto optimal solution set. The procedure of solution is described. The thesis discusses the characterization of the basic notions in parametric multiobjective rough convex programming problems (MRCPP) when parameters are in the constraints and roughness is in the multiobjective function. It also discusses the parametric study of MRCPP when parameters are in the deterministic multiobjective functions and roughness is in the feasible region. The concepts including the solvability set, the stability sets of the first kind, the second kind and fifth kind on rough environment are presented.
This thesis consists of six chapters as follows:
Chapter 1 introduces a survey to multiobjective nonlinear optimization problems, the general formulation of multiobjective nonlinear optimization problems and the concept of uncertainty. Also, different techniques for solving multiobjective
nonlinear optimization problems have been presented and optimization methods and their classification are described. The rough set definition and its applications is presented.
Chapter 2 describes multiobjective rough nonlinear optimization problem and its classifications according to roughness which may exist in objective functions and/or constraints. There are two solution sets of the MRNLOP: surely Pareto optimal solution set and possibly Pareto optimal solution set. The rough nonlinear optimization problem (RNLOP) and its classifications according to roughness is discussed. There are two solution sets of the RNLOP: surely optimal solution set and possibly optimal solution set. The procedure of solution is described for all classes of MRNLOP and RNLOP.
Chapter 3 discusses characterization of the basic notions in parametric multiobjective rough convex programming when parameters are in the constraints and roughness is in the multiobjective function. It discusses the parametric study of the multiobjective rough convex programming problems (MRCPP) when parameters are in the deterministic multiobjective functions and roughness is in the feasible region.
Chapter 4 describes the duality of each class of the rough nonlinear optimization problem. The procedure of solution for each dual form is described and its relations with its primal problem.
Chapter 5 addresses the duality of multiobjective nonlinear optimization problem in a simple form and its relations with primal problem. The duality of MRCPP is introduced for each class. The procedure of solution for each dual form is described.
Chapter 6 presents the conclusions and recommendations and suggests some points for further research.