The concepts of fuzziness and parametric analysis are of importance to treat uncertainty in mathematical model and may offer certain more viewpoints. The basic notions of the parametric study in nonlinearprogramming ...
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The concepts of fuzziness and parametric analysis are of importance to treat uncertainty in mathematical model and may offer certain more viewpoints. The basic notions of the parametric study in nonlinearprogrammingproblem are presented by Osman (Aplikace matematiky 22(5):318-332, 1977;Aplikace matematiky 22(5):333-348, 1977). In general, a parametric programmingproblem is not easy to be solved. In addition, sometime, solving a parametric programmingproblem with parameters in the objective is easier than solving a parametric problem with parameters in the constraints and vice versa. Therefore, a parametric study in duality space is important to facilitate solving a parametric programmingproblem. The fuzzynonlinearproblem is interested area for research as one of the tools for treating uncertainty. The fuzzynonlinearproblem when parameters in the objective function or constrains or both is called the fuzzy parametric nonlinearproblem. Therefore, dealing with fuzziness and duality parametric space is concerned. In this paper, a novelty introduction to the fuzzy basic notions of parametric programmingproblem are clarified, the relations between the concepts concerning duality in parametric spaces which introduced by Osman et al. (Int J Math Arch 6(12):161-165, 2016) and the fuzzy concepts are presented. We present and define the fuzzy parametric notions of the set of feasible parameters, the solvability set, and the stability sets of the first and second kind. These notions are not defined before. The theoretical relations and an illustration example are introduced.
In this study, the solution of the fuzzynonlinear optimization problems is achieved by a recurrent neural network model. Since there are a few researches for solving fuzzy optimization problems by neural networks, we...
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In this study, the solution of the fuzzynonlinear optimization problems is achieved by a recurrent neural network model. Since there are a few researches for solving fuzzy optimization problems by neural networks, we introduce a new model with reduced complexity to solve the problem. By reformulating the original program to an interval problem and then a weighting problem, the Karush-Kuhn-Tucker optimality conditions are stated. Moreover, we employ the optimality conditions into a neural network as a basic tool to solve the problem. Besides, the global convergence and the Lyapunov stability analysis of the system are debated in this study. Finally, different numerical examples allow to validate our algorithm with the proposed neural network compared to some other alternative networks.
In the presented study, the solution of the fuzzynonlinear optimization problems (FNLOPs) is calculated using a recurrent neural network (RNN) model. Since there is a few research for solving FNLOP by RNN's, we g...
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In the presented study, the solution of the fuzzynonlinear optimization problems (FNLOPs) is calculated using a recurrent neural network (RNN) model. Since there is a few research for solving FNLOP by RNN's, we give a new approach to solve the problem. By reducing the original program to an interval problem and then weighting problem, the Karush-Kuhn-Tucker (KKT) conditions are given. Moreover, we use the KKT conditions into a RNN as an important tool to solve the problem. Besides, the global convergence properties and the Lyapunov stability of the dynamic model are studied in this study. In the final step, some illustrative examples are considered to establish the obtained results. Reported results are compared with some others network models.
In this paper, the solution of the fuzzynonlinear optimization problems (FNLOPs) is given using a projection recurrent neural network (RNN) scheme. Since there is a few research for resolving of FNLOP by RNNs, we des...
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In this paper, the solution of the fuzzynonlinear optimization problems (FNLOPs) is given using a projection recurrent neural network (RNN) scheme. Since there is a few research for resolving of FNLOP by RNNs, we describe a new framework to solve the problem. By reformulating the original program to an interval problem and then weighting problem, the Karush-Kuhn-Tucker (KKT) conditions are obtained. Moreover, we utilize the KKT conditions into a RNN as a capable tool to solve the problem. Besides, the global convergence and the Lyapunov stability of the neuro-dynamic model are established. In the final step, some simulation examples are stated to validate the obtained results. Reported results are compared with some other previous neural networks.
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