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Duality in the fuzzy-parametric space for fuzzy-parametric nonlinear programming problem

OPSEARCH 2018年第3-4期55卷 662-676页

作者： Osman, M. S. Abd Elazeem, A. M. Elsisy, M. A. Rashwan, M. M. Al Asher Univ El Asher City Egypt October High Inst Engn & Technol Giza Egypt Benha Univ Fac Engn Benha Banha Egypt Cairo Univ Fac Econ & Polit Sci Cairo Egypt

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 nonlinear programming problem are presented by Osman (Aplikace matematiky 22(5):318-332, 1977;Aplikace matematiky 22(5):333-348, 1977). In general, a parametric programming problem is not easy to be solved. In addition, sometime, solving a parametric programming problem 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 programming problem. The fuzzy nonlinear problem is interested area for research as one of the tools for treating uncertainty. The fuzzy nonlinear problem when parameters in the objective function or constrains or both is called the fuzzy parametric nonlinear problem. Therefore, dealing with fuzziness and duality parametric space is concerned. In this paper, a novelty introduction to the fuzzy basic notions of parametric programming problem 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.

关键词： nonlinear programming problem Parametric Duality fuzzy set fuzzy nonlinear programming problem

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Solving fuzzy Convex programming problems via a Projection Neural Network Framework

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NEW MATHEMATICS AND NATURAL COMPUTATION 2025年第1期21卷 159-193页

作者： Jahangiri, Mohammadreza Nazemi, Alireza Shahrood Univ Technol Fac Math Sci POB ***-316 Shahrood Iran

In this paper, the solution of the fuzzy nonlinear 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.

关键词： Neural networks fuzzy nonlinear programming problem fuzzy parameters stability convergence

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An efficient RNN based algorithm for solving fuzzy nonlinear constrained programming problems with numerical experiments

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2025年 463卷

作者： Jahangiri, Mohammadreza Nazemi, Alireza Shahrood Univ Technol Fac Math Sci POB ***-316 Shahrood Iran

In this study, the solution of the fuzzy nonlinear 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.

关键词： Neural networks fuzzy nonlinear programming problem fuzzy parameters Stability Convergence

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A cooperative neural dynamic model for solving general convex nonlinear optimization problems with fuzzy parameters and an application in manufacturing systems

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2024年第6期38卷 2272-2300页

作者： Jahangiri, Mohammadreza Nazemi, Alireza Shahrood Univ Technol Fac Math Sci Shahrood Iran

In the presented study, the solution of the fuzzy nonlinear 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.

关键词： convergence fuzzy nonlinear programming problem fuzzy parameters neural networks stability

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