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- Title
An optimization model for fuzzy nonlinear programming with Beale's conditions using trapezoidal membership functions.
- Authors
Palanivel, K.; Muralikrishna, P.
- Abstract
Non-linear Programming (NLP) is an optimization technique for determining the optimum solution to a broad range of research issues. Many times, the objective function is nonlinear, owing to various economic behaviors such as demand, cost, and many others. Since the appearance of Kuhn and Tucker's fundamental theoretical work, a general NLP problem can be resolved using many methods to find the optimum results. This article tackles the challenge of nonlinear programming (NLP) problems with uncertainty in inequality constraints. Traditional, "crisp" NLP methods might not be ideal when dealing with imprecise or subjective data. Here, we propose a fuzzy mathematical model that incorporates Beale's condition to handle such NLPPs. Furthermore, the model demonstrates how quadratic programming problems can be solved using membership functions(MF's). This leads to more realistic and robust solutions. The model unfolds in three stages: Mathematical Formulation: Establishing the fuzzy NLP framework with Beale's condition and membership functions. Computational Procedures: Outlining algorithms for solving fuzzy NLP problems based on MF's and a robust ranking index. Numerical Illustration: Applying the model to a specific case study and comparing results from both approaches. Through comprehensive analysis, we demonstrate the model's ability to find optimal solutions while considering vagueness and uncertainty in NLPPs. This opens door for more adaptable and realistic optimization in various problem domains.
- Subjects
MEMBERSHIP functions (Fuzzy logic); NONLINEAR programming; QUADRATIC programming; MATHEMATICAL optimization; FUZZY algorithms; FUZZY sets; MATHEMATICAL models; NONLINEAR functions
- Publication
Proyecciones - Journal of Mathematics, 2024, Vol 43, Issue 2, p425
- ISSN
0716-0917
- Publication type
Article
- DOI
10.22199/issn.0717-6279-5468