Refined Minimization of Trapezoidal Fuzzy Quadratic Function: A Fuzzy-Parametric Steepest Descent
This article presents a fuzzy parametric steepest descent approach to address the nonlinear fuzzy optimization problem to achieve improved and refined optimal solutions. Specifically, we examine a quadratic function with trapezoidal fuzzy coefficients. We introduce a unique strategy for expressing t...
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| Format: | Article |
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Tsinghua University Press
2025-07-01
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| Series: | Fuzzy Information and Engineering |
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| Online Access: | https://www.sciopen.com/article/10.26599/FIE.2025.9270057 |
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| author | Shalini K Tharasi Dilleswar Rao |
| author_facet | Shalini K Tharasi Dilleswar Rao |
| author_sort | Shalini K |
| collection | DOAJ |
| description | This article presents a fuzzy parametric steepest descent approach to address the nonlinear fuzzy optimization problem to achieve improved and refined optimal solutions. Specifically, we examine a quadratic function with trapezoidal fuzzy coefficients. We introduce a unique strategy for expressing these trapezoidal fuzzy coefficients in parametric form. By fine-tuning of these parameters within the range [0, 1] for a given fuzzy function, we gain valuable insights into the convergence behavior of the problem. This innovative methodology allows us to control the solutions. To demonstrate the effectiveness of our method, we provided a numerical example for clarity, showing how our approach excels in managing complex fuzzy situations. |
| format | Article |
| id | doaj-art-7ea5cc4cffdf492e8299abf1beb6ae5c |
| institution | DOAJ |
| issn | 1616-8658 1616-8666 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj-art-7ea5cc4cffdf492e8299abf1beb6ae5c2025-08-20T02:58:11ZengTsinghua University PressFuzzy Information and Engineering1616-86581616-86662025-07-0117215417610.26599/FIE.2025.9270057Refined Minimization of Trapezoidal Fuzzy Quadratic Function: A Fuzzy-Parametric Steepest DescentShalini K0Tharasi Dilleswar Rao1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai 600127, IndiaDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai 600127, IndiaThis article presents a fuzzy parametric steepest descent approach to address the nonlinear fuzzy optimization problem to achieve improved and refined optimal solutions. Specifically, we examine a quadratic function with trapezoidal fuzzy coefficients. We introduce a unique strategy for expressing these trapezoidal fuzzy coefficients in parametric form. By fine-tuning of these parameters within the range [0, 1] for a given fuzzy function, we gain valuable insights into the convergence behavior of the problem. This innovative methodology allows us to control the solutions. To demonstrate the effectiveness of our method, we provided a numerical example for clarity, showing how our approach excels in managing complex fuzzy situations.https://www.sciopen.com/article/10.26599/FIE.2025.9270057non-linear fuzzy functionquadratic fuzzy functionparametric formtrapezoidal fuzzy numbersteepest descent methodoptimal solutions |
| spellingShingle | Shalini K Tharasi Dilleswar Rao Refined Minimization of Trapezoidal Fuzzy Quadratic Function: A Fuzzy-Parametric Steepest Descent Fuzzy Information and Engineering non-linear fuzzy function quadratic fuzzy function parametric form trapezoidal fuzzy number steepest descent method optimal solutions |
| title | Refined Minimization of Trapezoidal Fuzzy Quadratic Function: A Fuzzy-Parametric Steepest Descent |
| title_full | Refined Minimization of Trapezoidal Fuzzy Quadratic Function: A Fuzzy-Parametric Steepest Descent |
| title_fullStr | Refined Minimization of Trapezoidal Fuzzy Quadratic Function: A Fuzzy-Parametric Steepest Descent |
| title_full_unstemmed | Refined Minimization of Trapezoidal Fuzzy Quadratic Function: A Fuzzy-Parametric Steepest Descent |
| title_short | Refined Minimization of Trapezoidal Fuzzy Quadratic Function: A Fuzzy-Parametric Steepest Descent |
| title_sort | refined minimization of trapezoidal fuzzy quadratic function a fuzzy parametric steepest descent |
| topic | non-linear fuzzy function quadratic fuzzy function parametric form trapezoidal fuzzy number steepest descent method optimal solutions |
| url | https://www.sciopen.com/article/10.26599/FIE.2025.9270057 |
| work_keys_str_mv | AT shalinik refinedminimizationoftrapezoidalfuzzyquadraticfunctionafuzzyparametricsteepestdescent AT tharasidilleswarrao refinedminimizationoftrapezoidalfuzzyquadraticfunctionafuzzyparametricsteepestdescent |