Newton method for solving the multi-variable fuzzy optimization problem
type: Item
instance of: scholarly article
title: Newton method for solving the multi-variable fuzzy optimization problem
zbMATH Open document ID: 1282.90250
author: U. M. Pirzada
author: V. D. Pathak
published in: Journal of Optimization Theory and Applications
publication date: 2013-05-08T00:00:00Z
review text: The study is concerned with the following multivariable fuzzy optimization problem \[ \text{Minimize } f(x),\;x\in X, \] where \(f: X\to F(R)\) is a fuzzy-valued function, \(X\subset\mathbb{R}^n\), and \(F(R)\) is a family of fuzzy sets defined in \(R\). Considering a fuzzy-max order partial order relation defined on a set of fuzzy numbers and employing Hukuhara differentiability, proposed is the Newton method to solve the above optimization problem. The convergence of the Newton method is shown and a detailed optimization algorithm is provided. Some illustrative numeric examples are included.
reviewed by: Witold Pedrycz
Mathematics Subject Classification ID: 90C70
Mathematics Subject Classification ID: 90C53
zbMATH DE Number: 6161535
zbMATH Keywords: fuzzy arithmetic
zbMATH Keywords: Newton method
zbMATH Keywords: fuzzy function
zbMATH Keywords: fuzzy differentiability
zbMATH Keywords: Hukuhura differentiability
MaRDI profile type: Publication
full work available at URL: s10957-012-0141-3
OpenAlex ID: W2076964475
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DOI: 10.1007/S10957-012-0141-3
description: scientific article; zbMATH DE number 6161535