Optimization for multi-objective sum of linear and linear fractional programming problem: fuzzy nonlinear programming approach
type: Item
instance of: scholarly article
title: Optimization for multi-objective sum of linear and linear fractional programming problem: fuzzy nonlinear programming approach
zbMATH Open document ID: 1487.90598
author: C. Veeramani
author: S. Sharanya
author: Ali Ebrahimnejad
published in: Mathematical Sciences
publication date: 2021-07-15T00:00:00Z
review text: The paper introduces a method to obtain Pareto solutions of the so-called multi-objective linear plus linear fractional programming problem, which is defined by linear constraints and the objective function \(f=(f_1,f_2,\ldots,f_k):\mathbb{R}^n\to \mathbb{R}^k\), \[f_i(x)=p_i^tx+\theta_i+\frac{c^t_ix+\alpha_i}{d^t_ix+\beta_i},\quad\forall x\in \mathbb{R}^n,\] where \(p_i,c_i,d_i\in \mathbb{R}^n\) and \(\theta_i,\alpha_i,\beta_i\in \mathbb{R}\). The proposed method is based on reformulating the problem into a multi-objective nonlinear programming problem by applying hyperbolic and exponential membership functions to each component of a fuzzy version of the original multi-objective programming problem, which is built by considering an aspiration level and a tolerance limit for each component \(f_i\). The obtained multi-objective nonlinear programming problem is solved by applying a fuzzy goal programming approach to its linear approximation. The introduced procedure is compared with some existing methods in the literature and it is illustrated through two numerical examples and a real-life application problem.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C32
Mathematics Subject Classification ID: 90C70
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 7372035
zbMATH Keywords: goal programming
zbMATH Keywords: linear programming problem
zbMATH Keywords: multi-objective nonlinear programming problem
zbMATH Keywords: multi-objective linear plus linear fractional programming problem
reviewed by: C. Gutiérrez
MaRDI profile type: Publication
full work available at URL: s40096-020-00333-w
OpenAlex ID: W3034456946
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DOI: 10.1007/S40096-020-00333-W
description: scientific article; zbMATH DE number 7372035