Volume 57, Number 6, November-December 2023
|3117 - 3139
|30 November 2023
An optimization method to solve a fully intuitionistic fuzzy non-linear separable programming problem
Visvesvaraya National Institute of Technology Nagpur, Nagpur 440010, Maharashtra, India
2 Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
3 Indian Institute of Technology Kharagpur, Kharagpur 721302, West Bengal, India
* Corresponding author: firstname.lastname@example.org
Accepted: 20 September 2023
This paper presents an optimization method to solve a non-linear separable programming problem with coefficients and variables as generalized trapezoidal intuitionistic fuzzy numbers. Such optimization problems are known as fully intuitionistic fuzzy non-linear separable programming problems. The optimization method is based on the linear approximation of fully intuitionistic fuzzy non-linear separable functions. The concept of an intuitionistic fuzzy line segment between two intuitionistic fuzzy points is introduced to find the required linear approximation. In this way, a fully intuitionistic fuzzy non-linear programming problem is converted into an intuitionistic fuzzy linear programming problem. The defuzzification and component-wise comparison techniques are then used to convert the fully intuitionistic fuzzy linear programming problem to a linear programming problem with crisp coefficients which can then be solved by using traditional optimization techniques. The application of the proposed approach in an investment problem faced by a businessman has been presented.
Mathematics Subject Classification: 90C30 / 91B28 / 90C70
Key words: Intuitionistic fuzzy line segment / investment problem / ranking function / non-linear separable programming problem
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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