An optimization method to solve a fully intuitionistic fuzzy non-linear separable programming problem

¹ 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: vishnupratapsingh56@gmail.com

Received: 27 September 2022
Accepted: 20 September 2023

Abstract

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.