Interactive Fuzzy Goal Programming Based on Taylor Series to Solve Multiobjective Nonlinear Programming Problems with Interval Type 2 Fuzzy Numbers

TL;DR

This paper introduces an interactive fuzzy goal programming method utilizing Taylor series to efficiently solve multiobjective nonlinear programming problems with interval type 2 fuzzy numbers, transforming them into linear problems for easier solution.

Contribution

It presents a novel approach combining fuzzy goal programming and Taylor series to handle complex nonlinear problems with fuzzy data, simplifying them into linear programming problems.

Findings

Effective transformation of fuzzy nonlinear problems into linear ones.

Successful application to numerical examples demonstrating practicality.

Utilization of Maple optimization toolbox for solution implementation.

Abstract

This paper presents an interactive fuzzy goal programming (FGP) approach for solving multiobjective nonlinear programming problems (MONLPP) with interval type 2 fuzzy numbers (IT2 FNs). The cost and time of the objective functions, the resources, and the requirements of each kind of resources are taken to be trapezoidal IT2 FNs. Here, the considered problem is first transformed into an equivalent crisp MONLPP, and then the transformed MONLPP is converted into an equivalent Multiobjective Linear Programming Problem (MOLPP). By using a procedure based on Taylor series, this problem is reduced into a single objective linear programming problem (LPP) which can be easily solved by Maple 18.02 optimization toolbox. Finally, the proposed solution procedure is illustrated by two numerical examples.