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

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.