Linear Programming Problems with some Multi-Choice Fuzzy Parameters

Abstract

In this paper, we consider some Multi-choice linear programming (MCLP) problems where the alternative values of the multi-choice parameters are fuzzy numbers. There are some real-life situations where we need to choose the value for a parameter from a set of alternative choices to optimize our objective and the values of the parameters can be imprecise or fuzzy. We formulate this situation as a mathematical model by using some fuzzy numbers for those alternatives. A defuzzification method based on incentre point of
a triangle is used to find the defuzzified values of the fuzzy numbers. An equivalent crisp multi-choice linear programming model has been established. To tackle the multichoice parameters, we use Lagrange’s interpolating polynomial. Then, we establish a transformed mixed integer nonlinear programming problem. By solving the transformed non-linear programming problem, we obtain the optimal solution for the original problem. Finally, two numerical examples are presented to demonstrate the proposed model and methodology.