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 a value for a parameter from a set of different choices to optimize our objective, and those values of the parameters can be imprecise or fuzzy. We formulate these situations as a mathematical model by using some fuzzy numbers for the alternatives. A defuzzification method based on incentre point of a triangle has been used to find the defuzzified values of the fuzzy numbers. We determine an equivalent crisp multi-choice linear programming model. To tackle the multi-choice parameters, we use Lagranges interpolating polynomials. Then, we establish a transformed mixed integer nonlinear programming problem. By solving the transformed non-linear programming model, we obtain the optimal solution for the original problem. Finally, two numerical examples are presented to demonstrate the proposed model and methodology.