Approximation of goal constraint coefficients in fuzzy goal programming

It is sometimes difficult in real situations to estimate the coefficients of decision variables in multi-objective model. Even though mathematical analysis may contribute to determine these coefficients, historical data used may contain fuzzy and random properties and should be treated properly. Thus, this paper introduces a fuzzy random regression to approximate the coefficients; specifically the goal constraints of goal programming model. We propose a two phase-based approach for the solution model; first, we construct the goal constraints using fuzzy random regression model and, second, we solve the multi-objective problem with a fuzzy additive goal programming. A numerical example is presented to illustrate the model.