Probabilistic Fuzzy Goal Programming Problems Involving Pareto Distribution: Some Additive Approaches

In many real-life decision making problems, probabilistic fuzzy goal programming problems are used where some of the input parameters of the problem are considered as random variables with fuzzy aspiration levels. In the present paper, a linearly constrained probabilistic fuzzy goal programming programming problem is presented where the right hand side parameters in some constraints follows Pareto distribution with known mean and variance. Also the aspiration levels are considered as fuzzy. Further, simple, weighted, and preemptive additive approaches are discussed for probabilistic fuzzy goal programming model. These additive approaches are employed to aggregating the membership values and form crisp equivalent deterministic models. The resulting models are then solved by using standard linear mathematical programming techniques. The developed methodology and solution procedures are illustrated with a numerical example.