A Computational Study for Probabilistic Fuzzy Linear Programming Using Machine Learning in the Case of Poisson Distribution

Abstract

This paper presents a computational study for probabilistic fuzzy linear programming using machine learning. Two opposite probabilistic fuzzy constraints are considered, where the random variable in the two constraints is discrete with a Poisson distribution. The data was generated from a Poisson distribution under different scenarios. Five scenarios are investigated based on either the same mean parameter and different dispersions of the values of the random variable or the same values of the random variable and different mean parameters. While eight cases are derived by considering different combinations of fuzzy probabilities. These many configurations of different scenarios and cases allow us to compare how models perform while varying both the mean parameter and the range of the values through different combinations of fuzzy probabilities. This setup allows for a thorough evaluation of how these changes impact model performance using machine learning models. Nine machine learning models have been considered in this study for evaluating different scenarios and cases in predicting the target decision variables. Since the Poisson distribution is beneficial in fields such as telecommunications, healthcare, logistics, and reliability engineering, where the frequency of arrivals, failures, or demands exhibits Poisson-like behavior but is additionally impacted by ambiguity or incomplete information. Therefore, this study provides a useful tool to the decision-makers to carefully select the combinations of the fuzzy probabilities in the light of the possible values of the Poisson random variable, especially when the associated probabilities are not specified.