Prediction of Transportation Costs Using Trapezoidal Neutrosophic Fuzzy Analytic Hierarchy Process and Artificial Neural Networks

Abstract

Transportation is one of the critical functions in any business, and its cost depends on many constraints, including driver behavior, weather, distance, and demand in the market. This study proposes a novel approach for multi-criteria decision-making problems using the analytical hierarchy process (AHP) with the trapezoidal neutrosophic fuzzy numbers to produce the best criteria for evaluating total transportation cost. The proposed trapezoidal neutrosophic fuzzy analytical hierarchy process (TNF-AHP) determines the most significant criteria to be considered for further investigation in ANN training. In this study on the transportation problem (TP), the demands at different destination points and the distances between source and demand cities were determined. An artificial neural network (ANN) model has been proposed for the collected data of the TP to investigate the prediction of total transportation cost. The proposed ANN model predicts the total transportation cost with two input which were chosen by the TNF-AHP. Collected data are trained from 2 to 25 neurons with a logsig activation function, and the ideal model for ANN has been observed by Levenberg-Marquardt’s feed-forward back-propagation (trainlm) learning algorithm with a single hidden layer (6-9-1) topology. It is found that the ANN model can predict the total transportation cost with high efficiency as the R values indicate a high degree of correlation. The recommended ANN model, mean absolute percentage error, Pearson product-moment correlation coefficient (R), and mean square error have been obtained adequately. The ANN model validation has been conducted, and its results are compared with the collected data.

Keywords

• Analytical hierarchy process
• artificial neural network
• feed forward back propagation learning algorithm
• transportation problem
• trapezoidal neutrosophic fuzzy number