A New Algorithm for the Discrete Shortest Path Problem in a Network Based on Ideal Fuzzy Sets

Ebrahimnejad, Sadollah; Mousavi, Seyed Meysam; Vahdani, Behnam

A New Algorithm for the Discrete Shortest Path Problem in a Network Based on Ideal Fuzzy Sets

Authors

¹ Assistant Professor, Department of Industrial Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran

² Ph.D. Student, Young Researches Club, South Tehran Branch, Islamic Azad University, Tehran, Iran

³ Assistant Professor, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

Abstract

A shortest path problem is a practical issue in networks for real-world situations. This paper addresses the fuzzy shortest path (FSP) problem to obtain the best fuzzy path among fuzzy paths sets. For this purpose, a new efficient algorithm is introduced based on a new definition of ideal fuzzy sets (IFSs) in order to determine the fuzzy shortest path. Moreover, this algorithm is developed for a fuzzy network problem including three criteria, namely time, cost and quality risk. Several numerical examples are provided and experimental results are then compared against the fuzzy minimum algorithm with reference to the multi-labeling algorithm based on the similarity degree in order to demonstrate the suitability of the proposed algorithm. The computational results and statistical analyses indicate that the proposed algorithm performs well compared to the fuzzy minimum algorithm.

Keywords