Solving the shortest path problem on networks with fuzzy arc lengths using the complete ranking method

The fuzzy shortest path problem provides the shortest way to the decision-maker having least possible distance from source to destination. Niroomand et al. (Oper Res 17:395–411, 2017) recently advanced a method for solving the fuzzy shortest path problem. They divided the problem into two sub-problems and solved them separately. They asserted that their method always meets a unique upper and lower bound on the fuzzy shortest distance from source to destination for each α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}. The proposed study focuses on a significant omission in Niroomand et al. method. The flaws in their approach stem from not clearly revealing the solution concept for the shortest path problem. The flaws of their approach are addressed in this study, and new approaches are proposed to overcome these flaws. The proposed approaches use the complete ranking method to solve the fuzzy shortest path problem. The proposed approaches ensure that the fuzzy shortest distance is equal among all possible shortest paths. The proposed research is carried out using numerical examples of fuzzy shortest path problems. The computational results of proposed approaches are compared to existing methods.