An optimization study based on Dijkstra algorithm for a network with trapezoidal picture fuzzy numbers

Abstract

Path finding models attempt to provide efficient approaches for finding shortest paths in networks. A well-known shortest path algorithm is the Dijkstra algorithm. This paper redesigns it in order to tackle situations in which the parameters of the networks may be uncertain. To be precise, we allow that the parameters take the form of special picture fuzzy numbers. We use this concept so that it can flexibly fit the vague character of subjective decisions. The main contributions of this article are fourfold: $$\mathrm{(i)}$$ The trapezoidal picture fuzzy number along with its graphical representation and operational laws is defined. $$\mathrm{(ii)}$$ The comparison of trapezoidal picture fuzzy numbers on the basis of their expected values is proposed in terms of their score and accuracy functions. $$\mathrm{(iii)}$$ Based on these elements, we put forward an adapted form of the Dijkstra algorithm that works out a picture fuzzy shortest path problem, where the costs associated with the arcs are captured by trapezoidal picture fuzzy numbers. Also, a pseudocode for the application of our solution is provided. $$\mathrm{(iv)}$$ The proposed algorithm is numerically evaluated on a transmission network to prove its practicality and efficiency. Finally, a comparative analysis of our proposed method with the fuzzy Dijkstra algorithm is presented to support its cogency.