Solving the fuzzy shortest path problem using multi-criteria decision method based on vague similarity measure

Many researchers have focused on the fuzzy shortest path problem in a network with non-deterministic information due to its importance to various applications. The goal of this paper is to select the shortest path in multi-constrained network using multi-criteria decision method based on vague similarity measure. In our approach, each arc length represents multiple metrics. The multi-constraints are equivalent to the concept of multi-criteria based on vague sets. We propose a similarity measure of vague sets in which the positive constraints and the negative constraints are defined. Furthermore, the procedures are developed to obtain the “best” and “worst” ideal paths. We evaluate similarity degrees between all candidate paths and two ideal paths with the proposed similarity measure. Through comparing the relative degrees of paths, it is shown that the path with the largest relative degree is the shortest path. Finally, we conduct two sets of numerical experiments—using Matlab to verify the feasibility and correctness of the proposed algorithm and developing a routing decision simulation system (RDSS) to demonstrate that the proposed approach is reasonable and effective.

Graphical abstractThe routing decision results of the tasks 0–99 SM-MCR algorithm were able to select different paths in a self-adapting manner and distribute the transmission load evenly to more paths to reduce link failure. Therefore, SM-MCR results in better load balance.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► We use vague sets to express uncertain network information. Vague sets are considered superior in mathematical analysis of uncertain information. ► We develop an approach using multi-criteria decision method based on vague similarity measure. The reasonable and effective path can be selected using the proposed approach in multi-constrained network. ► We conduct two sets of numerical experiments—using Matlab to verify the feasibility and correctness of the proposed algorithm and developing a routing decision simulation system (RDSS) to demonstrate that the proposed approach is reasonable and effective. ► This approach may be applied to other decision support systems that are oriented to finding the shortest path by modifying the constraints according to the requirements of decision makers.