On the Shortest Path to Solve the Problem Based on Vague Sets

Abstract

The shortest path problem (SPP) is currently being greatly studied in fuzzy sets and systems area. Previously published algorithms and methods for the fuzzy shortest path problem based on discrete or continuous types fuzzy sets of fuzzy arc lengths. However, to present an arc real length in vague set is more reasonable than in fuzzy set. Moreover,carrying on various kinds of operation between the fuzzy numbers and sets, we find that some information will be lost.In this paper , we present a novel approach to solve the shortest path problem in network base on vague sets. Firstly, we determine the vague shortest path length from source node to the destination node in the classical directed network. Secondly, by mean of vague similarity measure to evaluate similarity degree between vague path lengths. At last ,Comparing the result of similarity measure,the path with the highest similarity degree is the shortest path. An illustrative example is given to demonstrate that the result of the approach with vague sets is closer to intuitive judgment.