A New Approach for the Shortest Path Problem with Vague Sets

The greatly studies show that it is quite appropriate to use fuzzy theory to solve the shortest path problem. This paper analyses the general method of dealing with the shortest path problem by using discrete fuzzy arc length, and points out the issue of such methods. As carrying on various kinds of operation between the fuzzy numbers and sets, some information will be lost. In this paper, some related vague sets operations and vague similarity measure are presented, and a new approach is developed to solve the shortest path problem in network base on vague sets. The discrete vague shortest length method is proposed to find the vague shortest length, and the vague similarity measure is utilized to obtain the shortest path. At last, an illustrative example is given to demonstrate that the result of vague sets method is closer to intuitive judgment than fuzzy sets method.