An algorithm for the shortest path problem on a network with fuzzy parameters applied to a tourist problem

In problems of graphs involving uncertainties, the shortest path problem is one of the most studied topics as it has a wide range of applications in different areas (e.g. telecommunications, transportation, manufacturing, etc.) and therefore warrants special attention. However, due to its high computational complexity, previously published algorithms present peculiarities and problems that need to be addressed (e.g. they find costs without an existing path, they determine a fuzzy solution set but do not give any guidelines to help the decision-maker choose the best path, they can only be applied in graphs with fuzzy non-negative parameters, etc.). Therefore, in this chapter is presented an iterative algorithm with a generic order relation that solves the cited disadvantages. This algorithm is applied in a tourist problem. It has been implemented using certain order relations, where some can find a set of fuzzy path solutions while others find only the shortest path.