Optimal path problem with possibilistic weights

Abstract

The selection of optimal path is one of the classic problems in graph theory. Its utilization have various practical uses ranging from the transportation, civil engineering and other applications. Rarely those applications take into account the uncertainty of the weights of the graph. However this uncertainty can have high impact on the results. Several studies offer solution by implementing the fuzzy arithmetic for calculation of the optimal path but even in those cases neither of those studies proposed complete solution to the problem of ranking of the fuzzy numbers. In the study the ranking system based on the Theory of Possibility is used. The biggest advantage of this approach is that it very well addresses the indistinguishability of fuzzy numbers. Lengths of the paths are compared based on the possibility and the necessity of being smaller than the alternative. The algorithm offers the user more information than only the optimal path, instead the list of possible solutions is calculated and the alternatives can be ranked using the possibility and the necessity to identify the possibly best variant.