Fuzzy Domination Graphs in Decision Support Tasks

In decision support tasks, one often has to deal with uncertainty due to fuzzy judgments of the decision maker or the expert. This paper proposes methods that allow you to rank the alternatives based on fuzzy evaluations. This is achieved by using fuzzy weighted summation, fuzzy implication, a computation graph showing the criteria, and a fuzzy dominance graph showing the alternatives. If the criteria have equal importance, then fuzzy graphs corresponding to the dominance of each of the criteria are used. An algorithm that is used for both the transition from fuzzy dominance graphs and the ranking of alternatives is proposed. This algorithm is based on the idea of constructing Kemeny medians or other concordant rankings at a given confidence level in the existence of corresponding arcs. Computational experiments have shown the performance of these approaches. It is reasonable to apply them in problems that require complex expert evaluations with a large number of alternatives and criteria.