DOI: 10.11118/978-80-7509-990-7-0060

THE USABILITY OF ALGORITHMS FROM GRAPH THEORY IN THE FIELD OF MULTICRITERIA ANALYSIS

Radim Farana¹

¹ Department of Informatics, Faculty of Business and Economics, Mendel University in Brno, Zemědělská 1, 613 00 Brno, Czech Republic

The main ideas, on how to use algorithms from the Graph Theory to improve the process of Multicriteria Analysis were presented in the paper (Farana, 2016). This paper presents practical results obtained by the use of these algorithms in practical decision-making procedures when multicriteria analysis has been used. Graph algorithms were used in two situations when determining the values of the weights of decision criteria. First was the checking, if the Fuller’s triangle, filled in by an expert, is filled in correctly. For this verification, a complete graph is used in which the vertices represent the criteria the orientation of the edges their mutual significance. A method of gluing vertices could be used for criteria with the same significance. The resulting graph must be acyclic. Twenty-five decision tasks with seven or more criteria were analyzed and the obtained results will be presented in the paper. The second application was the elimination of the overdetermination of the assessment in Saaty’s method. A spanning tree describing dependencies between criteria has been used according to the algorithm in (Farana, 2016). Obtained results were compared with the full Saaty’s matrix when the number of compared pairs of criteria is k – 1 for k criteria, compared to the number of k(k – 1)/2 in the classic Saaty’s method. Fifteen decision tasks with seven or more criteria were analyzed and the obtained results will be presented in the paper. The paper presents the differences between the assessment given directly by experts and the assessment obtained using the spanning tree and shows that the described method is applicable in practice. The experience of experts using the proposed procedure, obtained through a guided interview, was mostly positive.

Klíčová slova: decision making, multicriteria analysis, graph theory, Fuller triangle, Saaty’s method, acyclic graph, spanning tree

stránky: 60-64, online: 2024