Interactive Procedure For Non-Transitivity Revealing And Correcting Under Pairwise Comparisons

Abstract

The paper considers the problem of revealing and correcting non-transitivity in DM’s preferences (if the assumption about the transitivity of binary relation is valid). Being formed binary relation is represented as digraph which vertices correspond to the objects of the initial set. After the DM’s answer the corresponding arc is added to graph if and only if its addition does not form cycles in graph. The revealing of the cycles is carried out through the search of the paths between the compared vertices in direction opposite to the last reply. The presence of such paths shows that the last DM’s answer contradicts his previous answers (violation of transitivity). If DM insists on the last answer the paths between the corresponding pair of objects are displayed in succession to DM, begining from the shortest paths, for analysis and correction of arising contradictions. After breaking all cycles the arc corresponding to the last answer may be added in graph. If it is not a success to break all of the cycles the assumption about transitivity is considered as invalid.

Résumé

Le travail présente la problème de révélation et correction de l’intransitivitée dans les préférances de preneur décision (PD), si la supposition de la transitivitée de relation binard est juste. On représente la relation binard à former en espèce de graph orienté, le sommets de qui répondent aux objects d’ensemble original. Aprés recevoir la réponse de PD on ajoute l’arc correspondant dans le graph alors et seulement alors, si cet addition ne fait pas de cycles dans le graph. La révélation des cycles se réalise au moyen de recherche des chemins entre les sommets à comparer dans le sens inverse à réponse dernier, L’existence de chemins dit que le dernier réponse de PD contredit les réponses précédents (la violation de transitivitée). Si le PD insiste sur le réponse dernier, on lui montre consiquement les chemins entre la paire de objets correspondant, en commencant par les chemins les plus courts, pour l’analyse et corrections les contradictions surgits. Après la rupture de tous les cycles. l’arc correspondant au réponse dernier, peut âtre ajoutée dans le graph. Si on ne peut pas onvrir tous les cycles, on compte la supposition de transitivitée injuste.

Additional information

Notes on contributors

E. M. Furems

Eugenia Furems (born in 1951, Moscow) received her M.S. in economical cybernetics (1973) from Moscow Institute for management. She holds Ph.D. degree in system analysis (1984) from the USSR Academy of Sciences Institute for System Studies and now is the senior researcher at the same institute laboratory of decision making theory and applications. She is engaged in the combinatorial models in decision making and the problems of knowledge acquisition for expert systems and decision support systems design.

L. S. Gnedenko

Ludmila Gnedenko (born in 1945, Bravichi) received her M.S. in mathematics (1967) from the Moscow State University. Now she is the researcher at the laboratory of decision making theory and applications of the USSR Academy of Sciences Institute for System Studies. She is engaged in multicriteria decision making methods and the problems of knowledge acquisition for expert systems and decision support systems design.