RUBIS: a bipolar-valued outranking method for the choice problem. (English) Zbl 1151.90450

Summary: The main concern of this article is to present the RUBIS method for tackling the choice problem in the context of multiple criteria decision aiding. Its genuine purpose is to help a decision maker to determine a single best decision alternative. Methodologically we focus on pairwise comparisons of these alternatives which lead to the concept of bipolar-valued outranking digraph. The work is centred around a set of five pragmatic principles which are required in the context of a progressive decision aiding methodology. Their thorough study and implementation in the outranking digraph lead us to define a choice recommendation as an extension of the classical digraph kernel concept.


90B50 Management decision making, including multiple objectives
05C20 Directed graphs (digraphs), tournaments


digraphs; Rubis
Full Text: DOI


[1] Belton V, Stewart T (2002) Multiple criteria decision analysis: an integrated approach. Kluwer, Dordrecht · Zbl 1200.90122
[2] Berge C (1970) Graphes et hypergraphes. Dunod, Paris · Zbl 0213.25702
[3] Bisdorff R (1997) On computing kernels from l-valued simple graphs. In: Proceedings of the 5th European Congress on intelligent techniques and soft computing, vol 1, pp 97–103. EUFIT’97, Aachen
[4] Bisdorff R (2000) Logical foundation of fuzzy preferential systems with application to the electre decision aid methods. Comput Oper Res 27:673–687 · Zbl 0968.90044
[5] Bisdorff R (2002) Logical foundation of multicriteria preference aggregation. In: Bouyssou D, Jacquet-Lagrèze E, Perny P, Slowinski R, Vanderpooten D, Vincke PH (eds) Aiding decisions with multiple criteria: essays in honour of Bernard Roy. Kluwer, Dordrecht, pp 379–403
[6] Bisdorff R (2004) Concordant outranking with multiple criteria of ordinal significance. 4OR, Quarterly Journal of the Belgian, French and Italian Operations Research Societies, vol 2(4). Springer, Heidelberg, pp 293–308 · Zbl 1112.90343
[7] Bisdorff R (2006a) The Python digraph implementation for RuBy: user manual. University of Luxembourg, Luxembourg, http://sma.uni.lu/bisdorff/Digraph
[8] Bisdorff R (2006b) On enumerating the kernels in a bipolar-valued outranking digraph. In: Bouyssou D, Roberts F, Tsoukiás A (eds) Proceedings of the DIMACS-LAMSADE workshop on voting theory and preference modelling, Paris, 25–28 October 2006, vol 6 of Annales du LAMSADE, pp 1–38. Université Paris-Dauphine, CNRS, Paris
[9] Bisdorff R, Roubens M (1998) On defining and computing fuzzy kernels from l-valued simple graphs. In: Ruan D, D’hondt P, Govaerts P, Kerre E (eds) Intelligent systems and soft computing for nuclear science and industry, FLINS’96 workshop. World Scientific Publishers, Singapoure, pp 113–123
[10] Bisdorff R, Roubens M (2003) Choice procedures in pairwise comparison multiple-attribute decision making methods. In: Berghammer R, Möller B, Struth G (eds) Relational and Kleene-algebraic methods in computer science: 7th international seminar on relational methods in computer science and 2nd international workshop on applications of Kleene algebra, vol 3051 of lecture notes in computer science. Springer, Heidelberg, pp 1–7
[11] Bisdorff R, Pirlot M, Roubens M (2006) Choices and kernels in bipolar valued digraphs. Eur J Oper Res 175:155–170 · Zbl 1137.91347
[12] Bouyssou D (1996) Outranking relations: do they have special properties? J Multi Criteria Decision Anal 5:99–111 · Zbl 0847.90001
[13] Chvátal V (1973) On the computational complexity of finding a kernel. Technical report, Report No. CRM-300, Centre de recherches mathématiques, Université de Montréal, Montréal
[14] Kitainik L (1993) Fuzzy decision procedures with binary relations: towards a unified theory. Kluwer, Boston · Zbl 0821.90001
[15] Richardson M (1953) Solution of irreflectice relations. Ann Math 58:573–580 · Zbl 0053.02902
[16] Roy B (1968) Classement et choix en présence de points de vue multiples (la méthode ELECTRE). Rev Fr Inf Rech Oper 2:57–75
[17] Roy B (1985) Méthodologie multicritère d’aide à la décision. Economica, Paris
[18] Roy B, Bouyssou D (1993) Aide multicritère à la décision : Méthodes et cas. Economica, Paris · Zbl 0925.90230
[19] Roy B, Vanderpooten D (1996) The European school of MCDA: emergence, basic features and current works. J Multi Criteria Decis Anal 5:22–38 · Zbl 0953.90536
[20] Windelband W (1884) Beiträge zur Lehre vom negativen Urteil. In: Straßburger Abhandlungen zur Philosophie: Eduard Zeller zu seinem 70. Geburtstage, pp 165–195. Strasbourg
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.