By Jacques Lesourne (auth.), Denis Bouyssou, Eric Jacquet-Lagrèze, Patrice Perny, Roman Słowiński, Daniel Vanderpooten, Philippe Vincke (eds.)
Aiding judgements With a number of standards: Essays in Honor of BernardRoy is prepared round wide subject matters:
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Extra info for Aiding Decisions with Multiple Criteria: Essays in Honor of Bernard Roy
B. Roy gives additional properties of the orientation (Roy 1967): (c) Any vertex x with c(x) sets 8h- 1 , 8 h- 2 , . · · , 8 1 . =h has a predecessor in each one of the (d) Every stable set 8h is (inclusion-wise) maximal in the subgraph of G induced by 8h, 8 h+ 1 , ... ,8k' Connectivity, Transitivity and Chromaticity 3 33 2 (a) G with X(G) (b) = 4 and An orientation without circuit in G a 4-coloring and the coloring of Theorem 9 (a) 2 (e) A 4-coloring having Property (b) of Theorem 9 (b) Figure 4.
In: Progress in Graph Theory (Waterloo, Onto 1982). Academic Press, Toronto, 105-108. , and Duchet, P. (1984). Strongly perfect graphs. Ann. of Discrete Mathematics 21:57-6l. , and Ghouila-Houri, A. (1965). Programming, games and transportation networks. Methuen, London. , and Thomassen, C. (1981). Cycles in digraphs - A survey. J. of Graph Theory 5:1-43. , and Krarup, J. (1969). A modified cascade algorithm for shortest paths. METRA VIII 231-24l. Bondy, J. A. (1976). Disconnected orientations and a conjecture of Las Vergnas.
556 For example, the Dow Jones Index is a simple arithmetic average calculated using a limited number of shares ... but this in no way prevents the index from serving as a reference and therefore as a reality for a certain number of financial markets. Decision-Aid Between Tools And Organisations 49 tools were used in a closed, conforming perspective, and all the weaker when the tools were used in an open, exploratory perspective6 . The crisis in operational research that took place during the second half of the 1970s, when a certain number of tool designers and managers using them began to have misgivings about the performance of models, can be analysed as a crisis in the prescription process [Hatchuel, 1996].