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 equipped round vast subject matters:
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Additional resources for Aiding Decisions with Multiple Criteria: Essays in Honor of Bernard Roy
1959a). Contribution de la theorie des graphes al'etude de certains problemes lineaires. C. R. Acad. Sci. Paris 248:2437-2439. Roy, B. (1959b). Transitivite et connexite. C. R. Acad. Sci. Paris 249:216-218. Roy, B. (1962). Cheminement et connexite dans les graphes: application aux problemes d'ordonnancement. METRA Serie Speciale No 1 (Mai 1962). Roy, B. (1967). Nombre chromatique et plus long chemins d'un graphe. Rev. Info. et Rech. Oper 5:129-132. Roy, B. (1969). Graph partial s-connexe extremum.
As before, let Ti be a transformation applied to L defined by Ti . L = (f hk ) with fhk := min(fhk' fhi + fik)' This means that the distance between Xh and Xk is at most equal to the minimum of the length fhk of a path from Xh to Xk and of the sum of the lengths fhi of a path from Xh to Xi and fik of a path from Xi to Xk. With some adaptation the proof of Theorem 6 shows that Tn . Tn-I' .. Tl . L = t. A further extension to the maximum capacity path can be made by starting from a matrix C = (Chk) where Chk is the capacity of arc (Xh' Xk) if it exists and 0 otherwise.
Math. 13:213-221. Gondran, M. (1975). Path algebra and algorithms. In: Combinatorial Programming: Methods and Applications. (B. ) NATO Adv. Study Inst. 19, Reidel, Dordrecht, 137-148. REFERENCES 41 Gondran, M. (1996a). Analyse MINMAX. C. R. Acad. Sci. Paris 323:1249-1252. Gondran, M. (1996b). Analyse MINPLUS. C. R. Acad. Sci. Paris 323:371-375. , and Minoux, M. (1984). Linear algebra in dioids: a survey of recent results. Ann. of Discrete Mathematics 19:147-164. , and Minoux, M. (1997). Valeurs propres et fonctions propres d'endomorphismes a diagonale dominante en analyse Min-Max.
Aiding Decisions with Multiple Criteria: Essays in Honor of Bernard Roy by Jacques Lesourne (auth.), Denis Bouyssou, Eric Jacquet-Lagrèze, Patrice Perny, Roman Słowiński, Daniel Vanderpooten, Philippe Vincke (eds.)