New PDF release: Advances in Decision Analysis

By Hervé Raynaud (auth.), Nadine Meskens, Marc Roubens (eds.)

ISBN-10: 9048151678

ISBN-13: 9789048151677

ISBN-10: 9401706476

ISBN-13: 9789401706476

The current booklet fmds its roots within the overseas convention on equipment and purposes of a number of standards determination Making held in Mons in may well 1997. A small variety of contributions to that convention have been chosen through a refereeing approach and retained authors have been asked to incorporate of their ultimate model their newer effects. This explains why a few papers vary considerably from the unique presentation. The introductory paper of Raynaud addresses the lengthy diversity forecasts in a number of standards determination Making at the foundation of a Delphi method that used to be run earlier than and through the congress. In a moment half, the French writer explains how he and a few of his companions might locate the facts of an incredible conjecture : the generation of a strongly monotonic selection functionality isn't a strongly monotonic rating functionality. the second one a part of the publication covers methodological facets of selection concept. The contribution of Bouyssou and Pirlot matters the reformulation of classical conjoint dimension types that set off an entire and transitive choice binary relation at the set of choices which appear to be unrealistic while choice makers are requested to check gadgets evaluated on a number of attributes. The authors suggest to contemplate non transitive, non entire and non additive decomposable conjoint versions. They outline houses that represent such models.

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The whole set X is a trivial example of a covering set. It is not difficult to see that the Uncovered set is also a covering set. More surprising is the fact that there exists a unique non-empty subset which is contained in every covering sets and which is itself covering. Proposition 3 The set of covering sets for (X,g) has a minimal element (by inclusion). This non-empty subset ofX is called the Minimal Covering set and is denoted MC(X,g). The original proof of this proposition is Dutta (1988), in the tournament case.

Notice that, despite the interpretation, in voting problems, of the minmax number, the MinMax rule is an ordinal one. Proposition 6 The MinMax set satisfies the Monotonicity property but not the Aizerman property. Proposition 7 The MinMax set is Condorcet-consistent. Comparison of the MinMax set with other choice correspondences has been done by De Donder, Le Breton and Truchon (1997). A prudent strategy cannot be covered but need not belong to the Minimal Covering set. The sign-MinMax set, MM± is not very interesting, but it eliminates the Condorcet losers.

1993) Decision Theory - An Introduction to the Mathematics of Rationality, Ellis Horwood. M. (1991) Decomposable Threshold Models, Journal of Mathematical Psychology 35,64-79. L. and H. Raiffa (1976) Decisions with Multiple Objectives - Preferences and value tradeoffs, Wiley, New York. Krantz D .. D. Luce , P. Suppes and A. , New-York. O. (1954) Intransitivity, utility and the aggregation of preference patterns, Econometrica 22, 1-13. Roy B. (1968) Classement et choix en presence de points de vue multiples (la methode ELECTRE), Revue d'In/ormatique et de Recherche Operationnelie (RIRO) 8,57-75.

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Advances in Decision Analysis by Hervé Raynaud (auth.), Nadine Meskens, Marc Roubens (eds.)


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