Multifarious Comparisons for Objectives and Attributes

  • Willem K. Brauers
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 73)


The previous chapter concluded that multifarious comparisons of alternatives are preferred above binary ones. For multifarious comparison, this chapter moves from some theoretically self-evident approaches to situations in which the alternatives seem to be incomparable. Indeed, an a priori priority between the objectives gives the impression that the problem is easily solved. This seems also the case, if some alternatives are dropped out, due to not satisfying some minimum or maximum requirements. In addition, domination of one alternative over all the others would easily solve the problem. The problem remains if a ranking turns out to be impossible with incomparably looking alternatives.


Multiobjective Optimization Marginal Utility Pareto Optimum Capital Requirement Soft Constraint 
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Notes Part 3 Chapter 3

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    The full details of the model with simulations not only for one country but also for the economic integration of several countries are given in: W.K. Brauers, Input-Output Analysis and International Economic Integration (in Dutch with English Summary), Standaard Uitg., Antwerpen-Utrecht, 1968. W.K. Brauers, Prévisions économiques à l’aide de la méthode entrées-sorties, Economica, Paris, 1995.Google Scholar
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    We represented lower bounds and upper limits by scalars, but these constraints could also be linear functions. In fact in the example of Chapter 2.4 and in Figure 3.2 the constraints are linear functions. Even nonlinear constraints are acceptable. The underlying idea we developed for the linear constraints still apply for the nonlinear ones. For nonlinear constraints, see: L.E. Edlefsen, The Comparative Statics of Hedonic Price Functions and other Nonlinear Constraints, Econometrica, vol.49, 1981, 1501–1520.CrossRefGoogle Scholar
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Willem K. Brauers
    • 1
  1. 1.Faculty of Applied Economics and Institute for Development Policy and ManagementUniversity of AntwerpBelgium

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