• Jaime Gil-Aluja
Part of the Applied Optimization book series (APOP, volume 32)


Up to this point we have seen that, in the sphere of decision taking, the concepts of relation, assignment and grouping have acquired special relevance, particularly in a context of uncertainty. However, it is perhaps the notion of order, that is the fundamental element on which the act of decision revolves.


Equivalency Class Class Graph Transitive Relation Dominant Eigenvalue Boolean Matrix 
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  1. 1.
    We have insisted on this aspect of the problem in order to arrive at a greater fluidity in our presentation.Google Scholar
  2. 2.
    From this point forward we will no longer include with the word characteristic, those of property and/or peculiarity but it must be understood that the term characteristic includes both of these terms.Google Scholar
  3. 3.
    As we have done in the other parts of this work, from now on we will be using the simplified nomenclature: that is lowercase letters for the object and uppercase letters for the characteristics.Google Scholar
  4. 4.
    See in this respect Gil Aluja. J.: Modelo de seleccion de inversiones con desconocimiento de las magnitudes econômico-finacieras. Proceedings of the VI Jornadas Luso-Espanholas de Gestao Cientifica, Funchal, 10–12 December 1992, Vol 1 (with no general page numbering).Google Scholar
  5. 5.
    This example has been taken from Gil Aluja, J.: Invertir en la incertidumbre, Ed. Pirâmide. Madrid 1997, pages 310–313.Google Scholar
  6. 6.
    Kaufman, A. and Gil Aluja, J.: Grafos neuronales para la economia y la gestion de empresas. Ed. Pirâmide, Madrid 1995, pages 43–46.Google Scholar
  7. 7.
    Demoocrom, M.: Work presented to Cie, de Machines Bull. Paris 1964.Google Scholar
  8. 8.
    For greater detail consult: Kaufmann, A. and Gil Aluja, J.: Nuevas técnicas para la direccion estratégica. Ed. Universidad de Barcelona, Barcelona. 1991, section 6.Google Scholar
  9. 9.
    Let us remember that an elemental path is formed by a succession of vertices without any repetition occurring among them, taking into account the arcs of the graph.Google Scholar
  10. 10.
    Kaufmann, A. and Gil Aluja, J.: Técnicas operativas de gestion para el tratamiento de la incertidumbre. Ed. Hispano Europea, Barcelona 1987 pages 219–234Google Scholar
  11. 11.
    In this sense work has also been done, for arriving at other objectives, by Saaty, T.L. in Exploring the interface between hierarchies, multiple objectives and fuzzy sets. Fuzzy Sets and Systems Vol. I No. 1, pages 57–68, and also Dinh Xuan Ba in A method for estimating the membership function of a fuzzy set. Revue Busefal L.S.I. University Paul Sabatier. Toulouse 1984 No 19, pages 68–82.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Jaime Gil-Aluja
    • 1
    • 2
  1. 1.Barcelona UniversitySpain
  2. 2.Paris-Dauphine UniversityFrance

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