Using Homogeneous Groupings in Portfolio Management

  • Jaime Gil-Aluja
  • Anna M. Gil-Lafuente
  • Jaime Gil-Lafuente
Conference paper
Part of the New Economic Windows book series (NEW)


Often, in situations of uncertainty in portfolio management, it is difficult to apply the numerical methods based on the linearity principle. When this happens it is possible to use nonnumeric techniques to assess the situations with a non linear attitude. One of the concepts that can be used in these situations is the concept of grouping.

In the last thirty years, several studies have tried to give good solutions to the problems of homogeneous groupings. For example, we could mention the Pichat algorithm, the affinities algorithms and several studies developed by the authors of this work.

In this paper, we use some topological axioms in order to develop an algorithm that is able to reduce the number of elements of the power sets of the related sets by connecting them to the sets that form the topologies. We will apply this algorithm in the grouping of titles listed in the Stock Exchange or in its dual perspective.


Homogeneous Grouping Stock Exchange Fuzzy Subset Portfolio Management Fuzzy Topological Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Badard, R., (1981). Fuzzy pre-topological spaces and their representation. Journal of Mathematical Analysis and Applications, 81, 211–220MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bayoumi, F., (2005). On initial and final L-topological groups. Fuzzy Sets and Systems, 156, 43–54MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Chang, C.L., (1968). Fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 24, 182–190MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Du, S.H., Qin, Q.M., Wang, Q., Li, B., (2005). Fuzzy description of topological relations I: A unified fuzzy 9-intersection model. In: Advances in Natural Computation. Pt 3, Proceedings. Springer-Verlag, Berlin, pp. 1261–1273CrossRefGoogle Scholar
  5. 5.
    Fang, J.M., Chen, P.W., (2007). One-to-one correspondence between fuzzifying topologies and fuzzy preorders. Fuzzy Sets and Systems, 158, 1814–1822MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Fang, J.M., Yue, Y.L., (2004). K. Fan’s theorem in fuzzifying topology. Information Sciences, 162, 139–146MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Gil-Aluja, J., (1999). Elements for a theory of decision under uncertainty, Kluwer Academic Publishers, DordrechtCrossRefGoogle Scholar
  8. 8.
    Gil-Aluja, J. (2003). Clans, affinities and Moore’s fuzzy pretopology. Fuzzy Economic Review, 8, 3–24Google Scholar
  9. 9.
    Gil-Aluja, J., Gil-Lafuente, A.M., (2007). Algoritmos para el tratamiento de fenómenos económicos complejos (In Spanish). Ed. CEURA, MadridGoogle Scholar
  10. 10.
    Kaufmann, A., Gil-Aluja, J., (1991). Selection of affinities by means of fuzzy relation and Galois lattices. Proceedings of the XIEURO Congress, Aachen, GermanyGoogle Scholar
  11. 11.
    Saadati, R., Park, J.H., (2006). On the intuitionistic fuzzy topological spaces. Chaos, Solitons & Fractals, 27, 331–344MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Yan, C.H., Wu, C.X., (2007). Fuzzifying vector topological spaces, International Journal of General Systems, 36, 513–535MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Yue, Y.L., (2007). Lattice-valued induced fuzzy topological spaces. Fuzzy Sets and Systems, 158, 1461–1471MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2010

Authors and Affiliations

  • Jaime Gil-Aluja
    • 1
  • Anna M. Gil-Lafuente
    • 2
  • Jaime Gil-Lafuente
    • 2
  1. 1.Department of Business AdministrationRovira i Virgili UniversityReusSpain
  2. 2.Department of Business AdministrationUniversity of BarcelonaBarcelonaSpain

Personalised recommendations