Nonparametric recursive aggregation process

Elena Tsiporkova; Veselka Boeva

Kybernetika (2004)

  • Volume: 40, Issue: 1, page [51]-70
  • ISSN: 0023-5954

Abstract

top
In this work we introduce a nonparametric recursive aggregation process called Multilayer Aggregation (MLA). The name refers to the fact that at each step the results from the previous one are aggregated and thus, before the final result is derived, the initial values are subjected to several layers of aggregation. Most of the conventional aggregation operators, as for instance weighted mean, combine numerical values according to a vector of weights (parameters). Alternatively, the MLA operators apply recursively over the input values a vector of aggregation operators. Consequently, a sort of unsupervised self-tuning aggregation process is induced combining the individual values in a certain fashion determined by the choice of aggregation operators.

How to cite

top

Tsiporkova, Elena, and Boeva, Veselka. "Nonparametric recursive aggregation process." Kybernetika 40.1 (2004): [51]-70. <http://eudml.org/doc/33685>.

@article{Tsiporkova2004,
abstract = {In this work we introduce a nonparametric recursive aggregation process called Multilayer Aggregation (MLA). The name refers to the fact that at each step the results from the previous one are aggregated and thus, before the final result is derived, the initial values are subjected to several layers of aggregation. Most of the conventional aggregation operators, as for instance weighted mean, combine numerical values according to a vector of weights (parameters). Alternatively, the MLA operators apply recursively over the input values a vector of aggregation operators. Consequently, a sort of unsupervised self-tuning aggregation process is induced combining the individual values in a certain fashion determined by the choice of aggregation operators.},
author = {Tsiporkova, Elena, Boeva, Veselka},
journal = {Kybernetika},
keywords = {multilayer aggregation operators; powermeans; monotonicity; multilayer aggregation operators; power means; monotonicity},
language = {eng},
number = {1},
pages = {[51]-70},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Nonparametric recursive aggregation process},
url = {http://eudml.org/doc/33685},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Tsiporkova, Elena
AU - Boeva, Veselka
TI - Nonparametric recursive aggregation process
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 1
SP - [51]
EP - 70
AB - In this work we introduce a nonparametric recursive aggregation process called Multilayer Aggregation (MLA). The name refers to the fact that at each step the results from the previous one are aggregated and thus, before the final result is derived, the initial values are subjected to several layers of aggregation. Most of the conventional aggregation operators, as for instance weighted mean, combine numerical values according to a vector of weights (parameters). Alternatively, the MLA operators apply recursively over the input values a vector of aggregation operators. Consequently, a sort of unsupervised self-tuning aggregation process is induced combining the individual values in a certain fashion determined by the choice of aggregation operators.
LA - eng
KW - multilayer aggregation operators; powermeans; monotonicity; multilayer aggregation operators; power means; monotonicity
UR - http://eudml.org/doc/33685
ER -

References

top
  1. Fodor J. C., Roubens M., Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer, Dordrecht 1994 Zbl0827.90002
  2. Matkowski J., Iterations of mean-type mappings and invariant means, Ann. Math. Sil. 13 (1999), 211–226 (1999) Zbl0954.26015MR1735204
  3. Matkowski J., 10.1007/PL00013194, Aequationes Math. 64 (2002), 297–303 MR1941960DOI10.1007/PL00013194
  4. Mesiar R., Aggregation operators: some classes and construction methods, Proceedings of IPMU’2000, Madrid, 2000, pp. 707–711 
  5. Mizumoto M., 10.1016/0165-0114(89)90087-0, Part 2: Cases of compensatory and self-dual operators. Fuzzy Sets and Systems 32 (1989), 245–252 (1989) Zbl0709.03524MR1011380DOI10.1016/0165-0114(89)90087-0
  6. Moser B., Tsiporkova, E., Klement K. P., Convex combinations in terms of triangular norms: A characterization of idempotent, bisymmetrical and self-dual compensatory operators, Fuzzy Sets and Systems 104 (1999), 97–108 (1999) Zbl0928.03063MR1685813
  7. Páles Z., 10.7153/mia-03-20, Mathematical Inequalities & Applications 3 (2000), 169–176 MR1749294DOI10.7153/mia-03-20
  8. Tsiporkova E., Boeva V., Multilayer aggregation operators, In: Proc. Summer School on Aggregation Operators 2003 (AGOP’2003), Alcalá de Henares, Spain, pp. 165–170 
  9. Turksen I. B., 10.1016/0165-0114(92)90020-5, Fuzzy Sets and Systems 51 (1992), 295–307 (1992) MR1192450DOI10.1016/0165-0114(92)90020-5
  10. Yager R. R., 10.1016/0020-0255(93)90124-5, Inform. Sci. 69 (1993), 259–273 (1993) DOI10.1016/0020-0255(93)90124-5
  11. Yager R. R., 10.1016/0165-0114(95)00325-8, Fuzzy Sets and Systems 85 (1997), 73–82 (1997) Zbl0903.04005MR1423474DOI10.1016/0165-0114(95)00325-8
  12. Zimmermann H.-J., Zysno P., Latent connectives in human decision making, Fuzzy Sets and Systems 4 (1980), 37–51 (1980) Zbl0435.90009

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.