Skip to main content

2018 | OriginalPaper | Buchkapitel

On the Problem of Aggregation of Partial T-Indistinguishability Operators

verfasst von : Tomasa Calvo Sánchez, Pilar Fuster-Parra, Óscar Valero

Erschienen in: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper we focus our attention on exploring the aggregation of partial T-indistinguishability operators (relations). Concretely we characterize, by means of (T-\(T_{\min }\))-tuples, those functions that allow to merge a collection of partial T-indistinguishability operators into a single one. Moreover, we show that monotony is a necessary condition to ensure that a function aggregates partial T-indistinguishability operators into a new one. We also provide that an inter-exchange composition function condition is a sufficient condition to guarantee that a function aggregates partial T-indistinguishability operators. Finally, examples of this type of functions are also given.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
6.
Zurück zum Zitat Bouchon-Meunier, B. (ed.): Aggregation and Fusion of Imperfect Information. Sudies in Fuzziness and Soft Computing, vol. 12. Physica-Verlag, Heidelberg (1998)MATH Bouchon-Meunier, B. (ed.): Aggregation and Fusion of Imperfect Information. Sudies in Fuzziness and Soft Computing, vol. 12. Physica-Verlag, Heidelberg (1998)MATH
8.
Zurück zum Zitat Calvo, T., Fuster-Parra, P., Valero, O.: On the problem of relaxed indistinguishability aggregation operators. In: Proceedings of the Workshop on Applied Topological Structures, WATS 2017, pp. 19–26 (2017) Calvo, T., Fuster-Parra, P., Valero, O.: On the problem of relaxed indistinguishability aggregation operators. In: Proceedings of the Workshop on Applied Topological Structures, WATS 2017, pp. 19–26 (2017)
11.
Zurück zum Zitat Drewniak, J., Dudziak, U.: Aggregation preserving classes of fuzzy relations. Kybernetica 41, 265–284 (2005)MathSciNetMATH Drewniak, J., Dudziak, U.: Aggregation preserving classes of fuzzy relations. Kybernetica 41, 265–284 (2005)MathSciNetMATH
12.
Zurück zum Zitat Dudziak, U.: Preservation of t-norm and t-conorm based properties of fuzzy relations during aggregation process. In: Proceedings of the 8th Conference of European Society for Fuzzy Logic and Technology, EUSFLAT 2013, pp. 376–383 (2013) Dudziak, U.: Preservation of t-norm and t-conorm based properties of fuzzy relations during aggregation process. In: Proceedings of the 8th Conference of European Society for Fuzzy Logic and Technology, EUSFLAT 2013, pp. 376–383 (2013)
13.
Zurück zum Zitat Fuster-Parra, P., Martín, J., Miñana, J.J., Valero, O.: A study on the relationship between relaxed metrics and indistinguishability operators (2017, submitted) Fuster-Parra, P., Martín, J., Miñana, J.J., Valero, O.: A study on the relationship between relaxed metrics and indistinguishability operators (2017, submitted)
14.
Zurück zum Zitat Fuster-Parra, P., Martín, J., Recasens, J., Valero, O.: On the metric behavior of partial indistinguishability operators. preprint (2018) Fuster-Parra, P., Martín, J., Recasens, J., Valero, O.: On the metric behavior of partial indistinguishability operators. preprint (2018)
15.
Zurück zum Zitat Gottwald, S.: On t-norms which are related to distances of fuzzy sets. BUSEFAL 50, 25–30 (1992) Gottwald, S.: On t-norms which are related to distances of fuzzy sets. BUSEFAL 50, 25–30 (1992)
16.
Zurück zum Zitat Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, New York (2009)CrossRef Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, New York (2009)CrossRef
17.
Zurück zum Zitat Grigorenko, O., Lebendinska, J.: On another view of aggregation of fuzzy relations. In: Galichet, S., Montero, J., Mauris, G. (eds) Proceedings of the 7th Conference on EUSFLAT 2011 and LFA 2011, pp. 21–27. Atlantis Press (2011) Grigorenko, O., Lebendinska, J.: On another view of aggregation of fuzzy relations. In: Galichet, S., Montero, J., Mauris, G. (eds) Proceedings of the 7th Conference on EUSFLAT 2011 and LFA 2011, pp. 21–27. Atlantis Press (2011)
18.
Zurück zum Zitat Höhle, U.: Fuzzy equalities and indistinguishability. In: Proceedings of EUFIT 1993, Aachen, vol. 1, pp. 358–363 (1993) Höhle, U.: Fuzzy equalities and indistinguishability. In: Proceedings of EUFIT 1993, Aachen, vol. 1, pp. 358–363 (1993)
20.
Zurück zum Zitat Klement, P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)CrossRef Klement, P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)CrossRef
21.
Zurück zum Zitat Mayor, G., Recasens, J.: Preserving T-transitivity. In: Nebot, A., et al. (eds.) Artificial Intelligence Research and Development, vol. 288, pp. 79–87. IOS Press (2016) Mayor, G., Recasens, J.: Preserving T-transitivity. In: Nebot, A., et al. (eds.) Artificial Intelligence Research and Development, vol. 288, pp. 79–87. IOS Press (2016)
22.
Zurück zum Zitat Ovchinnikov, S.V.: Representations of transitive fuzzy relations. In: Skala, H.J., Termini, S., Trillas, E. (eds.) Aspects of Vageness. Theory and Decision Library (An International Series in the Philosophy and Methodology of the Social and Behavioral Sciences), vol. 39, pp. 105–118. Springer, Dordrecht (1984). https://doi.org/10.1007/978-94-009-6309-2_7CrossRef Ovchinnikov, S.V.: Representations of transitive fuzzy relations. In: Skala, H.J., Termini, S., Trillas, E. (eds.) Aspects of Vageness. Theory and Decision Library (An International Series in the Philosophy and Methodology of the Social and Behavioral Sciences), vol. 39, pp. 105–118. Springer, Dordrecht (1984). https://​doi.​org/​10.​1007/​978-94-009-6309-2_​7CrossRef
25.
Zurück zum Zitat Pradera, A., Trillas, E., Castiñeira, E.: On distances aggregation. In: Bouchon-Meunier, B. et al. (eds.) Proceedings of Information Processing and Management of Uncertainty in Knowledge-Based Systems International Conference, vol. II, pp. 693–700. Universidad Politécnica de Madrid Press (2000) Pradera, A., Trillas, E., Castiñeira, E.: On distances aggregation. In: Bouchon-Meunier, B. et al. (eds.) Proceedings of Information Processing and Management of Uncertainty in Knowledge-Based Systems International Conference, vol. II, pp. 693–700. Universidad Politécnica de Madrid Press (2000)
26.
Zurück zum Zitat Pradera, A., Trillas, E., Castiñeira, E.: On the aggregation of some classes of fuzzy relations. In: Bouchon-Meunier, B., Gutierrez, J., Magdalena, L., Yager, R. (eds.) Technologies for Constructing Intelligent Systems. STUDFUZZ, vol. 90, pp. 125–136. Physica, Heidelberg (2002). https://doi.org/10.1007/978-3-7908-1796-6_10CrossRef Pradera, A., Trillas, E., Castiñeira, E.: On the aggregation of some classes of fuzzy relations. In: Bouchon-Meunier, B., Gutierrez, J., Magdalena, L., Yager, R. (eds.) Technologies for Constructing Intelligent Systems. STUDFUZZ, vol. 90, pp. 125–136. Physica, Heidelberg (2002). https://​doi.​org/​10.​1007/​978-3-7908-1796-6_​10CrossRef
29.
Zurück zum Zitat Trillas, E.: Assaig sobre les relacions d’indistingibilitat. In: Proceedings of the Primer Congrés Catalá de Lógica Matemática, Barcelona, pp. 51–59 (1982) Trillas, E.: Assaig sobre les relacions d’indistingibilitat. In: Proceedings of the Primer Congrés Catalá de Lógica Matemática, Barcelona, pp. 51–59 (1982)
Metadaten
Titel
On the Problem of Aggregation of Partial T-Indistinguishability Operators
verfasst von
Tomasa Calvo Sánchez
Pilar Fuster-Parra
Óscar Valero
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-91473-2_18