Skip to main content
Erschienen in: Progress in Artificial Intelligence 3/2016

01.08.2016 | Regular Paper

Unbalanced interval-valued OWA operators

verfasst von: Laura De Miguel, Humberto Bustince, Edurne Barrenechea, Miguel Pagola, Javier Fernandez

Erschienen in: Progress in Artificial Intelligence | Ausgabe 3/2016

Einloggen

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

search-config
loading …

Abstract

In this work, we introduce a new class of functions defined on the interval-valued setting. These functions extend classical OWA operators but allow for different weighting vectors to handle the lower bounds and the upper bounds of the considered intervals. As a consequence, the resulting functions need not be an interval-valued aggregation function, so we study, in the case of the lexicographical order, when these operators give an interval as output and are monotone. We also discuss an illustrative example on a decision making problem in order to show the usefulness of our developments.

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

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!

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!

Literatur
1.
Zurück zum Zitat Barrenechea, E., Fernandez, J., Pagola, M., Chiclana, F., Bustince, H.: Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations. Application to decision making. Knowl. Based Syst. 58, 33–44 (2014)CrossRef Barrenechea, E., Fernandez, J., Pagola, M., Chiclana, F., Bustince, H.: Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations. Application to decision making. Knowl. Based Syst. 58, 33–44 (2014)CrossRef
2.
Zurück zum Zitat Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. Studies in Fuzziness and Soft Computing. Springer, Berlin (2007) Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. Studies in Fuzziness and Soft Computing. Springer, Berlin (2007)
3.
Zurück zum Zitat Beliakov, G., Bustince, H., Calvo, T.: A Practical Guide to Averaging Functions. Springer, Berlin (2016)CrossRef Beliakov, G., Bustince, H., Calvo, T.: A Practical Guide to Averaging Functions. Springer, Berlin (2016)CrossRef
4.
Zurück zum Zitat Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J.: Interval-valued fuzzy sets constructed from matrices: application to edge detection. Fuzzy Sets Syst. 160(13), 1819–1840 (2009)MathSciNetCrossRefMATH Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J.: Interval-valued fuzzy sets constructed from matrices: application to edge detection. Fuzzy Sets Syst. 160(13), 1819–1840 (2009)MathSciNetCrossRefMATH
5.
Zurück zum Zitat Bustince, H., Calvo, T., Baets, B.D., Fodor, J., Mesiar, R., Montero, J., Paternain, D., Pradera, A.: A class of aggregation functions encompassing two-dimensional \(\{\text{ OWA }\}\) operators. Inform. Sci. 180(10), 1977–1989 (2010)MathSciNetCrossRefMATH Bustince, H., Calvo, T., Baets, B.D., Fodor, J., Mesiar, R., Montero, J., Paternain, D., Pradera, A.: A class of aggregation functions encompassing two-dimensional \(\{\text{ OWA }\}\) operators. Inform. Sci. 180(10), 1977–1989 (2010)MathSciNetCrossRefMATH
6.
Zurück zum Zitat Bustince, H., Fernandez, J., Kolesárová, A., Mesiar, R.: Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets Syst. 220, 69–77 (2013)MathSciNetCrossRefMATH Bustince, H., Fernandez, J., Kolesárová, A., Mesiar, R.: Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets Syst. 220, 69–77 (2013)MathSciNetCrossRefMATH
7.
Zurück zum Zitat Bustince, H., Galar, M., Bedregal, B., Kolesárová, A., Mesiar, R.: A new approach to interval-valued Choquet integrals and the problem of ordering in interval-valued fuzzy set applications. IEEE Trans Fuzzy Syst. 21(6), 1150–1162 (2013)CrossRef Bustince, H., Galar, M., Bedregal, B., Kolesárová, A., Mesiar, R.: A new approach to interval-valued Choquet integrals and the problem of ordering in interval-valued fuzzy set applications. IEEE Trans Fuzzy Syst. 21(6), 1150–1162 (2013)CrossRef
8.
Zurück zum Zitat Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J., Xu, Z., Bedregal, B., Montero, J., Hagras, H., Herrera, F., De Baets, B.: A historical account of types of fuzzy sets and their relationships. IEEE Trans. Fuzzy Syst. In press (2015) Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J., Xu, Z., Bedregal, B., Montero, J., Hagras, H., Herrera, F., De Baets, B.: A historical account of types of fuzzy sets and their relationships. IEEE Trans. Fuzzy Syst. In press (2015)
9.
Zurück zum Zitat Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation operators: properties, classes and construction methods. In: Calvo, T., Mayor, G., Mesiar, R. (eds.) Aggregation Operators, Studies in Fuzziness and Soft Computing, vol. 97, pp. 3–104. Physica, Heidelberg (2002) Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation operators: properties, classes and construction methods. In: Calvo, T., Mayor, G., Mesiar, R. (eds.) Aggregation Operators, Studies in Fuzziness and Soft Computing, vol. 97, pp. 3–104. Physica, Heidelberg (2002)
10.
Zurück zum Zitat Choquet, G.: Theory of capacities. Annales de l Institut Fourier 5, 131–295 (1954) Choquet, G.: Theory of capacities. Annales de l Institut Fourier 5, 131–295 (1954)
11.
Zurück zum Zitat Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. In: Theory and Decision Library. Kluwer, Boston (1994) Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. In: Theory and Decision Library. Kluwer, Boston (1994)
12.
Zurück zum Zitat Grabisch, M., Marichal, J., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)CrossRefMATH Grabisch, M., Marichal, J., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)CrossRefMATH
13.
Zurück zum Zitat Komorníková, M., Mesiar, R.: Aggregation functions on bounded partially ordered sets and their classification. Fuzzy Sets Syst. 175(1), 48–56 (2011) Komorníková, M., Mesiar, R.: Aggregation functions on bounded partially ordered sets and their classification. Fuzzy Sets Syst. 175(1), 48–56 (2011)
14.
Zurück zum Zitat Miguel, L.D., Bustince, H., Fernandez, J., Induráin, E., Kolesárová, A., Mesiar, R.: Construction of admissible linear orders for interval-valued atanassov intuitionistic fuzzy sets with an application to decision making. Inform. Fusion 27, 189–197 (2016)CrossRef Miguel, L.D., Bustince, H., Fernandez, J., Induráin, E., Kolesárová, A., Mesiar, R.: Construction of admissible linear orders for interval-valued atanassov intuitionistic fuzzy sets with an application to decision making. Inform. Fusion 27, 189–197 (2016)CrossRef
15.
Zurück zum Zitat Sambuc, R.: Fonctions and floues: application a l’aide au diagnostic en pathologie thyroidienne. Faculté de Médecine de Marseille (1975) Sambuc, R.: Fonctions and floues: application a l’aide au diagnostic en pathologie thyroidienne. Faculté de Médecine de Marseille (1975)
16.
Zurück zum Zitat Sanz, J., Fernandez, A., Bustince, H., Herrera, F.: Ivturs: a linguistic fuzzy rule-based classification system based on a new interval-valued fuzzy reasoning method with tuning and rule selection. IEEE Trans. Fuzzy Syst. 21(3), 399–411 (2013)CrossRef Sanz, J., Fernandez, A., Bustince, H., Herrera, F.: Ivturs: a linguistic fuzzy rule-based classification system based on a new interval-valued fuzzy reasoning method with tuning and rule selection. IEEE Trans. Fuzzy Syst. 21(3), 399–411 (2013)CrossRef
18.
Zurück zum Zitat Xu, Z., Yager, R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35(4), 417–433 (2006)MathSciNetCrossRefMATH Xu, Z., Yager, R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35(4), 417–433 (2006)MathSciNetCrossRefMATH
19.
Zurück zum Zitat Xu, Z., Yager, R.: Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim. Decis. Mak. 8(2), 123–139 (2009)MathSciNetCrossRefMATH Xu, Z., Yager, R.: Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim. Decis. Mak. 8(2), 123–139 (2009)MathSciNetCrossRefMATH
20.
Zurück zum Zitat Yager, R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)MathSciNetCrossRefMATH Yager, R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)MathSciNetCrossRefMATH
Metadaten
Titel
Unbalanced interval-valued OWA operators
verfasst von
Laura De Miguel
Humberto Bustince
Edurne Barrenechea
Miguel Pagola
Javier Fernandez
Publikationsdatum
01.08.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Progress in Artificial Intelligence / Ausgabe 3/2016
Print ISSN: 2192-6352
Elektronische ISSN: 2192-6360
DOI
https://doi.org/10.1007/s13748-016-0086-0

Weitere Artikel der Ausgabe 3/2016

Progress in Artificial Intelligence 3/2016 Zur Ausgabe