A class of aggregation functions encompassing two-dimensional OWA operators

  • Authors:

  • H. Bustince;T. Calvo;B. De Baets;J. Fodor;R. Mesiar;J. Montero;D. Paternain;A. Pradera

  • Affiliations:

  • Departamento de Automática y Computación, Universidad Pública de Navarra, Campus Arrosadia s/n, P.O. Box 31006, Pamplona, Spain;Universidad de Alcalá, Spain;Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, 9000 Gent, Belgium;Institute of Intelligent Engineering Systems, Budapest Tech, Bécsi út 96/b, H-1034 Budapest, Hungary;Department of Mathematics and Descriptive Geometry, Slovak University of Technology, SK-813 68 Bratislava, Slovakia and Institute of Information Theory and Automation, Czech Academy of Sciences, C ...;Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain;Departamento de Automática y Computación, Universidad Pública de Navarra, Campus Arrosadia s/n, P.O. Box 31006, Pamplona, Spain;Departamento de Ciencias de la Computación, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2010

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Abstract

In this paper we prove that, under suitable conditions, Atanassov's K"@a operators, which act on intervals, provide the same numerical results as OWA operators of dimension two. On one hand, this allows us to recover OWA operators from K"@a operators. On the other hand, by analyzing the properties of Atanassov's operators, we can generalize them. In this way, we introduce a class of aggregation functions - the generalized Atanassov operators - that, in particular, include two-dimensional OWA operators. We investigate under which conditions these generalized Atanassov operators satisfy some properties usually required for aggregation functions, such as bisymmetry, strictness, monotonicity, etc. We also show that if we apply these aggregation functions to interval-valued fuzzy sets, we obtain an ordered family of fuzzy sets.