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A class of aggregation functions encompassing two-dimensional OWA operators

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Bustince, H. and Calvo, T. and De Baets, B. and Fodor, J. and Mesiar, R. and Montero, Javier and Paternain, D. and Pradera, A. (2010) A class of aggregation functions encompassing two-dimensional OWA operators. Information Sciences, 180 (10). pp. 1977-1989. ISSN 0020-0255

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Official URL: http://www.sciencedirect.com/science/article/pii/S0020025510000447


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Abstract

In this paper we prove that, under suitable conditions, Atanassov’s Ka 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 Ka 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.


Item Type:Article
Uncontrolled Keywords:OWA operators; interval-valued fuzzy sets; Ka operators;generalized Ka operators; dispersion
Subjects:Sciences > Computer science > Artificial intelligence
ID Code:16002
Deposited On:19 Jul 2012 09:17
Last Modified:07 Aug 2018 07:26

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