Weighted aggregation operators based on minimization

Authors:
Radko Mesiar;Jana Špirková;Lucia Vavríková
Affiliations:
Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia;Department of Quantitative Methods and Information Technology, Faculty of Economics, Matej Bel University, Tajovského 10, 975 90 Banská Bystrica, Slovakia;Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia
Venue:
Information Sciences: an International Journal
Year:
2008

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Abstract

Minimization based aggregation operators A"g","D are discussed. Special attention is paid to weighting function g based cases related to some fixed dissimilarity function D. When D"2(x,y)=(x-y)^2, we recognize mixture operators and we recall some sufficient conditions for g ensuring the monotonicity of A"g","D. For D"1(x,y)=|x-y| and non-decreasing (non-increasing) g, A"g","D is shown to be the upper (lower) median whenever A"g","D is an aggregation operator.