Weighted aggregation operators based on minimization

Minimization based aggregation operators Ag,D are discussed. Special attention is paid to weighting function g based cases related to some fixed dissimilarity function D  . When D2(x,y)=(x-y)2D2(x,y)=(x-y)2, we recognize mixture operators and we recall some sufficient conditions for g ensuring the monotonicity of Ag,D. For D1(x,y)=|x-y|D1(x,y)=|x-y| and non-decreasing (non-increasing) g, Ag,D is shown to be the upper (lower) median whenever Ag,D is an aggregation operator.