Weighted aggregation operators based on minimization

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) = vertical bar x - y vertical bar and non-decreasing (non-increasing) g, Ag,D is shown to be the upper (lower) median whenever Ag,D is an aggregation operator. (c) 2007 Elsevier Inc. All rights reserved.