Weighted operators based on dissimilarity function

This paper talks about weighted operators based on dissimilarity function and discusses the monotone non-decreasingness of these operators, i.e., it looks for conditions leading to aggregation operators. Moreover, the paper discusses the shift-invariance and weak monotone non-decreasingness of mentioned operators. It discusses minimization based operators Aw,D,Ag,D, where ww is a weighting vector, gg is a vector of weighting functions, and D   is a dissimilarity function D(x,y)=(f(x)-f(y))2D(x,y)=(f(x)-f(y))2. Following Aw,DAw,D we recognize the class of arithmetic means, ordered weighted averaging OWA   operators and their extensions. Operators Aw,DAw,D are monotone non-decreasing, and hence shift-invariant and weak monotone non-decreasing, too. By the operators Ag,DAg,D we introduce a generalization of the operators Aw,DAw,D. The operators Ag,DAg,D cover the class of mixture operators, quasi-mixture operators, and their extensions. In general, these operators need not be non-decreasing, nor shift-invariant, and hence nor weak monotone non-decreasing.