Induced weighted operators based on dissimilarity functions

Based on the minimization considering dissimilarity function D(x,y)=(f(x)-f(y))2D(x,y)=f(x)-f(y)2 induced ordered weighted averaging operators IOWA   and induced ordered generalized mixture operators IOMgIOMg are discussed. In general, these operators need not be monotone non-decreasing, thus they need not be the aggregation operators. This paper introduces conditions for their monotonicity and weak monotonicity. Several examples are included.