Induced weighted operators based on dissimilarity functions ?
Based on the minimization considering dissimilarity function D(x,y)=(f(x)-f(y))2 D ( x , y ) = f ( x ) - f ( y ) 2 induced ordered weighted averaging operators IOWA  and induced ordered generalized mixture operators IOMg IOM g 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.
operator dissimilarity function monotonicity weak monotonicity inducing variable argument variable