Let T* : [0,1]2-[0, 1] be an associative function with neutral element, f : [0,1]- [0, 1] be a monotone right continuous function and f(-1) : [0, 1]- [0, 1] be the pseudo-inverse of f. This article answers the question: what properties of the range of a generator f are sufficient and necessary for the corresponding generated function T : [0, 1]2-[0, 1] defined by T(x, y) = f(-1)(T*(f(x),f(y))) with property of T(...T(T(x1,x2),x3),...,xn) = f(-1)(T*(f(x1),...,f(xn))) forallnE {1, ...,n,...} withn >= 2 andforallx1,...,xn E [0, 1].
Triangular conormAssociative functionMonotone right continuous functionGeneratorADDITIVE GENERATORS
NETL
NSTL
Elsevier
