On the duality of aggregation operators and k-negations
In this paper we study a class of duality functions given by the solution of a system of functional equations related to the De Rham system. With the aid of a generalized dyadic representation system in the unit interval, we study a negation N which is a duality function for pairs of operators satisfying certain boundary conditions. New properties of N are investigated, including its singularity and fractal dimensions for several related sets. As an application we obtain an explicit expression for k-negations. (C) 2011 Elsevier B.V. All rights reserved.
aggregation operator k-negation de rham system generalized dyadic representation system singular function hausdorff dimension