Approximation of the Continuous Nilpotent Operator Class
József Dániel Dombi, Zsolt Gera · 2005
In this paper we propose an approximation of the class of continuous nilpotent operators. The proof is based on one hand the approximation of the cut function, and on the other hand the representation theorem of operators with zero divisors. The approximation is based on sigmoid functions which are found to be useful in machine intelligence and other areas, too. The continuous nilpotent class of operators play an important role in fuzzy logic due to their good theoretical properties. Besides them this operator family does not have a continuous gradient. The main motivation was to have a simple and continuously differentiable approximation which ensures good properties for the operator.