DeMorgan systems with an infinitely many negations in the strict monotone operator case

Abstract

We give a new representation theorem of negation based on the generator function of the strict operator. We study a certain class of strict monotone operators which build the DeMorgan class with infinitely many negations. We show that the necessary and sufficient condition for this operator class is f c ( x) f d ( x) = 1, where f c ( x) and f d ( x) are the generator functions of the strict t-norm and strict t-conorm.