Pliant Operator System

Abstract

AbstractWe 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. On the other hand our starting point is study of the relationship for Dombi aggregative operators, uninorms, strict t-norms and t-conorms. We present new representation theorem of strong negations where two explicitly contain the neutral value. Then relationships for aggregative operators and strong negations are verified as well as those for t-norm and t-conorm using the Pan operator concept. We will study a certain class of aggregative operators which build a self-DeMorgan class with infinitely many negation operators. We introduce the multiplicative pliant concept and characterize it by necessary and sufficient conditions.KeywordsRepresentation TheoremAggregation FunctionNeutral ElementNegation OperatorStrong NegationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.