Infinitely Many Specific Fuzzy Neural Network Operators Treated as Fuzzy Positive Linear Operators

Basic fuzzy multicomposite neural network operators are interpreted as fuzzy positive linear operators, and the related general fuzzy theory is applied. These fuzzy operators are defined by the composition of seven well-known activation functions. We are acting in the univariate case on a compact interval and in the multivariate case on a box, treating continuous functions from these to the fuzzy real numbers. We study quantitatively the rate of convergence of these fuzzy neural network operators to the fuzzy unit operator. Our inequalities involve the related fuzzy moduli of continuity. We derive pointwise, uniform and Lp (p≥1) fuzzy convergences. The amazing fact here is that these fuzzy convergences are enforced by the properties of the deterministic corresponding real-valued operators. We derive a plethora of infinitely many such fuzzy positive linear operators with the above behaviors. These are based on the infinitely many multicomposite combinations of our seven fundamental defining activation functions.