Neutrosophic Pseudo-t-Norm and Its Derived Neutrosophic Residual Implication

Abstract

First of all, on the basis of complete lattice, the concept of neutrosophic pseudo-t-norm
(NPT) is given. Definitions and examples of representable neutrosophic pseudo-t-norms (RNPTs)
are given, while unrepresentable neutrosophic pseudo-t-norms (UNPTs) is also given. Secondly,
De Morgan neutrosophic triples (DMNTs) consists of three operators: NPTs, neutrosophic negators
(NNs) and neutrosophic pseudo-s-norms (NPSs), where NPTs and NPSs are dual about NNs.
Again, we study the neutrosophic residual implications (NRIs) of NPTs, as well as their underlying
properties. Finally, we give a method to get NPTs from neutrosophic implications (NIs) and
construct non-commutative residuated lattices (NCRLs) based on NRIs and NPTs.