Lattice-valued logic and neural networks

Lattice-valued logic is a generalized logic whose definition function is set-valued. It can be applied to switching systems by defining a lattice-valued switch (LVS) whose parallel connection “∪” and cascade connection “∩” are generalized operators which may correspond respectively to the “max” (v) and “min” (∧) operators in fuzzy logic, or “+” and “·” operators in neural networks. Here, it is shown that both fuzzy logic based systems (FLS) and neural network based systems (NNS) can have a unified representation in the form of LVS. A fuzzy Boolean switching system which has the advantages of both FLS and NNS is introduced along with a method for its design