For the new concept of a multi-valued neural network introduced earlier, an analogueof the T-norm in fuzzy mathematics is considered. In the multi-valued neural network, allvariables are elements of the lattice of linguistic variables, i.e., they are all only partially-ordered. The lattice operations are used to build the network output by inputs. However, a latticeelements’ multiplication may also be used to determine such operations in the case when notall of them are allowed by the lattice construction. In this paper, the lattice is assumed to beresiduated, and the residual construction gives the analogue of a T-norm. The lattice elements’multiplication determines the implication which is used, together with other lattice operations, inoutput determining of the neural network. Though, such a construction determines a multi-valuedassociative memory similar to the Brouwer lattice case considered earlier, this variant is morenatural to use in the Kohonen-like networks that we demonstrate with the example of a robotgroup management.