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For the new concept of a multi-valued neural network introduced earlier, an analogue of the T-norm in fuzzy mathematics is considered. In the multi-valued neural network, all variables 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 lattice elements' multiplication may also be used to determine such operations in the case when not all of them are allowed by the lattice construction. In this paper, the lattice is assumed to be residuated, 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, in output determining of the neural network. Though, such a construction determines a multi-valued associative memory similar to the Brouwer lattice case considered earlier, this variant is more natural to use in the Kohonen-like networks that we demonstrate with the example of a robot group management.