In this paper, a neural network (NN)-based multi-agent classifier system (MACS) utilising the trustnegotiation-communication (TNC) reasoning model is proposed. A novel trust measurement method, based on the combination of Bayesian belief functions, is incorporated into the TNC model. The Fuzzy Min-Max (FMM) NN is used as learning agents in the MACS, and useful modifications of FMM are proposed so that it can be adopted for trust measurement. Besides, an auctioning procedure, based on the sealed bid method, is applied for the negotiation phase of the TNC model. Two benchmark data sets are used to evaluate the effectiveness of the proposed MACS. The results obtained compare favourably with those from a number of machine learning methods. The applicability of the proposed MACS to two industrial sensor data fusion and classification tasks is also demonstrated, with the implications analysed and discussed.