Fuzzy uncertainty assessment in RBF Neural Networks using neutrosophic sets for multiclass classification

In this paper we introduce a fuzzy uncertainty assessment methodology based on Neutrosophic Sets (NS). This is achieved via the implementation of a Radial Basis Function Neural-Network (RBF-NN) for multiclass classification that is functionally equivalent to a class of Fuzzy Logic Systems (FLS). Two types of uncertainties are considered: a) fuzziness and b) ambiguity, with both uncertainty types measured in each receptive unit (RU) of the hidden layer of the RBF-NN. The use of NS assists in the quantification of the uncertainty and formation of the rulebase; the resulting RBF-NN modelling structure proves to have enhanced transparency features to interpretation that enables us to understand the influence of each system parameter thorughout the parameter identification. The presented methodology is based on firstly constructing a neutrosophic set by calculating the associated fuzziness in each rule - and then use this information to train the RBF-NN; and secondly, an ambiguity measure that is defined via the truth and falsity measures related to each normalised consequence of the fuzzy rules within the RUs. In order to evaluate the individual ambiguity in the RUs and then the average ambiguity of the whole system, a neutrosophic set is constructed. Finally, the proposed methodology is tested against two case studies: a benchmark dataset problem and a real industrial case study. On both cases we demonstrate the effectiveness of the developed methodology in automatically creating uncertainty measures and utilising this new information to improve the quality of the trained model.