AFSNN: A Classification Algorithm Using Axiomatic Fuzzy Sets and Neural Networks

In this study, we present a comprehensible classifier AFSNN that embeds a new type of coherence membership function, which builds upon the theoretical findings of the axiomatic fuzzy set (AFS) theory into the hidden layer of neural network with random weights (NNRWs). Borrowing from the idea of NNRWs that employs the random initialization technique, the relation among attributes, simple concepts, and complex concepts are randomly determined. Complex concepts are generated through the combination of randomly selected simple concepts by AFS logic operation. The output weights of NNRWs are utilized to evaluate the confidence of each complex concept for every target class, which means that the feasibility of complex concepts for every class is determined analytically rather than through the tuning parameters of constraint conditions such as in conventional AFS-based classifiers. For the proposed method, compared to other neural-network-based classification methods, the fuzzy descriptions generated from complex concepts in hidden layer make classification result human understandable. We have experimented with several benchmark datasets and compared the results with other neural network-based classifiers. We show that our method outperforms Ensemble, EvRBFN, NNEP, LVQ, and iRProp+ in the seven out of ten datasets. The results show that the performance of AFSNN is competitive in terms of classification accuracy and the network shows a distinctive capability of providing explicit knowledge in the form of linguistic description.