Research of Classification Tasks Solving Using Neural Fuzzy Production Based Network Models of Mamdani–Zadeh

The article considers solving the problem of object recognition of intersected classes using fuzzy inference systems and neural networks. New multi-output network of Wang–Mendel is compared to a new architecture of neural fuzzy production network based on the model of Mamdani–Zadeh. Learning results of these models are given in the interpretation of logical operations provided by Godel, Goguen and Lukasiewicz algebras. New Wang–Mendel's network can use minimum or sum-based formula as $T$-norm operation in accordance with an appropriate algebra rather than the standard multiplication only. Mamdani–Zadeh's network is designed as a cascade of $T$-norm, implication and S-norm operations defined by selected algebra. Moreover defuzzification layer is not presented in Mamdani–Zadeh's network. Both networks have several outputs in accordance with the number of subject area classes what differs them from the basic realizations. Compliance degrees of an input vector to defined classes are formed at the network outputs. To compare the models the standard Fisher's irises and Italian wines classification problems were used. This article presents the results calculated by training the networks by backpropagation algorithm. Classification error analysis shows that the use of these algebras as interpreting fuzzy logic operations proposed in this paper can reduce the classification error for both multi-output network of Wang-Mendel and a new network of Mamdani–Zadeh. The best learning results are shown by Godel algebra, but Lukasiewicz algebra demonstrates better generalizing properties while testing, what leads to a less number of classification errors.