Abstract
A complex-valued multistate Hopfield neural network (CMHNN) is a multistate model of a Hopfield neural network and has been applied as a multistate neural associative memory. CMHNNs require many resources for weight parameters. To reduce the number of weight parameters, twin-multistate activation functions were introduced. A quaternion-valued twin-multistate Hopfield neural network (QTMHNN) is the first model to employ a twin-multistate activation function. A bicomplex-valued twin-multistate Hopfield neural network (BTMHNN) was also introduced. Weak noise tolerance is a disadvantage of QTMHNNs and BTMHNNs. To improve the noise tolerance, a BTMHNN can be modified to a bicomplex-valued twin–hyperbolic Hopfield neural network (BTHHNN). A BTMHNN is defined by the decomposition of a bicomplex number to a pair of complex numbers, whereas a BTHHNN is defined by decomposition of a bicomplex number to a pair of hyperbolic numbers. Computer simulations have improved the noise tolerance of BTHHNNs.
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