Analyses of equilibrium by fuzzy connection networks related to max-min fuzzy Hopfield networks (Q5931180)

The fuzzy max-min Hopfield type of a neural network studied in this paper is expressed in the form NEWLINE\[NEWLINE{\mathbf x}(t+ 1)={\mathbf x}(t)\circ W,NEWLINE\]NEWLINE where \({\mathbf x}= [x_1,x_2,\dots, x_n]\) is a vector in the \(n\)-dimensional hypercube and \({\mathbf x}(t)\) and \(W\) are combined through a max-min composition operator. A fuzzy set \(B\) is called an attractor of \(W\) if \(B= B\circ W\). Attractors and attractive cycles of these network are studied. It is shown how elementary memories can be employed to improve a property of fault tolerance of the network.