Solving fuzzy relational equations through network training

Develops a neurallike network and a training algorithm for solving fuzzy relational equations. The fuzzy relational equation μ_Y (y)=sup_x[μ_X(x)μ _R(x,y)] is considered, where Y and R are known fuzzy sets and the problem is to determine μ_X(x). The basic idea is to represent the right-hand side of the fuzzy relational equation by a neurallike network, and then train the network to match the desired target μ_Y(y) using a gradient descent algorithm. The training data are generated by sampling the domains of x and y. It is proved that the training algorithm guarantees that the matching error decreases after a fixed number of steps of training. This approach is applied to solving a specific fuzzy relational equation. The results show that the training algorithm converges very fast and the solutions agree with intuition