Optimization of logical rules derived by neural procedures

Neural networks are used for initial determination of linguistic variables and extraction of logical rules from data. Hierarchical sets of rules for different accuracy/rejection trade-offs are obtained. Sets of logical rules are optimized by maximization of their predictive power. To avoid global minimization methods for crisp logical rules Gaussian uncertainties of inputs are assumed. Analytical formulas reproducing Monte Carlo results for such inputs are derived, leading to a "soft trapezoidal" membership functions instead of rectangular functions used for crisp logical rules. Such approach increases accuracy, gives probabilities of classification instead of the yes/no answers, and allows one to optimize sets of rules using gradient procedures. A few illustrative applications to benchmark and real life problems show the effectiveness of this approach.