A new methodology of extraction, optimization and application of crisp and fuzzy logical rules.

A new methodology of extraction, optimization, and application of sets of logical rules is described. Neural networks are used for initial rule extraction, local or global minimization procedures for optimization, and Gaussian uncertainties of measurements are assumed during application of logical rules. Algorithms for extraction of logical rules from data with real-valued features require determination of linguistic variables or membership functions. Contest-dependent membership functions for crisp and fuzzy linguistic variables are introduced and methods of their determination described. Several neural and machine learning methods of logical rule extraction generating initial rules are described, based on constrained multilayer perceptron, networks with localized transfer functions or on separability criteria for determination of linguistic variables. A tradeoff between accuracy/simplicity is explored at the rule extraction stage and between rejection/error level at the optimization stage. Gaussian uncertainties of measurements are assumed during application of crisp logical rules, leading to "soft trapezoidal" membership functions and allowing to optimize the linguistic variables using gradient procedures. Numerous applications of this methodology to benchmark and real-life problems are reported and very simple crisp logical rules for many datasets provided.