Neural optimization of linguistic variables and membership functions

Algorithms for extraction of logical rules from data that contains real-valued components require determination of linguistic variables or membership functions. Context-dependent membership functions for crisp and fuzzy linguistic variables are introduced and methods of their determination described. Methodology of extraction, optimization and application of sets of logical rules is described. Neural networks are used for initial determination of linguistic variables and rule extraction, followed by minimization procedures for optimization of the sets of rules. 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. Applications to a number of benchmark and real life problems yield very good results. Keywords— Logical rules, linguistic variables, neural networks, data mining, medical diagnosis