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

A new methodology of extraction, optimization, and application of sets of l ogical rules is described. Neural networks are used for initial rule extrac tion, local, or global minimization procedures for optimization, and Gaussi an uncertainties of measurements are assumed during application of logical rules, Algorithms for extraction of logical rules from data with real-value d features require determination of linguistic variables or membership func tions, Context-dependent membership functions for crisp and fuzzy linguisti c variables are introduced and methods of their determination described, Se veral neural and machine learning methods of logical rule extraction genera ting initial rules are described, based on constrained multilayer perceptro n, networks with localized transfer functions or on separability criteria f or determination of linguistic variables. A tradeoff between accuracy/simpl icity 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 trapez oidal" membership functions and allowing to optimize the linguistic variabl es 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.