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

Abstract

Abstract-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. Context-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.

SBL-PM: A Simple Algorithm for Selection of Reference Instances in Similarity Based Methods

“…1) in two dimensions, x 3 and x 4 , which are much more informative the other two (cf. [10]). In Fig 2. the reference set obtained by taking the value of ∆ from the leave-one-out test on the entire data and running the SBL-PM procedure for k = 1 is displayed.…”

Optimization and Interpretation of Rule-Based Classifiers

“…Even if stable and robust rules are found [1] the user should be warned about potential misclassifications, other probable classification possibilities and influence of each feature on the classification probability. In this paper optimization and interpretation of sets of rules have been described.…”

“…Previously [1]- [3] we have described a complete methodology of rule extraction from the data. It is composed from the following steps:…”

“…A solution to these problems facing crisp and fuzzy rule-based classifiers applied to data with continuous features is presented in this paper. Neural and machinelearning methods of rule extraction from data were described in our previous publications [1]- [3]. Therefore we will assume that a small number of crisp logical rules has already been found.…”

“…In many applications rule-based classifiers are created starting from machine learning, fuzzy logic or neural network methods [1]- [3]. If the number of rules is relatively small and accuracy is sufficiently high such classifiers are an optimal choice, because the reasons for their decisions are easily verified.…”