On [formula omitted]-insensitive simplification of fuzzy rules for fetal distress assessment

Abstract

Objective: The work introduces ε-insensitive distance based approach to simplification (by reducing the rules number) of the fuzzy classifier rule base. To obtain premises of the initial rules, a modified clustering with pairs of ε-hyperballs procedure is used. The goal of the presented solutions is to achieve high quality support for fetal distress assessment, based on cardiotocographic (CTG) signals classification with a reduced number of fuzzy rules.Methods: In the presented rule base simplification solution, two rules are considered similar (or contradictory) when the distances between their premises do not exceed the assumed value of ε. The proposed simplification process consists of two phases: the first with combining similar rules into representative rules, and the second (optional) with the removal of contradictory rules. In addition, two methods of determining conclusions for representative rules are considered: a representative rule retains the original (unchanged) conclusion, or from the conclusions of similar rules the one with the highest absolute value is chosen. In the introduced clustering with pairs of ε-hyperballs the sizes of object classes are taken into account, to reduce the potential adverse impact of the unbalanced classes in the considered research material. In experiments, two reference assessments for CTG signals based on the retrospective fetal state evaluation were considered.Results and conclusions: In the two-stage classification, the modified clustering outperformed the original procedure in terms of classification sensitivity and the QI index being the geometric mean of sensitivity and specificity. Among the examined rule base simplification methods, we consider the best to be the one based only on combining similar rules, with the unchanged value of conclusion for a representative rule. With the smallest number of rules (after simplification), an increased sensitivity, and in the case of pH-based reference assessment also increased QI value is obtained. Moreover, the achieved sensitivity and QI are higher in comparison to the reference methods and values reported in literature.Significance and main impact: The results confirmed the effectiveness of the ε-insensitive distance rule base simplification. The proposed methods can be applied to any fuzzy rules with premise membership functions with a defined center. Therefore, we believe that this work may have a positive impact on other studies concerning fuzzy rule-based systems.