New rough-neuro-fuzzy approach for regression task in incomplete data

Abstract

A fuzzy rule base is a crucial part of neuro-fuzzy systems. Data items presented to a neuro-fuzzy system activate rules in a rule base. For incomplete data the firing strength of the rules cannot be calculated. Some neuro-fuzzy systems impute the missing firing strength. This approach has been successfully applied. Unfortunately in some cases the imputed firing strength values are very low for all rules and data items are poorly recognized by the system. That may deteriorate the quality and reliability of elaborated results. The paper presents a new method for handling missing values in neuro-fuzzy systems in a regression task. The new approach introduces a new imputation technique (imputation with group centres) to avoid very low firing strength for incomplete data items. It outperforms previous method (elaborates lower error rates), avoids numerical problems with very low firing strengths in all fuzzy rules of the system. The proposed systems elaborated interval answer without Karnik-Mendel algorithm. The paper is accompanied by numerical examples and statistical verification on real life data sets.