On Combining Neuro-Fuzzy Architectures with the Rough Set Theory to Solve Classification Problems with Incomplete Data

This paper presents a new approach to fuzzy classification in the case of missing features. The rough set theory is incorporated into neuro-fuzzy structures and the rough-neuro-fuzzy classifier is derived. The architecture of the classifier is determined by the modified indexed center of gravity (MICOG) defuzzification method. The structure of the classifier is presented in a general form, which includes both the Mamdani approach and the logical approach-based on the genuine fuzzy implications. A theorem, which allows the determination of the structures of rough-neuro-fuzzy classifiers based on the MICOG defuzzification, is given and proven. Specific rough-neuro-fuzzy structures based on the Larsen rule, the Reichenbach, and the Kleene-Dienes implications are given in details. In the experiments, it is shown that the classifier with the Dubois-Prade fuzzy implication is characterized by the best performance in the case of missing features.