OR/AND neurons for fuzzy set connectives using ordinal sums and genetic algorithms

Abstract

The paper introduces a generalization of the fuzzy logic connectives AND and OR. To define the logical connectives different t-norms and t-conorms are used. To generalize the t-norms (t-conorms) the Ordinal Sums are introduced. To learn the parameters of the builded Ordinal Sums and the of weights of the connectives the Genetic Algorithms are applied. Two experiments using both synthetic and benchmark data are made. From one hand, a 2-dimensional classification problem to show the behavior of the approach is considered and on the other hand the Zimmermann-Zysno data set to show the capability of the model is analyzed. © Springer-Verlag Berlin Heidelberg 2006.