An overview of construction methods of fuzzy implications

Abstract

Fuzzy implications are useful in a wide range of applications. For these practical purposes, different classes of implications are used. Depending on the concrete application the implication is going to perform, several additional properties have to be fulfilled. In this paper, we recall briefly the most used classes of implications, (S,N) and R-implications, QL and D-operations, their generalizations to other aggregation functions and Yager's implications, and we show the new construction methods presented in recent years. These construction methods vary from implications defined from general aggregation functions or fuzzy negations, to implications generated from one or two initial implications. For every single class, we determine which additional properties are satisfied. © Springer-Verlag Berlin Heidelberg 2013.