On the implication operator in fuzzy logic (Q762138)

The implication operator in fuzzy logic can be translated into a suitable fuzzy relation in several ways. The problem is which translation/relation to choose. This question has been discussed by several authors so far. In this article various properties of relations, both already known and newly introduced, are thoroughly investigated, e.g. a partial ordering of these relations. This should help the user at his choice. Nevertheless it seems, taking into account the results of other authors, that the choice of the final relation is not still simple or unique.