The law of importation is an important property of fuzzy implication functions with interesting
applications in approximate reasoning and image processing. This property has been
extensively studied, and some open problems have been posed in the literature. In
particular, in this paper, we partially solve an open problem related to this property posed
some years ago. Specifically, given a fixed t-norm T, all fuzzy implication functions with
continuous natural negation that satisfy the law of importation with this t-norm T are …

In this work, we partially study a problem which generalizes and comes from an open
problem related to law of importation and suggested by international conference on fuzzy set
theory and applications 8th in 2006. In fact, this problem has also partially been investigated
in [16]. The obtained results in our paper dramatically extend the aforementioned ones. In
detail, we characterizes all fuzzy implications with a continuous α-natural negation which
satisfy the law of importation wrt a fixed uninorm U, where U is a uninorm continuous in (0, 1) …