The law of importation versus the exchange principle on fuzzy implications

The ⊛-composition of fuzzy implications: Closures with respect to properties, powers and families

“…In the literature, one finds many weaker versions of the law of importation (LI) where the t-norm T is generalised to a commutative conjunctor, for instance, see the version presented in Massanet and Torrens [34]. However, here in this work we deal only with the classical version of the law of importation (LI), i.e., where the conjunctor is a t-norm T .…”

On some properties of threshold generated implications

“…• The weak law of importation with a conjunctive, commutative and non-decreasing function F : [0, 1] 2 → [0, 1] (see [19]) Definition 3 (Baczyński and Jayaram [3,Definition 1.4.15]). Let I be a fuzzy implication.…”

“…Recently, the law of importation has been extensively studied (see [12,16,17]). In addition to their satisfaction for the most common classes of implications, even its relationship with other properties of fuzzy implications like (EP) and (WLI) has been established (see [19]). The results obtained for this property (in fact, for the weak law of importation) are quite similar to the ones of the exchange principle.…”

A new method of generating fuzzy implications from given ones

“…Recently, the law of importation has been extensively studied (see [15], [16], [17]). In addition to their satisfaction for the most common classes of implications, even its relationship with other properties of fuzzy implications like (EP) and (WLI) has been established (see [14]). The results obtained for this property (in fact, for the weak law of importation) are quite similar to the ones of the exchange principle.…”