The law of importation for discrete implications
Information Sciences: an International Journal
QL-implications: Some properties and intersections
Fuzzy Sets and Systems
Differently implicational universal triple I method of (1, 2, 2) type
Computers & Mathematics with Applications
On the suitability of the Bandler-Kohout subproduct as an inference mechanism
IEEE Transactions on Fuzzy Systems
The law of importation versus the exchange principle on fuzzy implications
Fuzzy Sets and Systems
On a new class of fuzzy implications: h-Implications and generalizations
Information Sciences: an International Journal
On the characterization of Yager's implications
Information Sciences: an International Journal
On some properties of threshold generated implications
Fuzzy Sets and Systems
Threshold generation method of construction of a new implication from two given ones
Fuzzy Sets and Systems
A generalization of Yager's f-generated implications
International Journal of Approximate Reasoning
On the Ordering Property and Law of Importation in Fuzzy Logic
International Journal of Artificial Life Research
Pseudo-uninorms and coimplications on a complete lattice
Fuzzy Sets and Systems
A new class of fuzzy implications derived from generalized h-generators
Fuzzy Sets and Systems
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The law of importation, given by the equivalence (x Lambda y) rarr z equiv (xrarr (y rarr z)), is a tautology in classical logic. In A-implications defined by Turksen et aL, the above equivalence is taken as an axiom. In this paper, we investigate the general form of the law of importation J(T(x, y), z) = J(x, J(y, z)), where T is a t-norm and J is a fuzzy implication, for the three main classes of fuzzy implications, i.e., R-, S- and QL-implications and also for the recently proposed Yager's classes of fuzzy implications, i.e., f- and g-implications. We give necessary and sufficient conditions under which the law of importation holds for R-, S-, f- and g-implications. In the case of QL-implications, we investigate some specific families of QL-implications. Also, we investigate the general form of the law of importation in the more general setting of uninorms and t-operators for the above classes of fuzzy implications. Following this, we propose a novel modified scheme of compositional rule of inference (CRI) inferencing called the hierarchical CRI, which has some advantages over the classical CRI. Following this, we give some sufficient conditions on the operators employed under which the inference obtained from the classical CRI and the hierarchical CRI become identical, highlighting the significant role played by the law of importation.