The law of importation has attracted the interest of many researchers devoted to fuzzy implication functions in the last decades. This property has several important applications, especially in approximate reasoning and image processing. Several generalizations of this property have been proposed. Specifically, one generalization related to the law of migrativity was recently introduced by Baczyński et al. in which two fuzzy implication functions are involved. In this paper, some advances on the solution of this functional equation for the particular case where the involved fuzzy conjunction is a t-norm are presented. Indeed, a complete characterization of all those pairs of fuzzy implication functions with a strict natural fuzzy negation satisfying the generalized law of importation is achieved.
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