N-vertical generated implications and their distributivities over t-norms and t-conorms

Abstract

One of the methods to construct a new fuzzy implication from given ones is to transform the given implications and appropriately scale the variables. In this paper, we firstly construct a N-vertical generated implication by changing the linear transformations of two initial implications of the recent introduced vertical e-threshold generated implication. Then we give the relationship between these two classes of fuzzy implications, that is, they are different except for some special cases. Moreover, we study some basic properties of N-vertical generated implications. Finally, we focus on the distributivity of this class of implications over t-norms and t-conorms, and obtain the nice preservation of distributivity from given implications to the corresponding N-vertical generated implication.