F-transforms determined by implicators

This work aims to study F-transforms based on general implicators and to investigate their basic properties. Interestingly, we show that some of the properties of  F-transforms fail to hold in the case of implicators, such as S- and QL-implicators. {Further, we establish an equivalence between L-fuzzy transformation systems and F-transforms}.

Keywords:

Implicator , L-fuzzy partition , F-transform , L-fuzzy transformation system