F-transforms determined by implicators

Document Type : Research Paper


1 Department of Mathematics \& Computing, Indian Institute of Technology (ISM) Dhanbad-826004, India

2 University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, NSC IT4Innovations, 30. dubna 22, 701 03, Ostrava 1, Czech Republic


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}.