Yuan-Liang Han - School of Mathematics and Statistics, Beijing Institute of Technology, Beijing ۱۰۰۰۸۱, P.R.China and College of Science, North China Institute of Science and Technology, Langfang ۰۶۵۲۰۱, P.R.China
Fu-gui Shi - School of Mathematics and Statistics, Beijing Institute of Technology, Beijing ۱۰۰۰۸۱, P.R.China

The main purpose of this paper is to use a new way to extend fuzzy implications I from a generalized sublattice M to a bounded lattice L, such that the extended implications preserve many of the considered properties of fuzzy implications on M.Furthermore, as a special case, we investigate the extension of (S,N)-implications. Results indicate that the extended implications preserve many of the considered properties of (S,N)-implications.

Extension-sublattice, Fuzzy implications, E-operator, Retraction