University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065415320180630A NEW WAY TO EXTEND FUZZY IMPLICATIONS7997395110.22111/ijfs.2018.3951ENYuan-LiangHanSchool of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R.China and College of Science, North China Institute of Science and Technology, Langfang 065201, P.R.ChinaFu-guiShiSchool of Mathematics and Statistics, Beijing Institute of Technology,
Beijing 100081, P.R.ChinaJournal Article20160317The 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 $M$.<br />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.http://ijfs.usb.ac.ir/article_3951_efdd3cdb9d602e0f91223bb4d9062db1.pdf