TY - JOUR
ID - 136
TI - L-FUZZIFYING TOPOLOGICAL GROUPS
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Zhang, Shai-yan
AU - Yan, Cong-hua
AD - School of Science, Southern Yangtze University, Wuxi, Jiangsu
214122, People0 s Republic of China
AD - school of Math. Sciences, Nanjing Normal Uni-
versity, Nanjing Jiangsu 210046, People0 s Republic of China
Y1 - 2012
PY - 2012
VL - 9
IS - 4
SP - 115
EP - 132
KW - L-fuzzifying topological groups
KW - L-fuzzifying topology
KW - L-fuzzifying
neighborhood structure
KW - category
DO - 10.22111/ijfs.2012.136
N2 - The main purpose of this paper is to introduce a concept of$L$-fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$-fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$-fuzzifying neighborhood structure of the unit is given. It isshown that the category of $L$-fuzzifying topological groups$L$-{\bf FYTPG} is topological over the category of groups {\bf GRP}with respect to the forgetful functor. As an application, theconclusion that the product of $L$-fuzzifying topological groups isalso an $L$-fuzzifying topological group is proved. Finally, it isproved the forgetful functor preserves the product.
UR - https://ijfs.usb.ac.ir/article_136.html
L1 - https://ijfs.usb.ac.ir/article_136_5aec0b42a085eb0d15775832efc7139a.pdf
ER -