%0 Journal Article
%T Convex structures via convex $L$-subgroups of an $L$-ordered group
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Liu, H.
%A Fan, W.
%A Wang, S.
%D 2019
%\ 12/01/2019
%V 16
%N 6
%P 75-87
%! Convex structures via convex $L$-subgroups of an $L$-ordered group
%K $L$-ordered group
%K convex $L$-subgroup
%K $L$-convex structure
%K convex $L$-subgroup degree
%K $L$-fuzzy convex structure
%R 10.22111/ijfs.2019.5021
%X In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of fourkinds of cut sets of an $L$-subset. Then we consider the homomorphic preimages and the product of convex $L$-subgroups.After that, we introduce an $L$-convex structure constructed by convex $L$-subgroups.Furthermore, the notion of the degree to which an $L$-subset of an $L$-ordered group is a convex $L$-subgroup is proposed and characterized. An $L$-fuzzy convex structure which results from convex $L$-subgroup degree is imported naturally, and its $L$-fuzzy convexity preserving mappings investigated.
%U http://ijfs.usb.ac.ir/article_5021_f27964e1e391c5aa503363f9dd143979.pdf