University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065416620191201Convex structures via convex $L$-subgroups of an $L$-ordered group7587502110.22111/ijfs.2019.5021ENH.LiuSchool of Science, Shandong Jianzhu University, Jinan 250101, P.R.ChinaW.FanSchool of surveying and Geo-Informatics, Shandong Jianzhu University, Jinan 250101, P.R.ChinaS.WangSchool of Science, Shandong Jianzhu University, Jinan 250101, P.R.ChinaJournal Article20191118In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of four<br />kinds of cut sets of an $L$-subset. Then we consider the homomorphic preimages and the product of convex $L$-subgroups.<br />After that, we introduce an $L$-convex structure constructed by convex $L$-subgroups.<br />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.http://ijfs.usb.ac.ir/article_5021_f27964e1e391c5aa503363f9dd143979.pdf