Convex structures via convex $L$-subgroups of an $L$-ordered group

Document Type: Research Paper

Authors

1 School of Science, Shandong Jianzhu University, Jinan 250101, P.R.China

2 School of surveying and Geo-Informatics, Shandong Jianzhu University, Jinan 250101, P.R.China

10.22111/ijfs.2019.5021

Abstract

In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of four
kinds 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.

Keywords