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.
Liu, H. , Fan, W. and Wang, S. (2019). Convex structures via convex $L$-subgroups of an $L$-ordered group. Iranian Journal of Fuzzy Systems, 16(6), 75-87. doi: 10.22111/ijfs.2019.5021
MLA
Liu, H. , , Fan, W. , and Wang, S. . "Convex structures via convex $L$-subgroups of an $L$-ordered group", Iranian Journal of Fuzzy Systems, 16, 6, 2019, 75-87. doi: 10.22111/ijfs.2019.5021
HARVARD
Liu, H., Fan, W., Wang, S. (2019). 'Convex structures via convex $L$-subgroups of an $L$-ordered group', Iranian Journal of Fuzzy Systems, 16(6), pp. 75-87. doi: 10.22111/ijfs.2019.5021
CHICAGO
H. Liu , W. Fan and S. Wang, "Convex structures via convex $L$-subgroups of an $L$-ordered group," Iranian Journal of Fuzzy Systems, 16 6 (2019): 75-87, doi: 10.22111/ijfs.2019.5021
VANCOUVER
Liu, H., Fan, W., Wang, S. Convex structures via convex $L$-subgroups of an $L$-ordered group. Iranian Journal of Fuzzy Systems, 2019; 16(6): 75-87. doi: 10.22111/ijfs.2019.5021
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