In this paper, the notion of subuniverses in the theory of universal algebras is generalized to L-fuzzy setting, which is called L-subuniverses. Some characterizations and representations of L-subuniverses are given. What is more, the relationship between L-subuniverses and L-convexities is discussed when L is a complete Heyting algebra. It is shown that there exists a one-to-one correspondence between L-subuniverses with the smallest L-subset and induced L-convexities.
HöhleU. and ŠostakA.P., Axiomatic Foundations of Fixed-Basis Fuzzy Topology, Springer, US, 1999.
9.
HuangH.L. and ShiF.G., L-fuzzy numbers and their properties, Information Sciences178 (2008), 1141–1151.
10.
JamisonR.E., A general theory of convexity, Dissertation, University of Washington, Seattle, Washington, 1974.
11.
KayD.C. and WombleE.W., Axiomatic convexity theory and relationships between the Carathéodory, Helly, and Radon numbers, Pacific Journal of Mathematics38 (1971), 471–485.
12.
LlinaresJ.V., Abstract convexity, some relations and applications, Optimization51 (2002), 797–818.
PangB. and ShiF.G., Subcategories of the category of L-convex spaces, Fuzzy Sets and Systems313 (2017), 61–74.
15.
RosaM.V., On fuzzy topology fuzzy convexity spaces and fuzzy local convexity, Fuzzy Sets and Systems62 (1994), 97–100.
16.
ShiF.G., L-fuzzy relations and L-fuzzy subgroups, The Journal of Fuzzy Mathematics8 (2000), 491–499.
17.
ShiF.G. and LiE.Q., The restricted hull operator of M-fuzzifying convex structures, Journal of Intelligent and Fuzzy Systems30 (2015), 409–421.
18.
ShiF.G. and XiuZ.Y., A new approach to the fuzzification of convex structures, Journal of Applied Mathematics2014 (2014), 1–12.
19.
SierksmaG., Extending a convexity space to an aligned space, Proceedings of the Koninklijke Nederlandse Akademie Van Wetenschappen87 (1984), 429–435.
20.
van de VelM., Theory of Convex Structures, North Holland, Amsterdam, 1993.
21.
WangG.J., Theory of topological molecular lattices, Fuzzy Sets and Systems47 (1992), 351–376.
22.
WechlerW., Universal Algebra for Computer Scientists, Springer-Verlag, Berlin Heidelberg, 1992, (Chapter I).
23.
WuX.Y. and BaiS.Z., On M-fuzzifying JHC convex structures and M-fuzzifying peano interval spaces, Journal of Intelligent and Fuzzy Systems30 (2016), 2447–2458.
