This paper studies the closure and interior operators in LM-fuzzy topological spaces. The algebraic structures associated with various collections of closed sets and open sets are identified. Further, certain lattices formed by these algebraic structures are obtained and some lattice theoretic properties of the same are investigated. Corresponding to every element in M, the study associates a lattice of monoids which is determined by various types of closed sets and open sets.
LeeE.P. and ImY.B., Mated fuzzy topological spaces, International Journal Fuzzy Logic and Intelligent Systems11(2) (2001), 161–165.
9.
MingL.Y. and KangL.M., Fuzzy topology, World Scientific (1997).
10.
MohammedF.M., NooraniM.S.M. and GhareebA., Generalized fuzzy b-closed and generalized *-fuzzy b-closed sets in double fuzzy topological spaces, Egyptian Journal of Basic and Applied Sciences3 (2016), 61–67.
11.
RamadanA.A., AbbasS.E. and Abd El-latifA.A., Compactness in intuitionistic fuzzy topological spaces, Int J Math Math Sci1 (2005), 19–32.
12.
VivekS. and MathewS.C., On the extensions of a double fuzzy topological space, Journal of Advanced Studies in Topology9(1) (2018), 75–93.
13.
VivekS. and MathewS.C., Certain algebraic structures associated with a double fuzzy topological space, Mathematical Sciences13 (2019), 325–334.
14.
VivekS. and MathewS.C., On regular fuzzy closed sets in a double fuzzy topological space, Advances in Fuzzy Sets and Systems24(2) (2019), 55–73.
15.
VivekS. and MathewS.C., Some lattices associated with a double fuzzy topological space, J Fuzzy Math27(1) (2019), 153–170.
16.
VivekS. and MathewS.C., Normality of the extensions of a double fuzzy topological space, Advances in Mathematics: Scientific Journal9(11) (2020), 9455–9462.
17.
VivekS. and MathewS.C., Regular fuzzy closed sets and extensions of a double fuzzy topological space, Journal of Mathematical Extension14(4) (2020).
18.
VivekS. and MathewS.C., Some De Morgan algebras associated with a double fuzzy topological space, Creat Math Inform30(1) (2021), 115–120.
ShiF.G. and LiangC., Measures of compactness in L-fuzzy pretopological spaces, Journal of Intelligent & Fuzzy Systems26 (2014), 1557–1561.
21.
ShiF.G. and PangB., Categories isomorphic to the category of L-fuzzy closure system spaces, Iranian Journal of Fuzzy Systems10(5) (2013), 127–146.
22.
SostakA.P., On a fuzzy topological structure, Rendiconti del Circolo Mathematico di Palermo Ser II11 (1985), 89–103.
23.
VargheseG. and MathewS.C., On the characterizing lattice of an L-fuzzy topological space, Far East Journal of Mathematical Sciences39(1) (2010), 15–27.
24.
VargheseG. and MathewS.C., On the level decompositions by the range of an L-fuzzy topological space, Fuzzy Information and Engineering3(3) (2011), 225–234.
25.
VargheseG. and MathewS.C., On the lattices of L-topologies, Fuzzy Sets Syst282 (2016), 21–30.
26.
ZhangJ., ShiF.G. and ZhengC.Y., On L-fuzzy topological spaces, Fuzzy Sets and Systems149 (2005), 473–484.
