Molodtsov introduced soft set theory. Soft set theory has been emerged as a mathematical tool to solve complicated problems with uncertainity. In this paper by combining lattices and soft group the new hybrid structure lattice ordered soft group and its algebraic operations are introduced. Finally an application of lattice ordered soft group on urban planning is analysed.
AktasH. and CagmanN., Soft sets and soft groups, Inform.Sciences177 (2007), 2726–2735.
2.
AliM.I., FengF., LiuX.Y., MinW.K. and ShabirM., On some new operations in soft set theory, Comput. Math. Appl.57 (2009), 1547–1553.
3.
AliM.I., Tahir Mahmood. Muti Ur Rehman and M. Fahim Aslam, On lattice ordered soft sets, Applied Soft Computing36 (2015), 499–505.
4.
AnusuyaV.S., Multi-criteria Decision making on lattice ordered multisets, In: Thampi S., Mitra S., Mukhopadhyay J., Li K.C., James A., Berretti S. (eds.) Intelligent Systems Technologies and Applications. ISTA 2017. Advances in Intelligent Systems and Computing, Vol 683. Springer, Cham. (2018).
5.
Anusuya IlamathiV.S. and VimalaJ., Implementation of boolean algebraic structure and its decision making approach over lattice ordered multisets, International Journal of Engineering and Technology7(1.3) (2018), 85–89.
6.
Arockia ReetaJ. and VimalaJ., Implementation of anti-lattice ordered fuzzy soft groups and its matrix operations in deciding process, Journal of Intelligent & Fuzzy Systems. DOI: 10.3233/JIFS-18914.
7.
CagmanN. and EnginogluS., Soft matrix theory and its decision making, Computers and Mathematics with Applications59 (2010), 3308–3314.
8.
BirkhoffGarett, Lattice Ordered Groups, Annals of Mathematics Second Series (1942).
MajumdarP. and SamanthaS.K., Similarity measure of soft sets, New Mathematics and Natural Computation4(1) (2008), 1–12.
13.
MolodtsovD.A., Soft set theory – first result, Comput. Math. Appl.37 (1999), 19–31.
14.
MajiP.K., BiswasR. and RoyA.R., An application of soft sets in a decision making problem, Comput. Math. Appl.44 (2002), 1077–1083.
15.
MajiP.K., BiswasR. and RoyA.R., Soft set theory, Comput. Math. Appl.45 (2003), 555–562.
16.
AslamMuhammad and QurashiSaqub Mazher, Some contributions to soft groups, Annals of Fuzzy Mathematics and Informatics4 (2012), 177–195.
17.
OnyeoziliI.A. and GwaryT.M., A study on the fundamentals of soft set theory, International Journal of Scientific and Technology Research3(4) (2014), 132–143.
18.
PandipriyaA.R., VimalaJ. and Sabeena BegamS., Lattice ordered interval – valued hesitant fuzzy soft sets in decision making problem, International Journal of Engineering & Technology7(1.3) (2018), 52–55.
19.
RoyA.R. and MajiP.K., A fuzzy soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics203 (2007), 412–418.
20.
Sabeena BegamS. and VimalaJ., Application of lattice ordered multi-fuzzy soft set in forecasting process, Journal of Intelligent and Fuzzy Systems36 (2019), 2323–2331.
21.
VijayalakshmiL. and VimalaJ., On lattice ordered soft groups, International Journal of Pure and Applied Mathematics112(1) (2017), 47–55.
22.
VijayalakshmiL., VimalaJ., A study on properties of lattice ordered soft group, International Journal of Applied and Advanced Scientific Research, Special issue (2017), 25–28.
23.
VimalaJ. and Arockia ReetaJ., A study on lattice ordered fuzzy soft group, International Journal of Applied Mathematical Sciences9(1) (2016), 1–10.
24.
VimalaJ., Arockia ReetaJ. and Anusuya IlamathiV.S., A study on fuzzy soft cardinality in lattice ordered fuzzy soft group and its application in decision making problems, Journal of Intelligent and Fuzzy Systems34 (2018), 1535–1542.
25.
YinXia and LiaoZuhua, Study on soft groups, Journal of Comp.8 (2013), 960–967.
26.
YingchaoShao and KeyunQinn, The lattice structure of the soft groups, Procedia Engineering15 (2011), 3621–3625.