Designing modular and distributive lattices using L-soft group: A survey

  • Authors

    • J. Vimala
    • L. Vijayalakshmi
    2017-12-31
    https://doi.org/10.14419/ijet.v7i1.3.9227
  • Soft sets, Soft groups, Lattice ordered soft sets, Modular L - soft group, Distributive L- soft group

  • Abstract

    Soft group was firstly introduced by Aktas and Cagmam. The concept of modular and distributive soft lattices over the soft sets was offered by Faruk Karaaslan. In this paper, we discuss the modular and distributive lattices on soft group. We study several characterizations of modular and distributive lattice ordered soft group (‘ - soft group) and derived its properties.

  • References

    1. [1] H.Aktas and N.Cagman, 2007, Soft sets and soft groups, Inform.Sciences.177, pp.2726-2735.

      [2] V.S.Anusuya Ilamathi and J.Vimala, 2018, Multi-criteria Decision Making on Lattice Ordered Multisets In: Thampi S., Mitra S., Mukhopadhyay J., Li KC., James A., Berretti S. (eds) Intelligent Systems Technologies and Applications. ISTA 2017. Advances in Intelligent Systems and Computing, vol 683. Springer, Cham. pp.401-416

      [3] J.Arockia Reeta and J.Vimala, 2016, A study on distributive and modular lattice ordered fuzzy soft group and its duality, Appl. Math. J. Chinese Univ., volume 31, 4, 491-502.

      [4] M.I.Ali, Tahir Mahmood.Muti Ur Rehman, M.Fahim Aslam, 2015, On Lattice Ordered Soft Sets, Applied Soft Computing.36, pp.499-505.

      [5] P.Bharathi and J.Vimala, 2016, The Role of Fuzzy l-ideals in a Commutative l-group, Global Journal of Pure and Applied Mathematics, volume 12, Number 3 , pp. 2067 - 2074.

      [6] P.Bharathi, J.Vimala, L.Vijayalakshmi and J.Arockia Reeta, 2017, Some Contributions of Congruence Relations on Lattices of Fuzzy l-ideal Appl. Math. inform. sci. II, No.2, pp. 1-5.

      [7] W.H. Cornish, 1977, Characterization distributive and modular semilattices, Math. Japonica, 22 pp. 159–174.

      [8] Faruk Karaaslan, Naim Cagman and Serdar Enginoglu, 2012, Soft Lattices , Journal of New Results in Science, No. 1, pp.5-17

      [9] Garett Birkhoff, Lattice theory, American Mathematical Society Colloqium Publications, volume XXV.

      [10] G. Gratzer, 1971, Lattice Theory: First Concepts and Distributive Lattices, Freeman and Company.

      [11] Grzegorz Dymek and Andrzej Walendziak, 2015, Soft Set Theory Applied To General Algebras, Demonstratio Mathematica, Vol. XLVIII, No. 1.

      [12] P.K.Maji,R.Biswas,A.R.Roy, 2003, soft set theory, Comput.Math.Appl., 45, pp.555-562.

      [13] D.A.Molodtsov, 1999, Soft set theory - First result, Comput. Math.Appl.,37, pp.19-31.

      [14] E.K.R.Nagarajan and P.Geetha, 2013, Characterization Theorems for Modular and Distributive Soft Lattices, Intnl.Jorl.of Innovative Research in science Eng. and Tech., 2, issue 11, pp. 2319-8753

      [15] Natarajan.R and Vimala.J, 2007, Distributive l-ideal in a commutativel-group, Acta Ciencia Indica, Vol.XXXIII M.No.2.517, MR 2392259.

      [16] Onyeozili I.A.,Gwary T.M, 2014, A Study on the Fundamentals of Soft Set Theory, International Journal of Scientific and Technology Research, Volume 3, issue 4, pp.132-143.

      [17] L.Vijayalakshmi and J.Vimala, 2017, On Lattice Ordered Soft Groups, International Journal of Pure and Applied Mathematics vol.112,issue 1 Article No.AP2016-31-108, pp. 47-55.

      [18] J.Vimala, 2014, Fuzzy Lattice Ordered Group, International Journal of Scientific and Engineering Research, Volume 5, Issue 9, pp.58-60

      [19] J.Vimala and J.Arockia Reeta, 2016, A study on lattice ordered fuzzy soft group, International Journal of Applied Mathematical Sciences,volume 9, No.1, pp.1-10.

      [20] J.Vimala, J.Arockia Reeta and V.S.Anusuya Ilamathi, A study on Fuzzy Soft Cardinality in Lattice Ordered Fuzzy Soft Group and its application in Decision Making Problems, Journal of Intelligent and Fuzzy Systems-IOS Press (Accepted). [21] Xia Yin, Zuhua Liao, 2013, Study on Soft Groups, Journal of Comp. vol.8.

      [22] Yingehao Shao,Keyun Qin, 2011, The Lattice structure of the soft groups, Procedia Engineering 15, pp.3621-3625.

  • Downloads

  • How to Cite

    Vimala, J., & Vijayalakshmi, L. (2017). Designing modular and distributive lattices using L-soft group: A survey. International Journal of Engineering & Technology, 7(1.3), 56-60. https://doi.org/10.14419/ijet.v7i1.3.9227

    Received date: 2018-01-21

    Accepted date: 2018-01-21

    Published date: 2017-12-31