Bipolar Fuzzy Sublattices and Ideals

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U. Venkata Kalyani, T. Eswarlal, J. KaviKumar, A. Iampan

Abstract

In this article, we introduce and study the theory of bipolar fuzzy sublattices (BFLs) and bipolar fuzzy ideals (BFIs) of a lattice, and some interesting properties of these BFLs and BFIs are established. Moreover, we study the properties of BFIs under lattice homomorphisms and also an application of BFLs.

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References

  1. K.M. Lee, Bipolar-Valued Fuzzy Sets and Their Operations, in: Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand, (2000), 307-312.
  2. K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87-96. https://doi.org/10.1016/s0165-0114(86)80034-3.
  3. K.V. Thomas, L.S. Nair, Intuitionistic Fuzzy Sublattices and Ideals, Fuzzy Inform. Eng. 3 (2011), 321-331. https://doi.org/10.1007/s12543-011-0086-5.
  4. L.A. Zadeh, Fuzzy Sets, Inform. Control. 8 (1965), 338-353. https://doi.org/10.1016/s0019-9958(65)90241-x.
  5. N. Ajmal, K.V. Thomas, Fuzzy Lattices, Inform. Sci. 79 (1994), 271-291. https://doi.org/10.1016/0020-0255(94)90124-4.
  6. U. Venkata Kalyani, T. Eswarlal, Homomorphism on Bipolar Vague Normal Groups, Adv. Math., Sci. J. 9 (2020), 3315-3324. https://doi.org/10.37418/amsj.9.6.11.
  7. U. Venkata Kalyani, T. Eswarlal, Bipolar Vague Cosets, Adv. Math., Sci. J. 9 (2020), 6777-6787. https://doi.org/10.37418/amsj.9.9.36.
  8. S. Boudaoud, S. Milles, L. Zedam, Principal Intuitionistic Fuzzy Ideals and Filters on a Lattice, Discuss. Math. Gen. Algebra Appl. 40 (2020), 75-88. https://doi.org/10.7151/dmgaa.1325.
  9. S. Milles, The Lattice of Intuitionistic Fuzzy Topologies Generated by Intuitionistic Fuzzy Relations, Appl. Appl. Math. 15 (2020), 942-956. https://digitalcommons.pvamu.edu/aam/vol15/iss2/13.
  10. H. Zhang, Q. Li, Intuitionistic Fuzzy Filter Theory on Residuated Lattices, Soft Comput. 23 (2018), 6777-6783. https://doi.org/10.1007/s00500-018-3647-2.
  11. S. Milles, L. Zedam, E. Rak, Characterizations of Intuitionistic Fuzzy Ideals and Filters Based on Lattice Operations, J. Fuzzy Set Valued Anal. 2017 (2017), 143-159. https://doi.org/10.5899/2017/jfsva-00399.
  12. B. Nageswararao, N. Ramakrishna, T. Eswarlal, Vague Lattices, Studia Rosenthaliana, 12 (2020), 191-202.
  13. R.P. Rao, V.S. Kumar, A.P. Kumar, Rough Vague Lattices, J. Xi’an Univ. Architect. Technol. 9 (2019), 115-124.
  14. M. Gorjanac Ranitovic, A. Tepavcevic, A Lattice-Theoretical Characterization of the Family of Cut Sets of IntervalValued Fuzzy Sets, Fuzzy Sets Syst. 333 (2018), 1-10. https://doi.org/10.1016/j.fss.2016.11.014.
  15. K. Jacob, S.P. Tiwari, N. Shamsidah AH, et al. Restricted Cascade and Wreath Products of Fuzzy Finite Switchboard State Machines, Iran. J. Fuzzy Syst. 16 (2019), 75-88. https://doi.org/10.22111/ijfs.2019.4485.