Interval Valued Intuitionistic Fuzzy β-Filters on β-Algebras

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Kaliyaperumal Palanivel
Prakasam Muralikrishna
Perumal Hemavathi
Ronnason Chinram
Pattarawan Singavananda

Abstract

This study establishes the concept of interval valued intuitionistic fuzzy (InVInF) β-filters on β-algebras and a few of its related properties are investigated. Some compelling results of interval valued fuzzy β-filters have been examined. Further, the notions of products and strong β-filters are also introduced. In addition that, the level set and homomorphism of interval valued intuitionistic fuzzy β-filters are too discussed. Furthermore, we enacted that the intersection between two interval valued intuitionistic fuzzy β−filters is again an interval valued intuitionistic fuzzy β-filter.

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References

  1. A. Al-Masarwah, H. Alshehri, Algebraic Perspective of Cubic Multi-Polar Structures on BCK/BCI-Algebras, Mathematics. 10 (2022), 1475. https://doi.org/10.3390/math10091475.
  2. R. Biswas, Rosenfeld’s Fuzzy Subgroups with Interval Valued Membership Functions, Fuzzy Sets Syst. 63 (1994), 87-90. https://doi.org/10.1016/0165-0114(94)90148-1.
  3. R.A. Borzooei, H.S. Kim, Y.B. Jun, S.S. Ahn, On Multipolar Intuitionistic Fuzzy B-Algebras, Mathematics. 8 (2020), 907. https://doi.org/10.3390/math8060907.
  4. S. Ghorbani, Intuitionistic Fuzzy Filters of Residuated Lattices, New Math. Nat. Comput. 7 (2011), 499-513. https://doi.org/10.1142/S1793005711002049.
  5. P. Hemavathi, P. Muralikrishna, K. Palanivel, A Note on Interval Valued Fuzzy β-Subalgebras, Glob. J. Pure Appl. Math. 11 (2015), 2553-2560.
  6. P. Hemavathi, P. Muralikrishna, K. Palanivel, On Interval Valued Intuitionistic Fuzzy β-Subalgebras, Afrika Math. 29 (2018), 249-262. https://doi.org/10.1007/s13370-017-0539-z.
  7. P. Hemavathi, P. Muralikrishna, K. Palanivel, R. Chinram, Conceptual Interpretation of Interval Valued T-Normed Fuzzy β-Subalgebra, Songklanakarin J. Sci. Technol. 44 (2022), 339-347. https://doi.org/10.14456/sjst-psu.2022.48.
  8. S.M. Hong, Y.B. Jun, S.J. Kim, G.I. Kim, Fuzzy BCI-subalgebras With Interval Valued Membership Functions, Int. J. Math. Math. Sci. 25 (2001), 135-143. https://doi.org/10.1155/S0161171201005087.
  9. C.S. Hoo, Filters and Ideals in BCI-Algebras, Math. Japan. 36 (1991), 987-997. https://cir.nii.ac.jp/crid/1570009749732647040.
  10. P. Kaliyaperumal, A. Das, A Mathematical Model for Nonlinear Optimization Which Attempts Membership Functions to Address the Uncertainties, Mathematics 10 (2022), Article number 1743 (20 pages). https://doi.org/10.3390/math10101743.
  11. G. Muhiuddin, M. Al-Tahan, A. Mahboob, S. Hoskova-Mayerova, S. Al-Kaseasbeh, Linear Diophantine Fuzzy Set Theory Applied to BCK/BCI-Algebras, Mathematics 10 (2022), Article number 2138 (11 pages). https://doi.org/10.3390/math10122138.
  12. J. Neggers, K. H. Sik, On β-Algebras, Math. Solvaca. 52 (2002), 517-530. http://dml.cz/dmlcz/131570.
  13. Y.B. Jun, S.Z. Song, On Fuzzy Implicative Filters of Lattice Implication Algebras, J. Fuzzy Math. 10 (2002), 893-900.
  14. Y. B. Jun, Fuzzy Positive Implicative and Fuzzy Associative Filters of Lattice Implication Algebras, Fuzzy Sets Syst. 121 (2001), 353-357. https://doi.org/10.1016/S0165-0114(00)00030-0.
  15. Y.B. Jun, S.Z. Song, Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras, Mathematics. 7 (2019), 1036. https://doi.org/10.3390/math7111036.
  16. Y.J. Seo, H.S. Kim, Y.B. Jun, S.S. Ahn, Multipolar Intuitionistic Fuzzy Hyper BCK-Ideals in Hyper BCK-Algebras, Mathematics. 8 (2020), 1373. https://doi.org/10.3390/math8081373.
  17. K. Sujatha, M. Chandramouleeswaran, P. Muralikrishna, Fuzzy Filters on β-Algebras, Int. J. Math. Arch. 6 (2015), 162-167.
  18. K. Sujatha, M. Chandramouleeswaran, P. Muralikrishna, Intuitionstic Fuzzy Filters on β-Algebras, Int. J. Math. Sci. Eng. Appl. 9 (2015), 117-123.
  19. M.M. Takallo, S.S. Ahn, R.A. Borzooei, Y.B. Jun, Multipolar Fuzzy p-Ideals of BCI-Algebras, Mathematics. 7 (2019), 1094. https://doi.org/10.3390/math7111094.
  20. W.T. Xu, Y. Xu, X.D. Pan, Intuitionistic Fuzzy Implicative Filter in Lattice Implication Algebras, J. Jiangnan Univ. (Nat. Sci. Ed.) 6 (2009), 736-739.
  21. L.A. Zadeh, The Concept of a Linguistic Variable and Its Application to Approximate Reasoning I, Inform. Sci. 8 (1975), 199-249. https://doi.org/10.1016/0020-0255(75)90036-5.