On Anti-Q-Fuzzy Deductive Systems of Hilbert Algebras

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DOI: https://doi.org/10.28924/2291-8639-21-2023-42
Published: May 9, 2023
Cite as:
M. Vasuki, P. Senthil Kumar, N. Rajesh, On Anti-Q-Fuzzy Deductive Systems of Hilbert Algebras, Int. J. Anal. Appl., 21 (2023), 42.

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M. Vasuki, P. Senthil Kumar, N. Rajesh

Abstract

In this paper, the concept of anti-Q-fuzzy deductive systems concepts of Hilbert algebras are introduced and proved some results. Further, we discuss the relation between anti-Q-fuzzy deductive system and level subsets of a Q-fuzzy set. Anti Q-fuzzy deductive system is also applied in the Cartesian product of Hilbert algebras.

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References

  1. B. Ahmad, A. Kharal, On Fuzzy Soft Sets, Adv. Fuzzy Syst. 2009 (2009), 586507. https://doi.org/10.1155/2009/586507.
  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. A.K. Adak, D.D. Salokolaei, Some Properties of Pythagorean Fuzzy Ideal of Near-Rings, Int. J. Appl. Oper. Res. 9 (2019), 1-9.
  4. M. Atef, M.I. Ali, T.M. Al-Shami, Fuzzy Soft Covering-Based Multi-Granulation Fuzzy Rough Sets and Their Applications, Comput. Appl. Math. 40 (2021), 115. https://doi.org/10.1007/s40314-021-01501-x.
  5. D. Busneag, A note on deductive systems of a Hilbert algebra, Kobe. J. Math. 2 (1985), 29-35. https://cir.nii.ac.jp/crid/1570854175360486400.
  6. D. Busneag, Hilbert algebras of fractions and maximal Hilbert algebras of quotients, Kobe. J. Math. 5 (1988), 161-172. https://cir.nii.ac.jp/crid/1570572702603831808.
  7. N. Caˇgman, S. Enginoˇglu, and F. Citak, Fuzzy soft set theory and its application, Iran. J. Fuzzy Syst. 8 (2011), 137-147.
  8. I. Chajda, R.Halas, Congruences and ideals in Hilbert algebras, Kyungpook Math. J. 39 (1999), 429-429.
  9. A. Diego, Sur les algébres de Hilbert, Collect. Log. Math. Ser. A (Ed. Hermann, Paris). 21 (1966), 1-52.
  10. W.A. Dudek, Y.B. Jun, On fuzzy ideals in Hilbert algebra, Novi Sad J. Math. 29 (1999), 193-207.
  11. W. A. Dudek, On fuzzification in Hilbert algebras, Contrib. Gen. Algebra, 11 (1999), 77-83.
  12. H. Garg, S. Singh, A novel triangular interval type-2 intuitionistic fuzzy sets and their aggregation operators, Iran. J. Fuzzy Syst. 15 (2018), 69-93. https://doi.org/10.22111/ijfs.2018.4159.
  13. H. Garg, K. Kumar, An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making, Soft Comput. 22 (2018), 4959-4970. https://doi.org/10.1007/s00500-018-3202-1.
  14. H. Garg, K. Kumar, Distance measures for connection number sets based on set pair analysis and its applications to decision-making process, Appl. Intell. 48 (2018), 3346-3359. https://doi.org/10.1007/s10489-018-1152-z.
  15. Y.B. Jun, Deductive systems of Hilbert algebras, Math. Japon. 43 (1996), 51-54. https://cir.nii.ac.jp/crid/1571417124616097792.
  16. K.H. Kim, On intuitionistic Q-fuzzy ideals of semigroups, Sci. Math. Japon. e–2006 (2006), 119-126.
  17. P.M. Sithar Selvam, T. Priya, K.T. Nagalakshmi, T. Ramachandran, A note on anti Q-fuzzy KU-subalgebras and homomorphism of KU-algebras, Bull. Math. Stat. Res. 1 (2013), 42-49.
  18. K. Tanamoon, S. Sripaeng, A. Iampan, Q-fuzzy sets in UP-algebras, Songklanakarin J. Sci. Technol. 40 (2018), 9-29.
  19. L.A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965), 338-353. https://doi.org/10.1016/s0019-9958(65)90241-x.
  20. J. Zhan, Z. Tan, Intuitionistic fuzzy deductive systems in Hilbert algebra, Southeast Asian Bull. Math. 29 (2005), 813-826.