International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

On Anti-Q-Fuzzy Deductive Systems of Hilbert Algebras

  • M. Vasuki
  • P. Senthil Kumar
  • N. Rajesh1*
  1. a:1:{s:5:"en_US";s:136:"Department of Mathematics, Rajah Serfoji Government College (affiliated to Bharathidasan University), Thanjavur-613005, Tamilnadu, India";}

* Corresponding author

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.

How to Cite

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

BibTeX
@article{Vasuki2023,
  author  = {Vasuki, M. and Kumar, P. Senthil and Rajesh, N.},
  title   = {On Anti-Q-Fuzzy Deductive Systems of Hilbert Algebras},
  journal = {Int. J. Anal. Appl.},
  volume  = {21},
  year    = {2023},
  pages   = {42},
  doi     = {10.28924/2291-8639-21-2023-42}
}

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.