SR-fuzzy set theory applied to Sheffer stroke BG-Algebras
DOI:
https://doi.org/10.5269/bspm.76490Resumo
The paper introduces and elucidates the concept of an SR-fuzzy SBG-subalgebra and a level set of an SR-fuzzy set within the framework of Sheffer stroke BG-algebras. These concepts play a pivotal role in comprehending the nuances of SR-logic within this algebraic setting. By establishing a correlation between subalgebras and level sets, the study unveils a fundamental relationship essential for understanding the algebraic structure. Specifically, it demonstrates that the level set of SR-fuzzy SBG-subalgebras corresponds to the subalgebra of the algebra, and vice versa, indicating a profound interconnection between these two concepts within this algebraic structure.
Referências
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2. P.J. Allen, J. Neggers and H.S. Kim, B-algebras and groups, Math. Japo. Online, 9 (2003), 9–17.
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8. I. Chajda, Sheffer operation in ortholattices, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 44(1) (2005), 19–23.
9. Jung R. Cho and H. S. Kim, On B-algebras and quasigroups, Quasigr. Relat. Syst., 7 (2001), 1–6.
10. C.B. Kim and H.S. Kim, On BG-algebras, Demonstr. Math., 41(3) (2008), 497–505. doi: 10.1515/dema-2013-0098
11. R. Muthuraj and S. Devi, Multi-fuzzy subalgebras of BG-Algebra and its level subalgebras, Int. J. Appl. Math. Sci., 9(1) (2016), 113–120.
12. R. Muthuraj, M. Sridharan and P.M. Sitharselvam, Fuzzy BG-ideals in BG-algebra, Int. J. Comput. Appl., 2(1) (2010), 26–30.
13. J. Neggers and H.S. Kim, On B-algebras, Mate. Vesnik, 54(1) (2002), 21–29.
14. T. Oner, T. Kalkan and N. Kircali Gursoy, Sheffer stroke BG-algebras, Int. J. Maps Math., 4(0) (2021), 27–30.
15. T. Oner, T. Kalkan, T. Katican and A. Rezaei, Fuzzy implicative SBG-ideals of Sheffer stroke BG-algebras, Facta Univ, Ser.. Math. Inform., 36(4) (2021), 913–926.
16. T. Oner and T. Katican, Sheffer stroke BG-algebras by filters and homomorphisms, Bull. Int. Math. Virtual Inst.., 11(2) (2021), 375–386.
17. A. Prasanna, M. Premkumar, H. S. Ismail Mohideen, Normalization of fuzzy BG-ideals In BG-algebra, Int. J. Math. Trends Technol., 53(4) (2018), 270–276.
18. A. Rosenfield, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512–517.
19. T. Senapati and G. Chen, Cubic closed ideals of BG-algebras and their products, Southeast Asian Bull. Math., 45(5)(2021), 739–749.
20. T. Senapati, M. Bhowmik, and M. Pal, Fuzzy dot structure of BG-algebras, Fuzzy Inf. Eng., 6(3)(2014), 315–329. https://doi.org/10.1016/j.fiae.2014.12.004
21. T. Senapati, M. Bhowmik, and M. Pal, Interval-valued intuitionistic fuzzy closed ideals of BG-algebras and their products, Int. J. Fuzzy Syst., 2(2) (2012), 27–44. DOI : 10.5121/ijs.2012.2203
22. H. M. Sheffer, A set of five independent postulates for Boolean algebras, with application to logical constants, Trans. Am. Math. Soc., 14(4) (1913), 481–488.
23. A. Walendziak, BG/BF1/B/BM-algebras are congruence permutable, Math. Aeterna, 5(2) (2015), 351–356.
24. S. Widianto, S. Gemawati, and Kartini, Direct product in BG-algebras, Int. J. Algebra, 13(5) (2019), 239–247. https://doi.org/10.12988/ija.2019.9619
25. L.A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353.
2. P.J. Allen, J. Neggers and H.S. Kim, B-algebras and groups, Math. Japo. Online, 9 (2003), 9–17.
3. T.M. Al-shami, H.Z. Ibrahim, A.A. Azzam, A.I. EL-Maghrabi, SR-fuzzy sets, and their weighted aggregated operators in application to decision-making, J. Funct. Spaces, 2022 (2022), 14 pages.
4. K.T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets Syst., 33(1) (1989), 37–45.
5. K.T. Atanassov, On intuitionistic fuzzy sets theory, Springer Verlag Berlin Heidelberg, 2002.
6. K.T. Atanassov, Intuitionistic fuzzy sets, In: VII ITKR’s Session, Sofia, Deposed in Central Sci. Techn. Library of Bulg. Acad. of Sci., 1983.
7. A. Borumand Saeid, Some results on interval-valued fuzzy BG-algebras, Int. J. Comput. Math., 1(5) (2007), 259–262.
8. I. Chajda, Sheffer operation in ortholattices, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 44(1) (2005), 19–23.
9. Jung R. Cho and H. S. Kim, On B-algebras and quasigroups, Quasigr. Relat. Syst., 7 (2001), 1–6.
10. C.B. Kim and H.S. Kim, On BG-algebras, Demonstr. Math., 41(3) (2008), 497–505. doi: 10.1515/dema-2013-0098
11. R. Muthuraj and S. Devi, Multi-fuzzy subalgebras of BG-Algebra and its level subalgebras, Int. J. Appl. Math. Sci., 9(1) (2016), 113–120.
12. R. Muthuraj, M. Sridharan and P.M. Sitharselvam, Fuzzy BG-ideals in BG-algebra, Int. J. Comput. Appl., 2(1) (2010), 26–30.
13. J. Neggers and H.S. Kim, On B-algebras, Mate. Vesnik, 54(1) (2002), 21–29.
14. T. Oner, T. Kalkan and N. Kircali Gursoy, Sheffer stroke BG-algebras, Int. J. Maps Math., 4(0) (2021), 27–30.
15. T. Oner, T. Kalkan, T. Katican and A. Rezaei, Fuzzy implicative SBG-ideals of Sheffer stroke BG-algebras, Facta Univ, Ser.. Math. Inform., 36(4) (2021), 913–926.
16. T. Oner and T. Katican, Sheffer stroke BG-algebras by filters and homomorphisms, Bull. Int. Math. Virtual Inst.., 11(2) (2021), 375–386.
17. A. Prasanna, M. Premkumar, H. S. Ismail Mohideen, Normalization of fuzzy BG-ideals In BG-algebra, Int. J. Math. Trends Technol., 53(4) (2018), 270–276.
18. A. Rosenfield, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512–517.
19. T. Senapati and G. Chen, Cubic closed ideals of BG-algebras and their products, Southeast Asian Bull. Math., 45(5)(2021), 739–749.
20. T. Senapati, M. Bhowmik, and M. Pal, Fuzzy dot structure of BG-algebras, Fuzzy Inf. Eng., 6(3)(2014), 315–329. https://doi.org/10.1016/j.fiae.2014.12.004
21. T. Senapati, M. Bhowmik, and M. Pal, Interval-valued intuitionistic fuzzy closed ideals of BG-algebras and their products, Int. J. Fuzzy Syst., 2(2) (2012), 27–44. DOI : 10.5121/ijs.2012.2203
22. H. M. Sheffer, A set of five independent postulates for Boolean algebras, with application to logical constants, Trans. Am. Math. Soc., 14(4) (1913), 481–488.
23. A. Walendziak, BG/BF1/B/BM-algebras are congruence permutable, Math. Aeterna, 5(2) (2015), 351–356.
24. S. Widianto, S. Gemawati, and Kartini, Direct product in BG-algebras, Int. J. Algebra, 13(5) (2019), 239–247. https://doi.org/10.12988/ija.2019.9619
25. L.A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353.
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2025-09-24
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Como Citar
Oner, T., Bordbar, H., Rajesh, N., & Rezaei, A. (2025). SR-fuzzy set theory applied to Sheffer stroke BG-Algebras. Boletim Da Sociedade Paranaense De Matemática, 43, 1-14. https://doi.org/10.5269/bspm.76490
