호남수학학술지 (Honam Mathematical Journal)

  • 제44권2호
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  • Pages.165-178
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  • 2022
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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BL-ALGEBRAS DEFINED BY AN OPERATOR

  • Oner, Tahsin (Department of Mathematics, Faculty of Science, Ege University) ;
  • Katican, Tugce (Department of Mathematics, Faculty of Arts and Sciences, Izmir University of Economics) ;
  • Saeid, Arsham Borumand (Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman)
  • 투고 : 2021.03.21
  • 심사 : 2022.03.12
  • 발행 : 2022.06.25
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초록

In this paper, Sheffer stroke BL-algebra and its properties are investigated. It is shown that a Cartesian product of two Sheffer stroke BL-algebras is a Sheffer stroke BL-algebra. After describing a filter of Sheffer stroke BL-algebra, a congruence relation on a Sheffer stroke BL-algebra is defined via its filter, and quotient of a Sheffer stroke BL-algebra is constructed via a congruence relation. Also, it is defined a homomorphism between Sheffer stroke BL-algebras and is presented its properties. Thus, it is stated that the class of Sheffer stroke BL-algebras forms a variety.

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참고문헌

  1. A. Borumand Saeid and A. Motamed, Normal filters in BL-algebras, World Appl. Sci. J. 7 (2009), 70-76.
  2. A. Borumand Saeid and W. Wei, Solutions to open problems on fuzzy filters of BLalgebras, Int. J. Comput. Intell. Syst 8 (2015), no. 1, 106-113. https://doi.org/10.1080/18756891.2014.963989
  3. I. Chajda, Sheffer operation in ortholattices, Acta Univ. Palack. Olomu. Facultas Rerum Naturalium. Mathematica 44 (2005), no. 1, 19-23.
  4. R. L. O. Cignoli, F. Esteva, l. Godo, and A. Torrens, Basic fuzzy logic is the logic of continuous t-norms and their residua, Soft Comput 4 (2000), no.2, 106-112. https://doi.org/10.1007/s005000000044
  5. A. Di Nola, G. Georgescu, and A. Iorgulescu, Pseudo-BL algebras: Part II, Multiple-Valued Logic (2002), 27 pages.
  6. F. Esteva, L. Godo, P. Hajek, and M. Navara, Residuated fuzzy logics with an involutive negation, Archiv. Math. Logic 39 (2000), 103-124. https://doi.org/10.1007/s001530050006
  7. G. Georgescu and A. Iorgulescu, Pseudo-BL algebras: A noncommutative extension of BL algebras, Abstract of the Fifth International Conference FSTA 2000, Slovakia, (2000),90-92.
  8. G. Gratzer, General Lattice Theory, Springer Science and Business Media, Basel, Switzerland, 2002.
  9. P. Hajek, Metamathematics of fuzzy logic, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998.
  10. M. Kondo and W. A. Dudek, Filter theory of BL-algebras, Soft Comput 12 (2008), 419-423. https://doi.org/10.1007/s00500-007-0178-7
  11. L. Liu and K. Li, Fuzzy filters of BL-algebras, Inf. Sci 173 (2005), 141-154. https://doi.org/10.1016/j.ins.2004.07.009
  12. L. Liu and K. Li, Fuzzy Boolean and positive implicative filters of BL-algebras, Fuzzy Sets Syst. 152 (2005), 333-348. https://doi.org/10.1016/j.fss.2004.10.005
  13. W. McCune, R. Veroff, B. Fitelson, K. Harris, A. Feist, and L. Wos, Short single axioms for Boolean algebra, J. Autom. Reason. 29 (2002), no. 1, 1-16. https://doi.org/10.1023/A:1020542009983
  14. B. L. Meng and X. L. Xin, On fuzzy ideals of BL-algebras, Sci. World J. (2014), 12 pages. http://dx.doi.org/10.1155/2014/757382.
  15. T. Oner, T. Katican and A. Borumand Saeid, (Fuzzy) filters of Sheffer stroke BL-algebras, Kragujev. J. Math 47 (2023), no. 1, 39-55.
  16. T. Oner, T. Katican and A. Borumand Saeid, Relation between Sheffer stroke and Hilbert Algebras, Categ. Gen. Algebr. Struct 14 (2021), no. 1, 245-268.
  17. T. Oner, T. Katican and A. Borumand Saeid, Fuzzy Filters of Sheffer stroke Hilbert algebras, J. Intell. Fuzzy Syst. 40 (2021), no. 1, 759-772. https://doi.org/10.3233/JIFS-200760
  18. T. Oner, T. Katican, and A. Borumand Saeid, On Sheffer stroke UP-algebras, Discuss. Math. - Gen. Algebra Appl. 41 (2021), 381-394. doi:10.7151/dmgaa.1368
  19. T. Oner, T. Katican, A. Borumand Saeid and M. Terziler, Filters of strong Sheffer stroke non-associative MV-algebras, Analele Stiint. ale Univ. Ovidius Constanta Ser. Mat. 29 (2021), no. 1, 143-164. doi:10.2478/auom-2021-0010
  20. T. Oner, T. Katican, and A. Rezaei, Neutrosophic N-structures on strong Sheffer stroke non-associative MV-algebras, Neutrosophic Sets Syst 40 (2021), 235-252. doi: 10.5281/zenodo.4549403
  21. H. M. Sheffer, A set of five independent postulates for Boolean algebras, with application to logical constants, Trans. Am. Math. Soc. 14 (1913), no. 4, 481-488. https://doi.org/10.1090/S0002-9947-1913-1500960-1
  22. E. Turunen, BL-algebras of basic Fuzzy logic, Mathw. soft comput. 6 (1999), 49-61.
  23. E. Turunen, Boolean deductive systems of BL-algebras, Arch. Math. Logic 40 (2001), 467-473. https://doi.org/10.1007/s001530100088
  24. E. Turunen, Mathematics Behind Fuzzy Logic, Physica-Verlag, Heidelberg, Germany, 1999.
  25. E. Turunen and S. Sessa, Local BL-algebras, Mult. Val. Logic (A special issue dedicated to the memory of G. C. Moisil) 6 (2001), no. 1-2, 229-250.
  26. X. N. Zhang, Fuzzy logic and its algebraic analysis, Science Press, Beijing, China, 2008.