On Neutrosophic Implicative Filters of BL-Algebra
DOI:
https://doi.org/10.26713/cma.v15i1.2685Keywords:
BL-algebra, Filter, Neutrosophic filter, Neutrosophic implicative filter, Neutrosophic n-fold implicative filterAbstract
We put forward the ideas of the neutrosophic implicative and \(n\)-fold implicative filters of BL-algebras. Additionally, we demonstrate that every implicative filter, including the \(n\)-fold implicative filter, is a neutrosophic filter. Moreover, we obtain an extension property for the neutrosophic implication. We then look at some comparable circumstances for neutrosophic implicative filters.
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K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87 – 86, DOI: 10.1016/S0165-0114(86)80034-3.
P. Hájek, Metamathematics of Fuzzy Logic, 1st edition, Trends in Logic series (TREN, Volume 4), Springer, Dordrecht, viii + 299 pages (1998), DOI: 10.1007/978-94-011-5300-3.
M. Haveshki, A. B. Saeid and E. Eslami, Some types of filters in BL algebras, Soft Computing 10 (2006), 657 – 664, DOI: 10.1007/s00500-005-0534-4.
A. Ibrahim and S. K. H. Gunaseeli, On neutrosophic filter and fantastic filter of BL-algebras, International Journal of Neutrosophic Science 21(2) (2023), 59 – 67, DOI: 10.54216/IJNS.210205.
A. Ibrahim and S. K. H. Gunaseeli, On neutrosophic filter of BL-algebras, Ratio Mathematica 47 (2023), 141 – 150, DOI: 10.23755/rm.v39i0.816.
L. Liu and K. Li, Fuzzy filters of BL-algebras, Information Sciences 173(1-3) (2005), 141 – 154, DOI: 10.1016/j.ins.2004.07.009.
S.-T. Park and S.-S. Ahn, On n-fold implicative vague filters in BE-algebras, The Pure and Applied Mathematics 19(2) (2012), 127 – 136, DOI: 10.7468/jksmeb.2012.19.2.127.
A. A. Salama and H. Alagamy, Neutrosophic filters, International Journal of Computer Science Engineering and Information Technology Research 3(1) (2013), 307 – 312, DOI: 10.5281/zenodo.23184.
F. Smarandache, A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press, Rehoboth (1998).
E. Turunen, Boolean deductive systems of BL-algebras, Archive for Mathematical Logic 40 (2001), 467 – 473, DOI: 10.1007/s001530100088.
M. Ward and R. P. Dilworth, Residuated lattices, Transactions of the American Mathematical Society 45 (1939), 335 – 354, DOI: 10.1090/S0002-9947-1939-1501995-3.
Y. Xu and K. Y. Qin, On filters of lattice implication algebra, The Journal of Fuzzy Mathematics 2 (1993), 251 – 260.
L. A. Zadeh, Fuzzy sets, Information and Control 8(3) (1965), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.
X. Zhang, X. Mao, Y. Wu and X. Zhai, Neutrosophic filters in pseudo-BCI algebras, International Journal for Uncertainty Quantification 8(6) (2018), 511 – 526, DOI: 10.1615/Int.J.UncertaintyQuantification.2018022057.
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