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On fuzzy filters of Heyting-algebras
1. | Department of Mathematics, Northwest University, Xi'an 710069, China |
2. | Department of Mathematics, Northwest University, Xi'an, 710069, China |
References:
[1] |
A. Micali and F. Zitan, On homogeneous weighted algebras, Communications in Algebra, 35 (2007), 2371-2385.
doi: 10.1080/00927870701325801. |
[2] |
E. Turunen, "Mathematics Behind Fuzzy Logic," Physica-Verlag, Heidelberg, 1999. |
[3] |
K. Iséki and S. Tanaka, Ideal theory of BCK-algebras, Math. Japon., 21 (1976), 351-366. |
[4] |
C. S. Hoo and S. Sessa, Implicative and Boolean ideals of MV-algebras, Math. Japon., 39 (1994), 215-219. |
[5] |
J. D. Bashford and P. D.Jarvis, The genetic code as a peridic table: algebraic aspects, BioSystems, 57 (2000), 147-161.
doi: 10.1016/S0303-2647(00)00097-6. |
[6] |
E. Turunen, Boolean deductive systems of BL-algebras, Arch. Math. Logic, 40 (2001), 467-473.
doi: 10.1007/s001530100088. |
[7] |
M. K. Kinyon and A. A. Sagle, Quadratic dynamical systems and algebras, J. Differential Equations, 117 (1995), 67-126.
doi: 10.1006/jdeq.1995.1049. |
[8] |
L. Frappat, A. Sciarrino and P.Sorba, Crystalizing the genetic code, J. Biological Physics, 27 (2001), 1-34, arXiv:physics/9812041.
doi: 10.1023/A:1011874407742. |
[9] |
J. J. Tian and B. L. Li, Coalgebraic structure of genetics inheritance, Mathematical Biosciences and Engineering, 1 (2004), 243-266. |
[10] |
L. Z. Liu and K. T. Li, Fuzzy Boolean and positive implicative filters of BL-algebras, Fuzzy Sets and Systems, 152 (2005), 333-348.
doi: 10.1016/j.fss.2004.10.005. |
[11] |
R. Sánchez, R. Grau and E. Morgado, A novel Lie algebra of the genetic code over the Galois field of four DNA bases, Mathematical Biosciences, 202 (2006), 156-174.
doi: 10.1016/j.mbs.2006.03.017. |
[12] |
L. Z. Liu and K. T. Li, Fuzzy filters of BL-algebras, Information Sciences, 173 (2005), 141-154.
doi: 10.1016/j.ins.2004.07.009. |
[13] |
J. J. Tian, "Evolution Algebras and their Applications," Springer-Verlag, Berlin, Heidelberg, 2008.
doi: 10.1007/978-3-540-74284-5. |
[14] |
O. Xi, Fuzzy $BCK$-algebras, Math. Japon., 36 (1991), 935-942. |
[15] |
Xiao-Hong Zhang, Young Bae Jun and Myung Im Doh, On fuzzy filters and fuzzy ideals of BL-algebras, Information Sciences, 20 (2006), 8-20. |
[16] |
C. S. Hoo, Fuzzy implicative and Boolean ideals of MV-algebras, Fuzzy Sets and Systems, 66 (1994), 315-327.
doi: 10.1016/0165-0114(94)90099-X. |
[17] |
Y. Xu and K. Y. Qin, On filters of lattice implication algebras, J. Fuzzy Math., 1 (1993), 251-260. |
[18] |
Y. Xu and K. Y. Qin, Fuzzy lattice implication algebras, J. Southwest Jiaotong Univ., 2 (1995), 121-127. |
[19] |
Y. B. Jun, Fuzzy positive implicative and fuzzy associative filters of lattice implication algebras, Fuzzy Sets and Systems, 121 (2001), 353-357.
doi: 10.1016/S0165-0114(00)00030-0. |
[20] |
Y. B. Jun and S. Z. Song, On fuzzy implicative filters of lattice implication algebras, J. Fuzzy Math., 10 (2002), 893-900. |
[21] |
L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
doi: 10.1016/S0019-9958(65)90241-X. |
show all references
References:
[1] |
A. Micali and F. Zitan, On homogeneous weighted algebras, Communications in Algebra, 35 (2007), 2371-2385.
doi: 10.1080/00927870701325801. |
[2] |
E. Turunen, "Mathematics Behind Fuzzy Logic," Physica-Verlag, Heidelberg, 1999. |
[3] |
K. Iséki and S. Tanaka, Ideal theory of BCK-algebras, Math. Japon., 21 (1976), 351-366. |
[4] |
C. S. Hoo and S. Sessa, Implicative and Boolean ideals of MV-algebras, Math. Japon., 39 (1994), 215-219. |
[5] |
J. D. Bashford and P. D.Jarvis, The genetic code as a peridic table: algebraic aspects, BioSystems, 57 (2000), 147-161.
doi: 10.1016/S0303-2647(00)00097-6. |
[6] |
E. Turunen, Boolean deductive systems of BL-algebras, Arch. Math. Logic, 40 (2001), 467-473.
doi: 10.1007/s001530100088. |
[7] |
M. K. Kinyon and A. A. Sagle, Quadratic dynamical systems and algebras, J. Differential Equations, 117 (1995), 67-126.
doi: 10.1006/jdeq.1995.1049. |
[8] |
L. Frappat, A. Sciarrino and P.Sorba, Crystalizing the genetic code, J. Biological Physics, 27 (2001), 1-34, arXiv:physics/9812041.
doi: 10.1023/A:1011874407742. |
[9] |
J. J. Tian and B. L. Li, Coalgebraic structure of genetics inheritance, Mathematical Biosciences and Engineering, 1 (2004), 243-266. |
[10] |
L. Z. Liu and K. T. Li, Fuzzy Boolean and positive implicative filters of BL-algebras, Fuzzy Sets and Systems, 152 (2005), 333-348.
doi: 10.1016/j.fss.2004.10.005. |
[11] |
R. Sánchez, R. Grau and E. Morgado, A novel Lie algebra of the genetic code over the Galois field of four DNA bases, Mathematical Biosciences, 202 (2006), 156-174.
doi: 10.1016/j.mbs.2006.03.017. |
[12] |
L. Z. Liu and K. T. Li, Fuzzy filters of BL-algebras, Information Sciences, 173 (2005), 141-154.
doi: 10.1016/j.ins.2004.07.009. |
[13] |
J. J. Tian, "Evolution Algebras and their Applications," Springer-Verlag, Berlin, Heidelberg, 2008.
doi: 10.1007/978-3-540-74284-5. |
[14] |
O. Xi, Fuzzy $BCK$-algebras, Math. Japon., 36 (1991), 935-942. |
[15] |
Xiao-Hong Zhang, Young Bae Jun and Myung Im Doh, On fuzzy filters and fuzzy ideals of BL-algebras, Information Sciences, 20 (2006), 8-20. |
[16] |
C. S. Hoo, Fuzzy implicative and Boolean ideals of MV-algebras, Fuzzy Sets and Systems, 66 (1994), 315-327.
doi: 10.1016/0165-0114(94)90099-X. |
[17] |
Y. Xu and K. Y. Qin, On filters of lattice implication algebras, J. Fuzzy Math., 1 (1993), 251-260. |
[18] |
Y. Xu and K. Y. Qin, Fuzzy lattice implication algebras, J. Southwest Jiaotong Univ., 2 (1995), 121-127. |
[19] |
Y. B. Jun, Fuzzy positive implicative and fuzzy associative filters of lattice implication algebras, Fuzzy Sets and Systems, 121 (2001), 353-357.
doi: 10.1016/S0165-0114(00)00030-0. |
[20] |
Y. B. Jun and S. Z. Song, On fuzzy implicative filters of lattice implication algebras, J. Fuzzy Math., 10 (2002), 893-900. |
[21] |
L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
doi: 10.1016/S0019-9958(65)90241-X. |
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