East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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ON SYMMETRIC BI-f-DERIVATIONS OF LATTICE IMPLICATION ALGEBRAS

  • Kim, Kyung Ho (Department of Mathematics, Korea National University of Transportation)
  • Received : 2019.09.30
  • Accepted : 2019.10.28
  • Published : 2020.01.31
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Abstract

In this paper, we introduce the notion of symmetric bi-f-derivation of lattice implication algebra and investigated some related properties. Also, we prove that if D is a symmetric bi-f-derivation of L, then D(x → y, z) = f(x) → D(y, z) for all x, y, z ∈ L.

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References

  1. L. Bolc and P. Borowik, Many-Valued Logic, Springer, Berlin, 1994.
  2. Yilmaz Ceven and Mehmet Ali Ozturk, On f-derivations of lattice, Bull. Korean Math. Soc, 45 (2008), 701-707. https://doi.org/10.4134/BKMS.2008.45.4.701
  3. Alev Firat, On f-derivations of BCC-algebras, Ars Combinatoria, XCVIIA (2010), 377-382.
  4. J. A. Goguen, The logic of inexact concepts, Synthese 19 (1969), 325-373. https://doi.org/10.1007/BF00485654
  5. S. D. Lee and K. H. Kim, On derivations of lattice implication algebras, Ars Combinatoria, 108 (2013), 279-288.
  6. J. Liu and Y. Xu, On certain filters in lattice implication algebras, Chinese Quarterly J. Math. 11(4) (1996), 106-111.
  7. J. Liu and Y. Xu, On the property (P) of lattice implication algebras, J. Lanzhou Univ. 32 (1996), 344-348.
  8. J. Liu and Y. Xu, Filters and structure of lattice implication algebras, Chinese Science Bulletin 42(18) (1997), 1517-1520. https://doi.org/10.1007/BF02882921
  9. C. Prabpayak and U. Leerawat, On derivations of BCC-algebras, Kasetsart J. 43 (2009), 398-401.
  10. Z. M. Song, Study on the theoretical foundation of uncertainty information processing based on lattice implication algebras and method of uncertainty reasoning, Ph. D. Thesis, Southwest Jiaotong University, China (1998) (in Chinese).
  11. Y. Xu, Lattice implication algebras, J. Southwest Jiaotong Univ. 1 (1993), 20-27.
  12. Y. Xu and K. Y. Qin, Lattice H implication algebras and lattice implication algebra classes, J. Hebei Mining and Civil Engineering Institute 3 (1992), 139-143.
  13. Y. Xu and K. Y. Qin, On filters of lattice implication algebras, J. Fuzzy Math. 1(2) (1993), 251-260.
  14. Y. H. Yon and K. H. Kim, On f-derivations of lattice implication algebras, Ars Combinatoria, 110 (2013), 205-215.