Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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STRONG DEDUCTIVE SYSTEMS OF BL-ALGEBRAS

  • Jun, Young-Bae (Department of Mathematics Education and (RINS) Gyeongsang National University) ;
  • Park, Chul-Hwan (Department of Mathematics University of Ulsan) ;
  • Doh, Myung-Im (Department of Mathematics Education and (RINS) Gyeongsang National University)
  • Received : 2007.06.20
  • Accepted : 2007.07.20
  • Published : 2007.09.25
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Abstract

The notion of strong deductive system of a BL-algebra is introduced, and a characterization of a strong deductive system is given. A relation between a strong deductive system and a deductive system is given. It will be seen that every strong deductive system can be expressed as the union of special sets.

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References

  1. D. Busneag and D. Piciu, On the lattice of deductive systems of a BL-algebra, Central European Journal of Mathematics 2 (2003), 221-237.
  2. R. Cignoli and A. Torrens, Hajek basic fuzzy logic and Lukasiewicz infinite-valued logic, Arch. Math. Logic 42 (2003), 361-370. https://doi.org/10.1007/s001530200144
  3. P. Hajek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998.
  4. Y. B. Jun and J. M. Ko, Deductive systems of BL-algebras, Honam Math. J. 28 (2006), no. 1, 45-56.
  5. Y. B. Jun and J. M. Ko, Grisly deductive systems of BL-algebras, Bull. Korean Math. Soc. 42 (2005), no. 3, 443-451. https://doi.org/10.4134/BKMS.2005.42.3.443
  6. Y. B. Jun, J. M. Ko and M. A. Ozturk, Some results on deductive systems of BL-algebras, Sci. Math. Jpn. 61 (2005), no. 2, 249-258, :e2004, 241-250.
  7. E. Turunen, Mathematics behind fuzzy logic, Physica-Verlag, Heidelberg, 1999