Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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L-FUZZY BI-CLOSURE SYSTEMS AND L-FUZZY BI-CLOSURE OPERATORS

  • Ko, Jung Mi (Department of Mathematics Gangneung-Wonju National University) ;
  • Kim, Yong Chan (Department of Mathematics Gangneung-Wonju National University)
  • Received : 2018.10.31
  • Accepted : 2019.06.12
  • Published : 2019.06.30
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Abstract

In this paper, we introduced the notions of right and left closure systems on generalized residuated lattices. In particular, we study the relations between right (left) closure (interior) operators and right (left) closure (interior) systems. We give their examples.

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References

  1. R. Belohlavek, Fuzzy Relational Systems, Kluwer Academic Publishers, New York, 2002.
  2. R. Belohlavek, Fuzzy Galois connection, Math. Log. Quart., 45 (2000), 497-504. https://doi.org/10.1002/malq.19990450408
  3. R. Belohlavek, Fuzzy closure operator, J. Math. Anal. Appl. 262 (2001), 473-486. https://doi.org/10.1006/jmaa.2000.7456
  4. R. Belohlavek, Lattices of fixed points of Galois connections, Math. Logic Quart. 47 (2001), 111-116. https://doi.org/10.1002/1521-3870(200101)47:1<111::AID-MALQ111>3.0.CO;2-A
  5. L. Biacino and G.Gerla, Closure systems and L-subalgebras, Inf. Sci. 33 (1984), 181-195. https://doi.org/10.1016/0020-0255(84)90027-6
  6. L. Biacino and G.Gerla, An extension principle for closure operators, J. Math. Anal. Appl. 198 (1996), 1-24. https://doi.org/10.1006/jmaa.1996.0064
  7. G.Gerla, Graded consequence relations and fuzzy closure operators, J. Appl. Non-classical Logics 6 (1996), 369-379. https://doi.org/10.1080/11663081.1996.10510892
  8. Jinming Fang and Yueli Yue, L-fuzzy closure systems, Fuzzy Sets and Systems 161 (2010), 1242-1252. https://doi.org/10.1016/j.fss.2009.10.002
  9. G. Georgescu and A. Popescue, Non-commutative Galois connections, Soft Computing 7 (2003), 458-467. https://doi.org/10.1007/s00500-003-0280-4
  10. G. Georgescu and A. Popescue, Non-dual fuzzy connections, Arch. Math. Log. 43 (2004), 1009-1039. https://doi.org/10.1007/s00153-004-0240-4
  11. P. Hajek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998.
  12. U. Hohle and E. P. Klement, Non-classical logic and their applications to fuzzy subsets , Kluwer Academic Publisher, Boston, 1995.
  13. U. Hohle and S.E. Rodabaugh, Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series 3, Kluwer Academic Publishers, Boston, 1999.
  14. H. Lai and D. Zhang, Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory, Int. J. Approx. Reasoning 50 (2009), 695-707. https://doi.org/10.1016/j.ijar.2008.12.002
  15. C.J. Mulvey, Quantales, Suppl. Rend. Cric. Mat. Palermo Ser.II 12,1986,99-104.
  16. M. Ward and R.P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc. 45 (1939), 335-354. https://doi.org/10.1090/S0002-9947-1939-1501995-3
  17. E. Turunen, Mathematics Behind Fuzzy Logic, A Springer-Verlag Co., 1999.

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