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L-filters and L-filter convergence

  • Ko, Jung-Mi (Department of Mathematics, Kangnung National University) ;
  • Kim, Yong-Chan (Department of Mathematics, Kangnung National University)
  • 발행 : 2009.03.01

초록

In this paper, we study the relations between L-fuzzy topologies and L-filters on a strictly two-sided, commutative quantale lattice L. We define an L-fuzzy neighborhood filter and introduce the notion of L-filter convergence in L-fuzzy topological spaces.

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참고문헌

  1. M.H.Burton, M.Muraleetharan and J.Gutierrez Garcia, "Generalised filters 1," Fuzzy Sets and Systems, vol. 106, pp. 275-284, 1999 https://doi.org/10.1016/S0165-0114(97)00262-5
  2. M.H.Burton, M.Muraeetharan and J.Gutierrez Garcia, "Generalised filters 2," Fuzzy Sets and Systems, vol.106, pp. 393-400, 1999 https://doi.org/10.1016/S0165-0114(97)00261-3
  3. M. Demirci, "Neighborhood stmctures in smooth topological spaces," Fuzzy Sets and Systems, vol.92, pp,123-128, 1997 https://doi.org/10.1016/S0165-0114(96)00132-7
  4. W.Gahler, "The general fuzzy filter approach to fuzzy topology I," Fuzzy Sets and Systems, vol.76, pp.205-224, 1995 https://doi.org/10.1016/0165-0114(95)00058-S
  5. W. Gahler, "The general fuzzy filter approach to fuzzy topology II," Fuzzy Sets and Systems, vol. 76, pp.225-246, 1995 https://doi.org/10.1016/0165-0114(95)00057-R
  6. U.Hohle and A.P.Sostak, Axiomatic foundation of fixed-basis fuzzy topology, Chapter 3 in Mathematics of Fuzzy Sets, Logic, Topology and Measure Theory, Handbook of fuzzy set series, Kluwer Academic Publisher, Dordrecht, 1999
  7. G. Jager, " Pretopological and topological latticevalued convergence spaces," Fuzzy Sets and Systems, vol. 158, pp. 424-435, 2007 https://doi.org/10.1016/j.fss.2006.10.016
  8. Y.C. Kim and J.M. Ko, Images and preimages of Lfilter bases, Fuzzy Sets and Systems, vol. 173, pp.93-113, 2005
  9. Liu Ying-Ming and Luo Mao-Kang, Fuzzu topology, World Scientific Publishing Co., Singapore, 1997
  10. C.J. Mulvey," Quantales," Suppl. Rend. Cric. Mat. Palermo Ser. II, vol. 12, pp. 99-104, 1986
  11. A.A. Ramadan, M.A. Abdel-Sattar and Y.C. Kim, "Some properties of smooth filters," J. Fuzzy Math., vol. 11, no. 2, pp.341-354, 2003
  12. A.P. Sostak, "On a fuzzy topological stmcture," Rend. Circ. Matem. Palermo Ser.II, vol. 11, pp. 89-103, 1985
  13. E. Tumnen, Mathematics Behind Fuzzy Logic, A Springer-Verlag Co., 1999
  14. Wei Yao, "On many-valued stratified L-convergence spaces," Fuzzh Sets and Systems, vol.159, pp. 2503-2519, 2008 https://doi.org/10.1016/j.fss.2008.03.003