DOI QR코드

DOI QR Code

(L, e)-filters on complete residuated lattices

  • Kim, Yong-Chan (Department of Mathematics, Gangneung-Wonju National University) ;
  • Ko, Jung-Mi (Department of Mathematics, Gangneung-Wonju National University)
  • 투고 : 2012.02.16
  • 심사 : 2012.06.29
  • 발행 : 2012.09.25

초록

We introduce the notion of (L, e)-filters with fuzzy partially order e on complete residuated lattice L. We investigate (L, e)-filters induced by the family of (L, e)-filters and functions. In fact, we study the initial and final structures for the family of (L, e)-filters and functions. From this result, we define the product and co-product for the family of (L, e)-filters and functions.

키워드

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.Muraleetharan 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. 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
  4. J. Gutierrez Garcia, I. Mardones Perez, M.H. Burton, "The relationship between various filter notions on a GL-monoid," J. Math. Anal. Appl., vol. 230, pp.291-302, 1999. https://doi.org/10.1006/jmaa.1998.6197
  5. U. Hohle, E.P. Klement, Non-classical Logic and Their Applications to Fuzzy Subsets, Kluwer Academic Publishers, Boston, 1995.
  6. U.Hohle, A.P.Sostak, "Axiomatic foundation of fixedbasis 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, J.M. Ko," Images and preimages of L-filter bases," Fuzzy Sets and Systems, vol. 173, pp. 93-113, 2005.
  9. Y.C. Kim, J.M. Ko," Ordered (L; e)-filters", to appear Mathematica Aeterna
  10. E. Turunen, Mathematics behind Fuzzy Logic, Physica-Verlag, Heidelberg, 1999.