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DOI QR Code

FILTER SPACES ON ECL-PREMONOIDS

  • Kim, Young-Hee (Ingenium College of Liberal Arts-Mathematics, Kwangwoon University) ;
  • Kang, Taewon (Department of Computer Science Engineering, Gangneung-Wonju National University) ;
  • Kim, Yong Chan (Department of Mathematics, Gangneung-Wonju National University)
  • Received : 2018.02.17
  • Accepted : 2018.10.30
  • Published : 2018.11.30

Abstract

In this paper, we introduce the notion of the (L, ${\ast}$)-filter spaces on ecl-premonoids. Moreover, we obtain various (L, ${\ast}$)-filters incuced by two (L, ${\ast}$)-filters and give their examples.

Keywords

References

  1. R. Belohlavek: Fuzzy Relational Systems. Kluwer Academic Publishers, New York, 2002.
  2. W. Gahler: The general fuzzy filter approach to fuzzy topology I. Fuzzy Sets and Systems 76 (1995), 205-224. https://doi.org/10.1016/0165-0114(95)00058-S
  3. W. Gahler: The general fuzzy filter approach to fuzzy topology II. Fuzzy Sets and Systems 76 (1995), 225-246. https://doi.org/10.1016/0165-0114(95)00057-R
  4. U. Hohle & 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.
  5. G. Jager: Subcategories of lattice-valued convergence spaces. Fuzzy Sets and Systems 156 (2005), 1-24. https://doi.org/10.1016/j.fss.2005.04.013
  6. G. Jager: Pretopological and topological lattice-valued convergence spaces. Fuzzy Sets and Systems 158 (2007), 424-435. https://doi.org/10.1016/j.fss.2006.10.016
  7. Jinming Fang: Stratified L-order convergence structures. Fuzzy Sets and Systems 161 (2010), 2130-2149. https://doi.org/10.1016/j.fss.2010.04.001
  8. Y.C. Kim & J.M. Ko: Images and preimages of L-filter bases. Fuzzy Sets and Systems 173 (2005), 93-113.
  9. Y.C. Kim & J.M. Ko: (L, *, ${\odot}$ )-quasiuniform convergence spaces. Submit to International Journal of Pure and Applied Mathematics.
  10. D. Orpen & G. Jager: Lattice-valued convergence spaces. Fuzzy Sets and Systems 190 (2012), 1-20. https://doi.org/10.1016/j.fss.2011.05.026