DOI QR코드

DOI QR Code

SOME NOTES ON RELATIVELY COMPACT SUBSETS OF FUZZY SETS

  • Kim, Yun Kyong (Department of Information Communication Engineering Dongshin University) ;
  • Kim, Joo-Mok (School of General Education Semyung University)
  • Received : 2016.09.21
  • Accepted : 2016.12.16
  • Published : 2017.02.15

Abstract

In this note, we deal with some characterizations of relative compactness on the $L_p$ metric space of fuzzy sets. And then, we point out that a characterization of relative compact subsets of fuzzy numbers with sendograph metric can be improved.

Keywords

References

  1. C. Degang, X. Xiaoping and Z. Liangkuan, On the integrable noncompact fuzzy number space, Appl. Math. Lett. 21 (2008), 1260-1266. https://doi.org/10.1016/j.aml.2007.12.024
  2. P. Diamond and P. Kloeden, Metric spaces of fuzzy sets: Theory and Applications, World Scientific, Singapore, 1994.
  3. T. Fan, On the compactness of fuzzy numbers with sendograph metric, Fuzzy Sets and Systems 143 (2004), 471-477. https://doi.org/10.1016/S0165-0114(03)00142-8
  4. G. H. Greco, Sendograph metric and relatively compact sets of fuzzy sets, Fuzzy sets and Systems 157 (2006), 286-291. https://doi.org/10.1016/j.fss.2005.07.003
  5. G. H. Greco, A characterization of relatively compact sets of fuzzy sets, Nonlinear Anal. 64 (2006), 518-529. https://doi.org/10.1016/j.na.2005.03.113
  6. G. H. Greco and M. P. Moschen, Supremum metric and relatively compact sets of fuzzy sets, Nonlinear Anal. 64 (2006), 1325-1335. https://doi.org/10.1016/j.na.2005.06.038
  7. S. Y. Joo and Y. K. Kim, Topological properties on the space of fuzzy sets, Jour. Math. Anal. Appl. 246 (2000), 576-590. https://doi.org/10.1006/jmaa.2000.6820
  8. Y. K. Kim, Some notes on $L_p$-metric space of fuzzy sets, Inter. Jour. Fuzzy Logic and Intelligent Systems 10 (2010), 242-246. https://doi.org/10.5391/IJFIS.2010.10.3.242
  9. V. Kratschmer, Some complete metrics on spaces of fuzzy subsets, Fuzzy Sets and Systems 130 (2002), 357-365. https://doi.org/10.1016/S0165-0114(02)00120-3
  10. M. Ming, Some notes on the characterization of compact sets in ($E^n,d_p$), Fuzzy Sets and Systems 56 (1993), 297-301. https://doi.org/10.1016/0165-0114(93)90209-Z
  11. C. Wu and Z. Zhao, Some notes on the characterization of compact sets with $L_p$ metric, Fuzzy Sets and Systems 159 (2008), 2104-2115. https://doi.org/10.1016/j.fss.2007.11.010
  12. Z. Zhao and C. Wu, The equivalence of convergence of sequences of fuzzy numbers and its applications to the characterization of compact sets, Information Sciences 179 (2009), 3018-3025. https://doi.org/10.1016/j.ins.2009.04.013