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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 627314, 6 pages
A Characterization for Compact Sets in the Space of Fuzzy Star-Shaped Numbers with Metric
1School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China
2Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Received 15 January 2013; Accepted 12 April 2013
Academic Editor: Marco Donatelli
Copyright © 2013 Zhitao Zhao and Congxin Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. Cel, “An optimal Krasnosel'skii-type theorem for an open starshaped set,” Geometriae Dedicata, vol. 66, no. 3, pp. 293–301, 1997.
- J. Cel, “Representations of starshaped sets in normed linear spaces,” Journal of Functional Analysis, vol. 174, no. 2, pp. 264–273, 2000.
- F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley & Sons, New York, NY, USA, 1983.
- I. Ekeland, “Nonconvex minimization problems,” Bulletin of the American Mathematical Society, vol. 1, no. 3, pp. 443–474, 1979.
- P. M. Gruber and T. I. Zamfirescu, “Generic properties of compact starshaped sets,” Proceedings of the American Mathematical Society, vol. 108, no. 1, pp. 207–214, 1990.
- D. A. Klain, “Invariant valuations on star-shaped sets,” Advances in Mathematics, vol. 125, no. 1, pp. 95–113, 1997.
- A. Kosinski, “Note on star-shaped sets,” Proceedings of the American Mathematical Society, vol. 13, no. 6, pp. 931–933, 1962.
- F. Maccheroni, “Homothetic preferences on star-shaped sets,” Decisions in Economics and Finance, vol. 24, no. 1, pp. 41–47, 2001.
- H. Mohebi and E. Naraghirad, “Cone-separation and star-shaped separability with applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 8, pp. 2412–2421, 2008.
- S. Park and J. Yoon, “Remarks on fixed point theorems on star-shaped sets,” Journal of the Korean Mathematical Society, vol. 18, no. 2, pp. 135–140, 1982.
- A. Shveidel, “Separability of star-shaped sets and its application to an optimization problem,” Optimization, vol. 40, no. 3, pp. 207–227, 1997.
- J. Chanussot, I. Nyström, and N. Sladoje, “Shape signatures of fuzzy star-shaped sets based on distance from the centroid,” Pattern Recognition Letters, vol. 26, no. 6, pp. 735–746, 2005.
- P. Diamond, “A note on fuzzy starshaped fuzzy sets,” Fuzzy Sets and Systems, vol. 37, no. 2, pp. 193–199, 1990.
- P. Diamond and P. Kloeden, Metric Spaces of Fuzzy Sets, World Scientific, River Edge, NJ, USA, 1994.
- D. Qiu, L. Shu, and Z.-W. Mo, “On starshaped fuzzy sets,” Fuzzy Sets and Systems, vol. 160, no. 11, pp. 1563–1577, 2009.
- C. Wu and Z. Zhao, “Some notes on the characterization of compact sets of fuzzy sets with metric,” Fuzzy Sets and Systems, vol. 159, no. 16, pp. 2104–2115, 2008.
- M. Ma, “Some notes on the characterization of compact sets in ,” Fuzzy Sets and Systems, vol. 56, no. 3, pp. 297–301, 1993.