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Zhao, Zhitao; Wu, Congxin

A characterization for compact sets in the space of fuzzy star-shaped numbers with \(L_p\) metric. (English) Zbl 1285.03069

Abstr. Appl. Anal. 2013, Article ID 627314, 6 p. (2013).
Summary: By means of some auxiliary lemmas, we obtain a characterization of compact subsets in the space of all fuzzy star-shaped numbers with \(L_p\) metric for \(1 \leq p < \infty\). The result further completes and develops the previous characterization of compact subsets given by C. Wu and Z. Zhao [Fuzzy Sets Syst. 159, No. 16, 2104–2115 (2008; Zbl 1175.54016)].

Cited in 3 Documents

MSC:

03E72 Theory of fuzzy sets, etc.
54A40 Fuzzy topology

Citations:

Zbl 1175.54016
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\textit{Z. Zhao} and \textit{C. Wu}, Abstr. Appl. Anal. 2013, Article ID 627314, 6 p. (2013; Zbl 1285.03069)
Full Text: DOI

References:

[1] Cel, J., An optimal Krasnosel’skii-type theorem for an open starshaped set, Geometriae Dedicata, 66, 3, 293-301 (1997) · Zbl 0908.46005
[2] Cel, J., Representations of starshaped sets in normed linear spaces, Journal of Functional Analysis, 174, 2, 264-273 (2000) · Zbl 0967.52002
[3] Clarke, F. H., Optimization and Nonsmooth Analysis (1983), New York, NY, USA: John Wiley & Sons, New York, NY, USA · Zbl 0582.49001
[4] Ekeland, I., Nonconvex minimization problems, Bulletin of the American Mathematical Society, 1, 3, 443-474 (1979) · Zbl 0441.49011
[5] Gruber, P. M.; Zamfirescu, T. I., Generic properties of compact starshaped sets, Proceedings of the American Mathematical Society, 108, 1, 207-214 (1990) · Zbl 0683.52008
[6] Klain, D. A., Invariant valuations on star-shaped sets, Advances in Mathematics, 125, 1, 95-113 (1997) · Zbl 0889.52007
[7] Kosinski, A., Note on star-shaped sets, Proceedings of the American Mathematical Society, 13, 6, 931-933 (1962) · Zbl 0111.35305
[8] Maccheroni, F., Homothetic preferences on star-shaped sets, Decisions in Economics and Finance, 24, 1, 41-47 (2001) · Zbl 1051.91015
[9] Mohebi, H.; Naraghirad, E., Cone-separation and star-shaped separability with applications, Nonlinear Analysis: Theory, Methods & Applications, 69, 8, 2412-2421 (2008) · Zbl 1190.90124
[10] Park, S.; Yoon, J., Remarks on fixed point theorems on star-shaped sets, Journal of the Korean Mathematical Society, 18, 2, 135-140 (1982) · Zbl 0485.54035
[11] Shveidel, A., Separability of star-shaped sets and its application to an optimization problem, Optimization, 40, 3, 207-227 (1997) · Zbl 0884.52009
[12] Chanussot, J.; Nyström, I.; Sladoje, N., Shape signatures of fuzzy star-shaped sets based on distance from the centroid, Pattern Recognition Letters, 26, 6, 735-746 (2005)
[13] Diamond, P., A note on fuzzy starshaped fuzzy sets, Fuzzy Sets and Systems, 37, 2, 193-199 (1990) · Zbl 0702.54008
[14] Diamond, P.; Kloeden, P., Metric Spaces of Fuzzy Sets (1994), River Edge, NJ, USA: World Scientific, River Edge, NJ, USA · Zbl 0843.54041
[15] Qiu, D.; Shu, L.; Mo, Z.-W., On starshaped fuzzy sets, Fuzzy Sets and Systems, 160, 11, 1563-1577 (2009) · Zbl 1184.03053
[16] Wu, C.; Zhao, Z., Some notes on the characterization of compact sets of fuzzy sets with \(L_p\) metric, Fuzzy Sets and Systems, 159, 16, 2104-2115 (2008) · Zbl 1175.54016
[17] Ma, M., Some notes on the characterization of compact sets in \((E^n, d_p)\), Fuzzy Sets and Systems, 56, 3, 297-301 (1993) · Zbl 0791.54011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.