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Some New Properties of Strongly Convex Fuzzy Sets

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Fuzzy Information and Engineering Volume 2

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 62))

Abstract

In this note, two interesting results about strongly convex fuzzy set are presented under weaker conditions. Moreover, a new property for fuzzy optimization involving strongly convex fuzzy set is obtained.

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References

  1. Brown, J.G.: A note on fuzzy sets. Inform. and Control 18, 32–39 (1971)

    Article  MATH  Google Scholar 

  2. Katsaras, A.K., Liu, D.B.: Fuzzy vector spaces and fuzzy topological vector space. J. Math. Anal. Appl. 58, 135–146 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  3. Liu, Y.M.: Some properties of convex fuzzy sets. J. Math. Anal. Appl. 111, 119–129 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  4. Lowen, R.: Convex fuzzy sets. Fuzzy Sets and Systems 3, 291–310 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  5. Lowen, R.: Fuzzy Set Theory: Basic Concepts. Techniques and Bibliography. Kluwer Academic Publishers, Dordrecht (1996)

    MATH  Google Scholar 

  6. Weiss, M.D.: Fixed points, separation and induced topologies for fuzzy sets. J. Math. Anal. Appl. 50, 142–150 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ammar, E.E., Metz, J.: On fuzzy convexity and parametric fuzzy optimization. Fuzzy Sets and Systems 49, 135–141 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  8. Yang, X.M.: A note on convex fuzzy sets. Fuzzy Sets and Systems 53, 117–118 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  9. Yang, X.M.: Some properties of convex fuzzy sets. Fuzzy Sets and Systems 72, 129–132 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Yang, X.M., Yang, F.M.: A property of convex fuzzy sets. Fuzzy Sets and Systems 126, 269–271 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. Syau, Y.R.: On convex and concave fuzzy mappings. Fuzzy Sets and Systems 103, 163–168 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  12. Syau, Y.R.: Closed and convex fuzzy sets. Fuzzy Sets and Systems 110, 287–291 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Zhang, P., Wang, Z., Wang, W.J.: A New Proof of Fuzzy Convexity. College Mathematics 22, 89–92 (2006) (in Chinese)

    Google Scholar 

  14. Zadeh, L.A.: Fuzzy sets. Inform. and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

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Peng, Zy., Long, Xj., Lin, Z. (2009). Some New Properties of Strongly Convex Fuzzy Sets. In: Cao, B., Li, TF., Zhang, CY. (eds) Fuzzy Information and Engineering Volume 2. Advances in Intelligent and Soft Computing, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03664-4_75

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  • DOI: https://doi.org/10.1007/978-3-642-03664-4_75

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03663-7

  • Online ISBN: 978-3-642-03664-4

  • eBook Packages: EngineeringEngineering (R0)

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