Advertisement

Ranking Fuzzy Numbers Based on Ideal Solution

  • Zhong-xin Wang
  • Ya-ni Mo
Part of the Advances in Soft Computing book series (AINSC, volume 54)

Abstract

In this paper,we consider the factor of the decision maker’s risk preference, and define the left and right deviation degree,respectively.Besides we propose the new formula of the fuzzy degree.Then we get the multiattribute matrix of fuzzy numbers. Making use of ideal solution we rank fuzzy numbers.Some numerical examples are displayed to illustrate the validity and advantage of the proposed ranking method.

Keywords

Fuzzy number ranking the left and right deviation degree fuzzy degree ideal solution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yao, J., Wu, K.: Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets and Systems 116, 275–288 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Chen, L.H., Lu, H.W.: An approximate approach for ranking fuzzy numbers based on left and right dominance. Computers and Mathemathics with Applications 41, 1589–1602 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Tran, L., Duckein, L.: Comparison of fuzzy numbers using a fuzzy distance measure. Fuzzy Sets and Systems 35, 331–341 (2002)CrossRefGoogle Scholar
  4. 4.
    Chu, T., Tsao, C.: Ranking fuzzy numbers with an area between the centroid point and original Point. Computers and Mathemathics with Applications 43, 11–117 (2002)MathSciNetGoogle Scholar
  5. 5.
    Asady, B., Zendehnam, A.: Ranking fuzzy numbers by distance minimization. Applied Mathematical Modelling 11, 2589–2598 (2006)Google Scholar
  6. 6.
    Chen, S.: Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets and Systems 17, 113–129 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Dubios, D., Prade, H.: Operations on fuzzy numbers. International Journal of systems science 9, 613–626 (1978)CrossRefGoogle Scholar
  8. 8.
    Voxman, W.: Some remarks on distances between fuzzy numbers. Fuzzy Sets and Systems 100, 353–365 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Cheng, C.H., Mon, D.L.: Fuzzy system reliability by confidence interval. Fuzzy Sets and Systems 56, 29–35 (1993)CrossRefGoogle Scholar
  10. 10.
    Deng, Y., Zhen-fu, Z., et al.: Ranking fuzzy numbers with an area method using Radius of Gyration. Computers and Mathemathics with Applications 51, 1127–1136 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Yager, R.R.: A procedure for ordering fuzzy subsets of the unit interval. Information science 24, 139–157 (1981)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Wang, Y.M., Yang, J.B., Xu, D.L., et al.: On the centroids of fuzzy numbers. Fuzzy Sets and Systems 157, 919–926 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Baldwin, J.F., Guild, N.C.F.: Comparison of fuzzy sets on the same decision space. Fuzzy Set and Systems 2 (1979)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Zhong-xin Wang
    • 1
  • Ya-ni Mo
    • 1
  1. 1.School of Math. and Inform. ScienceGuangXi Univ.NanningP.R. China

Personalised recommendations