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Ranking fuzzy numbers based on ideal solution

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Fuzzy Information and Engineering

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 a new formula of the fuzzy degree. Then we get the multiattribute matrix of fuzzy numbers. We rank fuzzy numbers with the help of an ideal solution. Some numerical examples are displayed to illustrate the validity and advantages of the proposed ranking method.

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References

  1. Yao J, Wu K (2000) Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets and Systems 116: 275–288

    Article  MATH  MathSciNet  Google Scholar 

  2. Chen L H, Lu H W (2001) An approximate approach for ranking fuzzy numbers based on left and right dominance. Computers and Mathematics with Applications 41: 1589–1602

    Article  MATH  MathSciNet  Google Scholar 

  3. Tran L, Duckein L (2002) Comparison of fuzzy numbers using a fuzzy distance measure. Fuzzy Sets and Systems 35: 331–341

    Article  Google Scholar 

  4. Chu T, Tsao C (2002) Ranking fuzzy numbers with an area between the centroid point and original point. Computers and Mathematics with Applications 43: 11–117

    Article  MathSciNet  Google Scholar 

  5. Tsai C F, Asady B, Zendehnam A (2006) Ranking fuzzy numbers by distance minimization. Applied Mathematical Modelling 11: 2589–2598

    Google Scholar 

  6. Chen S (1985) Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets and Systems 17: 113–129

    Article  MATH  MathSciNet  Google Scholar 

  7. Dubios D, Prade H (1978) Operations on fuzzy numbers. International Journal of Systems Science 9: 613–626

    Article  Google Scholar 

  8. William V (1998) Some remarks on distances between fuzzy numbers. Fuzzy Sets and Systems 100: 353–365

    Article  MATH  MathSciNet  Google Scholar 

  9. Cheng C H, Mon D L (1993) Fuzzy system reliability by confidence interval. Fuzzy Sets and Systems 56: 29–35

    Article  Google Scholar 

  10. Yong D, Zhu Z F (2006) Ranking fuzzy numbers with an area method using radius of gyration. Computers and Mathematics with Applications 51: 1127–1136

    Article  MATH  MathSciNet  Google Scholar 

  11. Yager R R (1981) A procedure for ordering fuzzy subsets of the unit interval. Information Science 24: 139–157

    Article  MathSciNet  Google Scholar 

  12. Wang Y M, Yang J B, Xu D L (2006) On the centroids of fuzzy numbers. Fuzzy Sets and Systems 157: 919–926

    Article  MATH  MathSciNet  Google Scholar 

  13. Baldwin J F, Guild N C F (1979) Comparison of fuzzy sets on the same decision space. Fuzzy Set and Systems 2: 213–231

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Correspondence to Zhong-xing Wang.

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Wang, Zx., Mo, Yn. Ranking fuzzy numbers based on ideal solution. Fuzzy Inf. Eng. 2, 27–36 (2010). https://doi.org/10.1007/s12543-010-0035-8

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  • DOI: https://doi.org/10.1007/s12543-010-0035-8

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