Skip to main content

A Method for the Priority Vector of Fuzzy Reciprocal Matrix

  • Conference paper
Fuzzy Information and Engineering

Part of the book series: Advances in Soft Computing ((AINSC,volume 40))

  • 777 Accesses

Abstract

In this paper, we discuss some new properties of fuzzy consistent matrix, propose a novel method to transform fuzzy reciprocal matrix into fuzzy consistent matrix and calculate the corresponding priority vector. Simultaneously, some concepts including fuzzy consistent index and fuzzy consistent ratio are put forward, and an acceptable value(< 0.1) is given to adjust fuzzy reciprocal matrix. Finally, we investigate the convergence of our proposed algorithm and use two numerical examples to illustrate our proposed method reasonable.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Kacprzyk, J.: Group decision making with a fuzzy linguistic majority. Fuzzy Sets and Systems 18, 105–118 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)

    MATH  Google Scholar 

  3. Vargas, L.G.: An overview of the analytic hierarchy process and its applications. European J. Oper. Res 116, 443–449 (1999)

    Article  Google Scholar 

  4. Chiclana, F., Herrera, F., Herrera-Viedma, E.: Integrating multiplicative preference relation in a multipurpose decision making model based on fuzzy preference relations. Fuzzy Sets and Systems 122, 277–291 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Tanino, T.: On group decision making under fuzzy preferences. In: Kacprzyk, J., Fedrizzi, M. (eds.) Multiperson Decision Making Using Fuzzy Sets and Possibility Theory, pp. 172–185. Kluwer Academic Publishers, Dordrecht (1990)

    Google Scholar 

  6. Zhang, Q., et al.: Multiple attribute decision making: approach integrating subjective and objective information. Internat. J. Manuf. Technol. Management 5, 338–361 (2003)

    Article  Google Scholar 

  7. Finan, J.S., Hurley, W.J.: The analytic hierarchy process: Does adjusting a pairwise comparison matrix to improve the consistency ratio help? Comput. Oper. Res. 24, 749–755 (1997)

    Article  MATH  Google Scholar 

  8. Switalski, Z.: Transitivity of fuzzy preference relation-—an empirical study. Fuzzy Sets and Systems 118, 503–508 (2001)

    Article  MathSciNet  Google Scholar 

  9. Song, G.X., Yang, D.L.: Methods for Identifying and Improving the Consistency of Fuzzy Judgement Matrix (in chinese). Systems Engineering 21(1), 110–116 (2003)

    MathSciNet  Google Scholar 

  10. Sun, Z.X., Qiu, W.H.: A method for improving the complementary and consistency of fuzzy judgment matrix (in chinese). Systems Engineering 23(4), 101–104 (2005)

    Google Scholar 

  11. Xu, Z.S.: Uncertain multiple attribute decision making: Methods and Applications. Tsinghua Publishing Press, Beijing (2004)

    Google Scholar 

  12. Ma, J., et al.: A method for repairing the inconsistency of fuzzy preference relations. Fuzzy sets and Systems 157, 20–33 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Yao, M., Shen, Z.: Applications of fuzzy consisent matrix in soft science (in chinese). Systems Engineering 15(2), 54–57 (1997)

    Google Scholar 

  14. Lu, Y.J.: Weight calculation method of fuzzy Analytical Hierarchy Process (in chinese). Fuzzy Systems and Maticsmaths 16(2), 80–85 (2002)

    Google Scholar 

  15. Zhang, J.J.: Fuzzy Analytic Hierarchy Process (FAHP) (in chinese). Fuzzy Systems and Maticsmaths 14(2), 80–88 (2000)

    Google Scholar 

  16. Herrera-Viedma, E., et al.: Some issues on consistency of fuzzy preference relations. European J. Oper. Res 154, 98–109 (2004)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Bing-Yuan Cao

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zeng, W., Xing, Y., Li, H. (2007). A Method for the Priority Vector of Fuzzy Reciprocal Matrix. In: Cao, BY. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71441-5_57

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-71441-5_57

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71440-8

  • Online ISBN: 978-3-540-71441-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics