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Transform for Simplified Weight Computations in the Fuzzy Analytic Hierarchy Process

  • Manju Pandey
  • Nilay Khare
  • S. Shrivastava
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 182)

Abstract

A simplified procedure for weight computations from the pair-wise comparison matrices of triangular fuzzy numbers in the fuzzy analytic hierarchy process is proposed. A transform T:R3→R1 has been defined for mapping the triangular fuzzy numbers to equivalent crisp values. The crisp values have been used for eigenvector computations in a manner analogous to the computations of the original AHP method. The objective is to retain both the ability to capture and deal with inherent uncertainties of subjective judgments, which is the strength of fuzzy modeling and the simplicity, intuitive appeal, and power of conventional AHP which has made it a very popular decision making tool.

Keywords

Fuzzy AHP Triangular Fuzzy Number Fuzzy Synthetic Extent Weight Vector Eigenvector Decision Making Optimization Decision Making 

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References

  1. 1.
    Saaty, T.L.: Decision making with the analytic hierarchy process. Int. J. Serv. Sci. 1(1), 83–98 (2008)MathSciNetGoogle Scholar
  2. 2.
    Saaty, T.L.: The Analytic Hierarchy Process. McGraw Hill, New York (1980)zbMATHGoogle Scholar
  3. 3.
    Saaty, T.L.: Decision Making for Leaders: The Analytic Hierarchy Process for Decisions in a Complex World. Wadsworth, Belmont (1982)Google Scholar
  4. 4.
    Saaty, T.L.: How to Make a Decision: the Analytic Hierarchy process. Interfaces 24(6), 19–43 (1994)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Haas, R., Meixner, O.: An Illustrated Guide to the Analytic Hierarchy Process (2006), http://www.fakr.noaa.gov/sustainablefisheries/sslmc/july-06/ahptutorial.pdf (accessed April 27, 2012)
  6. 6.
    Zadeh, L.A.: Fuzzy Sets. Inf. Control 8, 338–353 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Chang, D.Y.: Applications of the extent analysis method on fuzzy AHP. Eur. J. Oper. Res. 95(3), 649–655 (1996)zbMATHCrossRefGoogle Scholar
  8. 8.
    Zhu, K.J., Jing, Y., Chang, D.Y.: A discussion on Extent Analysis Method and applications of fuzzy AHP. Eur. J. Oper. Res. 116(2), 450–456 (1999)zbMATHCrossRefGoogle Scholar
  9. 9.
    Wang, Y.M., Luo, Y., Hua, Z.: On the extent analysis method for Fuzzy AHP and its applications. Eur. J. Oper. Res. 186(2), 735–747 (2008)zbMATHCrossRefGoogle Scholar
  10. 10.
    Kauffman, A., Gupta, M.M.: Introduction to Fuzzy Arithmetic – Theory and Applications. Van Nostrand Reinhold Company, New York (1985)Google Scholar
  11. 11.
    Haans, M.: Applied Fuzzy Arithmetic – An Introduction with Engineering Applications. Springer, Heidelberg (2005)Google Scholar
  12. 12.
    Verma, A.K., Srividya, A., Prabhu Gaonkar, R.S.: Fuzzy-Reliability Engineering Concepts and Applications. Narosa Publishing House Pvt. Ltd., New Delhi (2007)Google Scholar
  13. 13.
    Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic, 3rd edn. CRC Press (2006)Google Scholar
  14. 14.
    Kilic, H.S.: A Fuzzy AHP Based Performance Assessment System for the Strategic Plan of Turkish Municipalities. Int. J. Bus. Manag. 3(2), 77–86 (2011), http://www.sobiad.org/eJOURNALS/journal_IJBM/2011.html Google Scholar
  15. 15.
    Meixner, O.: Fuzzy AHP Group Decision Analysis and its Application for the Evaluation of Energy Sources. In: Proc. of the 10th Int. Symp. on the Analytic Hierarchy/Netw. Process Multi-criteria Decis. Mak., U of Pitt, PA, USA, pp. 1–14 (2009), http://www.isahp.org/2009Proceedings/index.html (accessed on April 27, 2012)
  16. 16.
    Kabir, G., Hasin, M.A.A.: Multiple criteria inventory classification using fuzzy analytic hierarchy process. Int. J. Ind. Engg. Comput. 3(2), 123–132 (2011), http://growingscience.com/ijiec/Vol3/Vol3No2.html (accessed on April 27, 2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Computer ApplicationsNIT RaipurRaipurIndia
  2. 2.Department of Computer Science and EngineeringMANIT BhopalBhopalIndia

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