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A New Approach to a Derivation of a Priority Vector from an Interval Comparison Matrix in a Group AHP Framework

  • Jiri MazurekEmail author
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 56)

Abstract

The aim of the article is to present a new approach to a derivation of a priority vector form an interval comparison matrix in a group AHP framework. It is supposed that preferences of individual decision makers are aggregated into a group interval comparison matrix, and the priority weights of all alternatives are estimated via the geometric mean method generalized to interval numbers with the use of interval arithmetic. This approach differs from usual solutions of the problem based on linear programming methods or a decomposition of the interval comparison matrix into crisp matrices, followed by the eigenvalue method. This new approach is demonstrated on an example, and a comparison with a standard group AHP is provided as well.

Keywords

AHP Group AHP Group decision making Interval AHP 

Notes

Acknowledgements

This research was supported by the grant project of GACR No. 14-02424S.

References

  1. 1.
    Dyer, R.F., Forman, E.H.: Group decision support with the analytic hierarchy process. Decis. Support Syst. 8(2), 99–124 (1992)CrossRefGoogle Scholar
  2. 2.
    Entani, T.: Interval AHP for a group of decision makers. In: IFSA-EUSFLAT, pp. 155–160 (2009)Google Scholar
  3. 3.
    Grošelj, P., Zadnik Stirn, L., Ayrilmis, N., Kuzman, M.K.: Comparison of some aggregation techniques using group analytic hierarchy process. Expert Syst. Appl. 42(4), 2098–2204 (2014)Google Scholar
  4. 4.
    Hickey, T., Ju, Q., van Emden, M.H.: Interval arithmetic: from principles to implementation. J. ACM 48(5), 1038–1068 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Liu, F.: Acceptable consistency analysis of interval reciprocal comparison matrices. Fuzzy Sets Syst. 160(18), 2686–2700 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ramanathan, R., Ganesh, L.S.: Group reference aggregation methods in AHP: an evaluation and an intrinsic process for deriving members’ weightages. Eur. J. Oper. Res. 79(2), 249–265 (1994)CrossRefzbMATHGoogle Scholar
  7. 7.
    Saaty, T.L.: The Analytic Hierarchy Process. McGraw Hill, New York (1980)zbMATHGoogle Scholar
  8. 8.
    Saaty, T.L.: Decision making with the analytic hierarchy process. Int. J. Serv. Sci. 1, 83–98 (2008)MathSciNetGoogle Scholar
  9. 9.
    Saaty, T.L., Vargas, L.G.: Uncertainty and rank order in the analytic hierarchy process. Eur. J. Oper. Res. 32(1), 107–117 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Saaty, T.L.: Group decision making and the AHP. In: Golden, B.L. et.al.(eds.) The Analytic Hierarchy Process: Applications and Studies, pp. 59–67. McGraw-Hill, New York (1989)Google Scholar
  11. 11.
    Xu, Z.: A direct approach to group decision making with uncertain additive linguistic preference relations. Fuzzy Optim. Decis. Making 5(1), 21–32 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Yu, J.R., Hsiao, Y.W., Sheiu, H.J.: A multiplicative approach to derive weights in the interval analytic hierarchy process. In: Int. J. Fuzzy Syst. 13(3) (2011)Google Scholar
  13. 13.
    Zadnik, S.L., Groselj, P.: Estimating priorities in group AHP using interval comparison matrices. Multiple Criteria Decis. Making 8, 143–159 (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Silesian University in Opava, School of Business Administration in KarvinaUniversity Square 1934/3KarvinaCzech Republic

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