Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Intelligent Decision Technologies 2016 (IDT 2016)

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 56))

Included in the following conference series:

  • 640 Accesses

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.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. Dyer, R.F., Forman, E.H.: Group decision support with the analytic hierarchy process. Decis. Support Syst. 8(2), 99–124 (1992)

    Article  Google Scholar 

  2. Entani, T.: Interval AHP for a group of decision makers. In: IFSA-EUSFLAT, pp. 155–160 (2009)

    Google Scholar 

  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. Hickey, T., Ju, Q., van Emden, M.H.: Interval arithmetic: from principles to implementation. J. ACM 48(5), 1038–1068 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Liu, F.: Acceptable consistency analysis of interval reciprocal comparison matrices. Fuzzy Sets Syst. 160(18), 2686–2700 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  8. Saaty, T.L.: Decision making with the analytic hierarchy process. Int. J. Serv. Sci. 1, 83–98 (2008)

    MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. Xu, Z.: A direct approach to group decision making with uncertain additive linguistic preference relations. Fuzzy Optim. Decis. Making 5(1), 21–32 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  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. Zadnik, S.L., Groselj, P.: Estimating priorities in group AHP using interval comparison matrices. Multiple Criteria Decis. Making 8, 143–159 (2013)

    Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

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

    Jiri Mazurek

Authors
  1. Jiri Mazurek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiri Mazurek .

Editor information

Editors and Affiliations

  1. Maritime University, Gdynia, Poland

    Ireneusz Czarnowski

  2. Artificial Intelligence Department, Universidad Politécnica de Madrid, Boadilla del Monte, Madrid, Spain

    Alfonso Mateos Caballero

  3. KES International, Shoreham-by-sea, United Kingdom

    Robert J. Howlett

  4. University of Canberra, Canberra, South Australia, Australia

    Lakhmi C. Jain

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Mazurek, J. (2016). A New Approach to a Derivation of a Priority Vector from an Interval Comparison Matrix in a Group AHP Framework. In: Czarnowski, I., Caballero, A., Howlett, R., Jain, L. (eds) Intelligent Decision Technologies 2016. IDT 2016. Smart Innovation, Systems and Technologies, vol 56. Springer, Cham. https://doi.org/10.1007/978-3-319-39630-9_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-39630-9_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39629-3

  • Online ISBN: 978-3-319-39630-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation