Skip to main content
SpringerLink
Log in

A New Consistency Coefficient in the Multi-criteria Decision Analysis Domain

  • Conference paper
  • First Online:
Computational Science – ICCS 2021 (ICCS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12742))

Included in the following conference series:

Abstract

The logical consistency of decision making matrices is an important topic in developing each multi-criteria decision analysis (MCDA) method. For instance, many published papers are addressed to the decisional matrix’s consistency in the Analytic Hierarchy Process method (AHP), which uses Saaty’s seventeen-values scale.

This work proposes a new approach to measuring consistency for using a simple three-value scale (binary with a tie). The paper’s main contribution is a proposal of a new consistency coefficient for a decision matrix containing judgments from an expert. We show this consistency coefficient based on an effective MCDA method called the Characteristic Objects METhod (COMET). The new coefficient is explained based on the Matrix of Expert Judgment (MEJ), which is the critical step of the COMET method. The proposed coefficient is based on analysing the relationship between judgments from the MEJ matrix and transitive principles (triads analysis). Four triads classes have been identified and discussed. The proposed coefficient makes it easy to determine the logical consistency and, thus, the expert responses’ quality is essential in the reliable decision-making process. Results are presented in some short study cases.

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 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
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

References

  1. Aguarón, J., Moreno-Jiménez, J.M.: The geometric consistency index: approximated thresholds. Eur. J. Oper. Res. 147(1), 137–145 (2003)

    Article  Google Scholar 

  2. Al-Harbi, K.M.A.S.: Application of the AHP in project management. Int. J. Project Manage. 19(1), 19–27 (2001)

    Article  Google Scholar 

  3. Baltazar, M.E., Jardim, J., Alves, P., Silva, J.: Air transport performance and efficiency: Mcda vs. dea approaches. Proced.-Soc. Behav. Sci. 111, 790–799 (2014)

    Google Scholar 

  4. Behzadian, M., Otaghsara, S.K., Yazdani, M., Ignatius, J.: A state-of the-art survey of TOPSIS applications. Expert Syst. Appl. 39(17), 13051–13069 (2012)

    Article  Google Scholar 

  5. Bozóki, S., Dezső, L., Poesz, A., Temesi, J.: Analysis of pairwise comparison matrices: an empirical research. Ann. Oper. Res. 211(1), 511–528 (2013). https://doi.org/10.1007/s10479-013-1328-1

    Article  MathSciNet  MATH  Google Scholar 

  6. Bozóki, S., Fülöp, J., Koczkodaj, W.W.: An LP-based inconsistency monitoring of pairwise comparison matrices. Math. Comput. Model. 54(1–2), 789–793 (2011)

    Article  MathSciNet  Google Scholar 

  7. Brunelli, M.: On the conjoint estimation of inconsistency and intransitivity of pairwise comparisons. Oper. Res. Lett. 44(5), 672–675 (2016)

    Article  MathSciNet  Google Scholar 

  8. Brunelli, M., Canal, L., Fedrizzi, M.: Inconsistency indices for pairwise comparison matrices: a numerical study. Ann. Oper. Res. 211(1), 493–509 (2013). https://doi.org/10.1007/s10479-013-1329-0

    Article  MathSciNet  MATH  Google Scholar 

  9. Faizi, S., Sałabun, W., Ullah, S., Rashid, T., Więckowski, J.: A new method to support decision-making in an uncertain environment based on normalized interval-valued triangular fuzzy numbers and COMET technique. Symmetry 12(4), 516 (2020)

    Article  Google Scholar 

  10. Huang, I.B., Keisler, J., Linkov, I.: Multi-criteria decision analysis in environmental sciences: ten years of applications and trends. Sci. Total Environ. 409(19), 3578–3594 (2011)

    Article  Google Scholar 

  11. Kendall, M.G., Smith, B.B.: On the method of paired comparisons. Biometrika 31(3/4), 324–345 (1940)

    Article  MathSciNet  Google Scholar 

  12. Kułakowski, K.: Inconsistency in the ordinal pairwise comparisons method with and without ties. Eur. J. Oper. Res. 270(1), 314–327 (2018)

    Article  MathSciNet  Google Scholar 

  13. Lane, E.F., Verdini, W.A.: A consistency test for AHP decision makers. Decis. Sci. 20(3), 575–590 (1989)

    Article  Google Scholar 

  14. Liberatore, M.J., Nydick, R.L.: The analytic hierarchy process in medical and health care decision making: a literature review. Eur. J. Oper. Res. 189(1), 194–207 (2008)

    Article  Google Scholar 

  15. Palczewski, K., Sałabun, W.: The fuzzy TOPSIS applications in the last decade. Proced. Comput. Sci. 159, 2294–2303 (2019)

    Article  Google Scholar 

  16. Piegat, A., Sałabun, W.: Comparative analysis of MCDM methods for assessing the severity of chronic liver disease. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2015. LNCS (LNAI), vol. 9119, pp. 228–238. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19324-3_21

    Chapter  Google Scholar 

  17. Riaz, M., Sałabun, W., Farid, H.M.A., Ali, N., Wątróbski, J.: A robust q-Rung orthopair fuzzy information aggregation using Einstein operations with application to sustainable energy planning decision management. Energies 13(9), 2155 (2020)

    Article  Google Scholar 

  18. Saaty, T.L.: A scaling method for priorities in hierarchical structures. J. Math. Psychol. 15(3), 234–281 (1977)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  20. Sałabun, W.: The characteristic objects method: a new distance-based approach to multicriteria decision-making problems. J. Multi-Criteria Dec. Anal. 22(1–2), 37–50 (2015)

    Article  Google Scholar 

  21. Sałabun, W., Piegat, A.: Comparative analysis of MCDM methods for the assessment of mortality in patients with acute coronary syndrome. Artif. Intell. Rev. 48(4), 557–571 (2017)

    Article  Google Scholar 

  22. Sałabun, W., Wątróbski, J., Piegat, A.: Identification of a multi-criteria model of location assessment for renewable energy sources. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2016. LNCS (LNAI), vol. 9692, pp. 321–332. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39378-0_28

    Chapter  Google Scholar 

  23. Sałabun, W., Ziemba, P., Wątróbski, J.: The rank reversals paradox in management decisions: the comparison of the AHP and COMET methods. In: Czarnowski, I., Caballero, A.M., Howlett, R.J., Jain, L.C. (eds.) Intelligent Decision Technologies 2016. SIST, vol. 56, pp. 181–191. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39630-9_15

    Chapter  Google Scholar 

  24. Schenkerman, S.: Avoiding rank reversal in AHP decision-support models. Eur. J. Oper. Res. 74(3), 407–419 (1994)

    Article  Google Scholar 

  25. Siraj, S., Mikhailov, L., Keane, J.A.: Contribution of individual judgments toward inconsistency in pairwise comparisons. Eur. J. Oper. Res. 242(2), 557–567 (2015)

    Article  MathSciNet  Google Scholar 

  26. Stein, W.E., Mizzi, P.J.: The harmonic consistency index for the analytic hierarchy process. Eur. J. Oper. Res. 177(1), 488–497 (2007)

    Article  Google Scholar 

  27. Szybowski, J., Kułakowski, K., Prusak, A.: New inconsistency indicators for incomplete pairwise comparisons matrices. Math. Soc. Sci. 108, 138–145 (2020)

    Article  MathSciNet  Google Scholar 

  28. Triantaphyllou, E., Mann, S.H.: Using the analytic hierarchy process for decision making in engineering applications: some challenges. Int. J. Ind. Eng. Appl. Pract. 2(1), 35–44 (1995)

    Google Scholar 

  29. Watróbski, J., Sałabun, W.: The characteristic objects method: a new intelligent decision support tool for sustainable manufacturing. In: Setchi, R., Howlett, R.J., Liu, Y., Theobald, P. (eds.) Sustainable Design and Manufacturing 2016. SIST, vol. 52, pp. 349–359. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-32098-4_30

    Chapter  Google Scholar 

  30. Zavadskas, E.K., Turskis, Z., Kildienė, S.: State of art surveys of overviews on MCDM/MADM methods. Technol. Econ. Dev. Econ. 20(1), 165–179 (2014)

    Article  Google Scholar 

  31. Ziemba, P.: Inter-criteria dependencies-based decision support in the sustainable wind energy management. Energies 12(4), 749 (2019)

    Article  Google Scholar 

Download references

Acknowledgments

The work was supported by the National Science Centre, Decision number UMO-2018/29/B/HS4/02725.

Author information

Authors and Affiliations

  1. Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Żołnierska 49, 71-210, Szczecin, Poland

    Wojciech Sałabun, Andrii Shekhovtsov & Bartłomiej Kizielewicz

Authors
  1. Wojciech Sałabun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrii Shekhovtsov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bartłomiej Kizielewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wojciech Sałabun .

Editor information

Editors and Affiliations

  1. AGH University of Science and Technology, Krakow, Poland

    Maciej Paszynski

  2. Ludwig-Maximilians-Universität München, Munich, Germany

    Dieter Kranzlmüller

  3. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

  4. University of Tennessee at Knoxville, Knoxville, TN, USA

    Jack J. Dongarra

  5. University of Amsterdam, Amsterdam, The Netherlands

    Peter M. A. Sloot

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sałabun, W., Shekhovtsov, A., Kizielewicz, B. (2021). A New Consistency Coefficient in the Multi-criteria Decision Analysis Domain. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12742. Springer, Cham. https://doi.org/10.1007/978-3-030-77961-0_57

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-77961-0_57

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-77960-3

  • Online ISBN: 978-3-030-77961-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation