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Consistency Indices in Analytic Hierarchy Process: A Review

Author

Listed:
  • Sangeeta Pant

    (Department of Mathematics, University of Petroleum & Energy Studies, Dehradun 248007, India
    These authors contributed equally to this work.)

  • Anuj Kumar

    (Department of Mathematics, University of Petroleum & Energy Studies, Dehradun 248007, India
    These authors contributed equally to this work.)

  • Mangey Ram

    (Department of Mathematics, Graphic Era Deemed to be University, Dehradun 248002, India
    Institute of Advanced Manufacturing Technologies, Peter the Great St. Petersburg Polytechnic University, 195251 Saint Petersburg, Russia)

  • Yury Klochkov

    (Academic Development Management, Peter the Great St. Petersburg Polytechnic University, 195251 Saint Petersburg, Russia)

  • Hitesh Kumar Sharma

    (School of Computer Science, University of Petroleum & Energy Studies, Dehradun 248007, India)

Abstract

A well-regarded as well as powerful method named the ‘analytic hierarchy process’ (AHP) uses mathematics and psychology for making and analysing complex decisions. This article aims to present a brief review of the consistency measure of the judgments in AHP. Judgments should not be random or illogical. Several researchers have developed different consistency measures to identify the rationality of judgments. This article summarises the consistency measures which have been proposed so far in the literature. Moreover, this paper describes briefly the functional relationships established in the literature among the well-known consistency indices. At last, some thoughtful research directions that can be helpful in further research to develop and improve the performance of AHP are provided as well.

Suggested Citation

  • Sangeeta Pant & Anuj Kumar & Mangey Ram & Yury Klochkov & Hitesh Kumar Sharma, 2022. "Consistency Indices in Analytic Hierarchy Process: A Review," Mathematics, MDPI, vol. 10(8), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1206-:d:788724
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    References listed on IDEAS

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    1. Aguaron, Juan & Moreno-Jimenez, Jose Maria, 2003. "The geometric consistency index: Approximated thresholds," European Journal of Operational Research, Elsevier, vol. 147(1), pages 137-145, May.
    2. Matteo Brunelli & Michele Fedrizzi, 2015. "Axiomatic properties of inconsistency indices for pairwise comparisons," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(1), pages 1-15, January.
    3. Szybowski, Jacek & Kułakowski, Konrad & Prusak, Anna, 2020. "New inconsistency indicators for incomplete pairwise comparisons matrices," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 138-145.
    4. Matteo Brunelli & Luisa Canal & Michele Fedrizzi, 2013. "Inconsistency indices for pairwise comparison matrices: a numerical study," Annals of Operations Research, Springer, vol. 211(1), pages 493-509, December.
    5. László Csató, 2018. "Characterization of an inconsistency ranking for pairwise comparison matrices," Annals of Operations Research, Springer, vol. 261(1), pages 155-165, February.
    6. Bice Cavallo, 2020. "Functional relations and Spearman correlation between consistency indices," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(2), pages 301-311, February.
    7. Zahir, Sajjad, 1999. "Geometry of decision making and the vector space formulation of the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 112(2), pages 373-396, January.
    8. Kou, Gang & Lin, Changsheng, 2014. "A cosine maximization method for the priority vector derivation in AHP," European Journal of Operational Research, Elsevier, vol. 235(1), pages 225-232.
    9. László Csató, 2019. "Axiomatizations of inconsistency indices for triads," Annals of Operations Research, Springer, vol. 280(1), pages 99-110, September.
    10. Lootsma, F. A., 1989. "Conflict resolution via pairwise comparison of concessions," European Journal of Operational Research, Elsevier, vol. 40(1), pages 109-116, May.
    11. Aupetit, Bernard & Genest, Christian, 1993. "On some useful properties of the Perron eigenvalue of a positive reciprocal matrix in the context of the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 70(2), pages 263-268, October.
    12. Gass, S. I. & Rapcsak, T., 2004. "Singular value decomposition in AHP," European Journal of Operational Research, Elsevier, vol. 154(3), pages 573-584, May.
    13. Paul Thaddeus Kazibudzki, 2016. "An examination of performance relations among selected consistency measures for simulated pairwise judgments," Annals of Operations Research, Springer, vol. 244(2), pages 525-544, September.
    14. Stein, William E. & Mizzi, Philip J., 2007. "The harmonic consistency index for the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 177(1), pages 488-497, February.
    15. Takeda, Eiji & Yu, Po-Lung, 1995. "Assessing priority weights from subsets of pairwise comparisons in multiple criteria optimization problems," European Journal of Operational Research, Elsevier, vol. 86(2), pages 315-331, October.
    16. Saaty, Thomas L., 1986. "A note on the AHP and expected value theory," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 397-398.
    17. Amarnath Bose, 2020. "Using genetic algorithm to improve consistency and retain authenticity in the analytic hierarchy process," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1070-1092, December.
    18. Jiří Mazurek, 2018. "Some notes on the properties of inconsistency indices in pairwise comparisons," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(1), pages 27-42.
    19. Michele Fedrizzi & Nino Civolani & Andrew Critch, 2020. "Inconsistency evaluation in pairwise comparison using norm-based distances," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 657-672, December.
    20. Abel, Edward & Mikhailov, Ludmil & Keane, John, 2018. "Inconsistency reduction in decision making via multi-objective optimisation," European Journal of Operational Research, Elsevier, vol. 267(1), pages 212-226.
    21. Kuenz Murphy, Catherine, 1993. "Limits on the analytic hierarchy process from its consistency index," European Journal of Operational Research, Elsevier, vol. 65(1), pages 138-139, February.
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