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Analytic Hierarchy Process and Its Extensions

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Book cover New Perspectives in Multiple Criteria Decision Making

Part of the book series: Multiple Criteria Decision Making ((MCDM))

Abstract

Analytic Hierarchy Process (AHP) is a popular and long used multi-criteria decision analysis method. Despite this fact, there are still space for new research in all its methodological steps. These include problem structuring, pairwise comparisons, priorities derivation, consistency and reduction techniques of pairwise comparisons. Moreover, future research agenda can also be found in the extensions of AHP: Analytic Network Process (for dealing with interactions) and AHPSort (for sorting problems). Finally, we discuss visualisation techniques for the Analytic Hierarchy Process.

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References

  • Barzilai, J. (1998). On the decomposition of value functions. Operations Research Letters, 22(4), 159–170.

    Article  Google Scholar 

  • Benítez, J., Izquierdo, J., Pérez-García, R., & Ramos-Martínez, E. (2014). A simple formula to find the closest consistent matrix to a reciprocal matrix. Applied Mathematical Modelling, 38(15–16), 3968–3974.

    Article  Google Scholar 

  • Bozóki, S., Fülöp, J., & Rónyai, L. (2010). On optimal completion of incomplete pairwise comparison matrices. Mathematical and Computer Modelling, 52(1), 318–333.

    Article  Google Scholar 

  • Brunelli, M., & Fedrizzi, M. (2014). Axiomatic properties of inconsistency indices for pairwise comparisons. Journal of the Operational Research Society, 66(1), 1–15.

    Article  Google Scholar 

  • Budescu, D., Zwick, R., & Rapoport, A. (1986). A comparison of the eigenvalue method and the geometric mean procedure for ratio scaling. Applied Psychological Measurement, 10(1), 69–78.

    Article  Google Scholar 

  • Carmone, F., Kara, A., & Zanakis, S. (1997). A Monte Carlo investigation of incomplete pairwise comparison matrices in AHP. European Journal of Operational Research, 102(3), 538–553.

    Article  Google Scholar 

  • Cho, E., & Wedley, W. (2004). A common framework for deriving preference values from pairwise comparison matrices. Computers & Operations Research, 31(6), 893–908.

    Article  Google Scholar 

  • Collins, A., Ishizaka, A., & Snowball, J. (2017). Film production incentives, employment transformation and domestic expenditure in South Africa: Visualizing subsidy effectiveness. International Journal of Cultural Policy. https://doi.org/10.1080/10286632.2016.1255206.

  • Corrente, S., Greco, S., & Ishizaka, A. (2016). Combining analytical hierarchy process and Choquet integral within non-additive robust ordinal regression. Omega (61), 2–18.

    Google Scholar 

  • Crawford, G., & Williams, C. (1985). A note on the analysis of subjective judgement matrices. Journal of Mathematical Psychology, 29(4), 387–405.

    Article  Google Scholar 

  • Csató, L., & Rónyai, L. (2016). Incomplete pairwise comparison matrices and weighting methods. Fundamenta Informaticae, 309–320(3–4).

    Google Scholar 

  • Dodd, F., & Donegan, H. (1995). Comparison of priotization techniques using interhierarchy mappings. Journal of the Operational Research Society, 46(4), 492–498.

    Article  Google Scholar 

  • Dung, T., Luan, N., & Quoc, L. (2016). The analytic approach in green supplier selection: a literature review. ARPN Journal of Engineering and Applied Sciences, 11(11), 6754–6762.

    Google Scholar 

  • Fedrizzi, M., & Giove, S. (2007). Incomplete pairwise comparison and consistency optimization. European Journal of Operational Research, 183(1), 303–313.

    Article  Google Scholar 

  • Forman, E., & Gass, S. (2001). The analytic hierarchy process—An exposition. Operations Research, 49(4), 469–486.

    Article  Google Scholar 

  • Golany, B., & Kress, M. (1993). A multicriteria evaluation of the methods for obtaining weights from ratio-scale matrices. European Journal of Operational Research, 69(2), 210–220.

    Article  Google Scholar 

  • Golden, B., Wasil, E., & Harker, P. (1989). The analytic hierarchy process: Applications and studies. Heidelberg: Springer-Verlag.

    Book  Google Scholar 

  • Gomez-Ruiz, J., Karanik, M., & Peláez, J. (2010). Estimation of missing judgments in AHP pairwise matrices using a neural network-based model. Applied Mathematics and Computation, 216(10), 2959–2975.

    Article  Google Scholar 

  • Grošelj, P., Zadnik Stirn, L., Ayrilmis, N., & Kuzman, M. (2015). Comparison of some aggregation techniques using group analytic hierarchy process. Expert Systems with Applications, 42(4), 2198–2204.

    Article  Google Scholar 

  • Harker, P. (1987). Incomplete pairwise comparisons in the analytic hierarchy process. Mathematical Modelling, 9(11), 837–848.

    Article  Google Scholar 

  • Harker, P., & Vargas, L. (1987). The theory of ratio scale estimation: Saaty’s analytic hierarchy process. Management Science, 33(11), 1383–1403.

    Article  Google Scholar 

  • Herman, M., & Koczkodaj, W. (1996). A Monte Carlo study of pairwise comparison. Information Processing Letters, 57(11), 25–29.

    Article  Google Scholar 

  • Ho, W. (2008). Integrated analytic hierarchy process and its applications—A literature review. European Journal of Operational Research, 186(1), 211–228.

    Article  Google Scholar 

  • Ihrig, S., Ishizaka, A., & Mohnen, A. (2017). Target setting for indirect processes: A new hybrid method for the continuous improvement management of indirect processes. Production Planning & Control, 28(3), 220–231.

    Article  Google Scholar 

  • Ishizaka, A. (2012). A multicriteria approach with AHP and clusters for the selection among a large number of suppliers. Pesquisa Operacional, 32(1), 1–15.

    Article  Google Scholar 

  • Ishizaka, A., Balkenborg, D., & Kaplan, T. (2010). Influence of aggregation and measurement scale on ranking a compromise alternative in AHP. Journal of the Operational Research Society, 62(4), 700–710.

    Article  Google Scholar 

  • Ishizaka, A., & Labib, A. (2009). Analytic hierarchy process and expert choice: Benefits and limitations. OR Insight, 22(4), 201–220.

    Article  Google Scholar 

  • Ishizaka, A., & Labib, A. (2011a). Review of the main developments in the analytic hierarchy process. Expert Systems with Applications, 38(11), 14336–14345.

    Google Scholar 

  • Ishizaka, A., & Labib, A. (2011b). Selection of new production facilities with the group analytic hierarchy process ordering method. Expert Systems with Applications, 38(6), 7317–7325.

    Article  Google Scholar 

  • Ishizaka, A., & López, C. (2018). Cost-benefit AHPSort for performance analysis of offshore providers. International Journal of Production Research. https://doi.org/10.1080/00207543.00202018.01509393.

  • Ishizaka, A., & Lusti, M. (2006). How to derive priorities in AHP: A comparative study. Central European Journal of Operations Research, 14(4), 387–400.

    Article  Google Scholar 

  • Ishizaka, A., & Nemery, P. (2013). Multi-criteria decision analysis. Chichester (United Kingdom): Wiley.

    Google Scholar 

  • Ishizaka, A., Nemery, P., & Pearman, C. (2012). AHPSort: An AHP based method for sorting problems. International Journal of Production Research, 50(17), 4767–4784.

    Article  Google Scholar 

  • Ishizaka, A., Siraj, S., & Nemery, P. (2016). Which energy mix for the UK? An evolutive descriptive mapping with the integrated GAIA-AHP visualisation tool. Energy, 95, 602–611.

    Article  Google Scholar 

  • Jandova, V., Krejci, J., Stoklasa, J., & Fedrizzi, M. (2017). Computing interval weights for incomplete pairwise-comparison matrices of large dimension—A weak consistency based approach. IEEE Transactions on Fuzzy Systems, PP(99), 1–1.

    Google Scholar 

  • Jones, D., & Mardle, S. (2004). A distance-metric methodology for the derivation of weights from a pairwise comparison matrix. Journal of the Operational Research Society, 55(8), 869–875.

    Article  Google Scholar 

  • Kainulainen, T., Leskinen, P., Korhonen, P., Haara, A., & Hujala, T. (2009). A statistical approach to assessing interval scale preferences in discrete choice problems. Journal of the Operational Research Society, 60(2), 252–258.

    Article  Google Scholar 

  • Krejčí, J., & Ishizaka, A. (2018). FAHPSort: A fuzzy extension of the AHPSort method. International Journal of Information Technology & Decision Making, 17(04), 1119–1145.

    Article  Google Scholar 

  • Kumar, S., & Vaidya, O. (2006). Analytic hierarchy process: An overview of applications. European Journal of Operational Research, 169(1), 1–29.

    Article  Google Scholar 

  • Kun, C., Gang, K., Tarn, M., & Yan, S. (2015). Bridging the gap between missing and inconsistent values in eliciting preference from pairwise comparison matrices. Annals of Operations Research, 235(1), 155–175.

    Article  Google Scholar 

  • Liberatore, M., & Nydick, R. (2008). The analytic hierarchy process in medical and health care decision making: A literature review. European Journal of Operational Research, 189(1), 194–207.

    Article  Google Scholar 

  • Lootsma, F. (1989). Conflict resolution via pairwise comparison of concessions. European Journal of Operational Research, 40(1), 109–116.

    Article  Google Scholar 

  • López, C., & Ishizaka, A. (2017). GAHPSort: A new group multi-criteria decision method for sorting a large number of the cloud-based ERP solutions. Computers in Industry, 92–93, 12–24.

    Article  Google Scholar 

  • Ma, D., & Zheng, X. (1991). 9/9–9/1 scale method of AHP. In Proceedings of 2nd International Symposium on the AHP (Vol. 1, pp. 197–202). Pittsburgh.

    Google Scholar 

  • Mareschal, B., & Brans, J.-P. (1988). Geometrical representations for MCDA. European Journal of Operational Research, 34(1), 69–77.

    Article  Google Scholar 

  • Marttunen, M., Lienert, J., & Belton, V. (2017). Structuring problems for multi-criteria decision analysis in practice: A literature review of method combinations. European Journal of Operational Research, 263(1), 1–17.

    Article  Google Scholar 

  • Meesariganda, B., & Ishizaka, A. (2017). Mapping verbal AHP scale to numerical scale for cloud computing strategy selection. Applied Soft Computing, 53, 111–118.

    Article  Google Scholar 

  • Mikhailov, L., & Singh, M. G. (1999). Comparison analysis of methods for deriving priorities in the analytic hierarchy process. In IEEE International Conference on Systems, Man, and Cybernetics, Tokyo.

    Google Scholar 

  • Nemery, P., Ishizaka, A., Camargo, M., & Morel, L. (2012). Enriching descriptive information in ranking and sorting problems with visualizations techniques. Journal of Modelling in Management, 7(2), 130–147.

    Article  Google Scholar 

  • Omkarprasad, V., & Sushil, K. (2006). Analytic hierarchy process: An overview of applications. European Journal of Operational Research, 169(1), 1–29.

    Article  Google Scholar 

  • Pöyhönen, M., Hamalainen, R., & Salo, A. (1997). An experiment on the numerical modelling of verbal ratio statements. Journal of Multi-Criteria Decision Analysis, 6(1), 1–10.

    Article  Google Scholar 

  • Rezaei, J. (2015). Best-worst multi-criteria decision-making method. Omega, 53, 49–57.

    Article  Google Scholar 

  • Saaty, T. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234–281.

    Article  Google Scholar 

  • Saaty, T. (1996). Decision making with dependence and feedback: The analytic network process. Pittsburgh: RWS Publications.

    Google Scholar 

  • Saaty, T. (2001). The analytic network process. Pittsburgh: RWS Publications.

    Book  Google Scholar 

  • Saaty, T., & Forman, E. (1992). The hierarchon: A dictionary of hierarchies. Pittsburgh: RWS Publications.

    Google Scholar 

  • Saaty, T., & Takizawa, M. (1986). Dependence and independence: From linear hierarchies to nonlinear networks. European Journal of Operational Research, 26(2), 229–237.

    Article  Google Scholar 

  • Salo, A., & Hamalainen, R. (1997). On the measurement of preference in the analytic hierarchy process. Journal of Multi-Criteria Decision Analysis, 6(6), 309–319.

    Article  Google Scholar 

  • Shim, J. (1989). Bibliography research on the analytic hierarchy process (AHP). Socio-Economic Planning Sciences, 23(3), 161–167.

    Article  Google Scholar 

  • Sipahi, S., & Timor, M. (2010). The analytic hierarchy process and analytic network process: An overview of applications. Management Decision, 48(5), 775–808.

    Article  Google Scholar 

  • Stillwell, W., von Winterfeldt, D., & John, R. (1987). Comparing hierarchical and non-hierarchical weighting methods for eliciting multiattribute value models. Management Science, 33(4), 442–450.

    Article  Google Scholar 

  • Vargas, L. (1990). An overview of the analytic hierarchy process and its applications. European Journal of Operational Research, 48(1), 2–8.

    Article  Google Scholar 

  • Weber, M., Eisenführ, F., & von Winterfeldt, D. (1988). The effects of spitting attributes on weights in multiattribute utility measurement. Management Science, 34(4), 431–445.

    Article  Google Scholar 

  • Zahedi, F. (1986). The analytic hierarchy process: A survey of the method and its applications. Interface, 16(4), 96–108.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Portsmouth Business School, Centre for Operational Research and Logistics, University of Portsmouth, Richmond Building, Portsmouth, PO1 3ED, UK

    Alessio Ishizaka

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  1. Alessio Ishizaka
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Correspondence to Alessio Ishizaka .

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Editors and Affiliations

  1. School of Production Engineering and Management, Technical University of Crete, Chania, Greece

    Michalis Doumpos

  2. CEG-IST, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    José Rui Figueira

  3. Department of Economics and Business, University of Catania, Catania, Italy

    Salvatore Greco

  4. School of Production Engineering and Management, Technical University of Crete, Chania, Greece

    Constantin Zopounidis

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Ishizaka, A. (2019). Analytic Hierarchy Process and Its Extensions. In: Doumpos, M., Figueira, J., Greco, S., Zopounidis, C. (eds) New Perspectives in Multiple Criteria Decision Making. Multiple Criteria Decision Making. Springer, Cham. https://doi.org/10.1007/978-3-030-11482-4_2

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