IDEAS home Printed from https://ideas.repec.org/a/spr/fuzodm/v17y2018i2d10.1007_s10700-017-9267-y.html
   My bibliography  Save this article

Deriving crisp and consistent priorities for fuzzy AHP-based multicriteria systems using non-linear constrained optimization

Author

Listed:
  • Raman Kumar Goyal

    (Panjab University)

  • Sakshi Kaushal

    (Panjab University)

Abstract

Fuzzy optimization models are used to derive crisp weights (priority vectors) for the fuzzy analytic hierarchy process (AHP) based multicriteria decision making systems. These optimization models deal with the imprecise judgements of decision makers by formulating the optimization problem as the system of constrained non linear equations. Firstly, a Genetic Algorithm based heuristic solution for this optimization problem is implemented in this paper. It has been found that the crisp weights derived from this solution for fuzzy-AHP system, sometimes lead to less consistent or inconsistent solutions. To deal with this problem, we have proposed a consistency based constraint for the optimization models. A decision maker can set the consistency threshold value and if the solution exists for that threshold value then crisp weights can be derived, otherwise it can be concluded that the fuzzy comparison matrix for AHP is not consistent for the given threshold. Three examples are considered to demonstrate the effectiveness of the proposed method. Results with the proposed constraint based fuzzy optimization model are more consistent than the existing optimization models.

Suggested Citation

  • Raman Kumar Goyal & Sakshi Kaushal, 2018. "Deriving crisp and consistent priorities for fuzzy AHP-based multicriteria systems using non-linear constrained optimization," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 195-209, June.
    • Handle: RePEc:spr:fuzodm:v:17:y:2018:i:2:d:10.1007_s10700-017-9267-y
    DOI: 10.1007/s10700-017-9267-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10700-017-9267-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10700-017-9267-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fedrizzi, Michele & Giove, Silvio, 2007. "Incomplete pairwise comparison and consistency optimization," European Journal of Operational Research, Elsevier, vol. 183(1), pages 303-313, November.
    2. Wang, Ying-Ming & Luo, Ying & Hua, Zhongsheng, 2008. "On the extent analysis method for fuzzy AHP and its applications," European Journal of Operational Research, Elsevier, vol. 186(2), pages 735-747, April.
    3. Kwiesielewicz, M., 1996. "The logarithmic least squares and the generalized pseudoinverse in estimating ratios," European Journal of Operational Research, Elsevier, vol. 93(3), pages 611-619, September.
    4. L Mikhailov, 2000. "A fuzzy programming method for deriving priorities in the analytic hierarchy process," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(3), pages 341-349, March.
    5. Herrera-Viedma, E. & Herrera, F. & Chiclana, F. & Luque, M., 2004. "Some issues on consistency of fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 154(1), pages 98-109, April.
    6. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    7. Chang, Da-Yong, 1996. "Applications of the extent analysis method on fuzzy AHP," European Journal of Operational Research, Elsevier, vol. 95(3), pages 649-655, December.
    8. Wang, Ling & Chu, Jian & Wu, Jun, 2007. "Selection of optimum maintenance strategies based on a fuzzy analytic hierarchy process," International Journal of Production Economics, Elsevier, vol. 107(1), pages 151-163, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kang Xu & Jiuping Xu, 2020. "A direct consistency test and improvement method for the analytic hierarchy process," Fuzzy Optimization and Decision Making, Springer, vol. 19(3), pages 359-388, September.
    2. Yanan Zhang & Zhaopeng Meng & Yan Zheng & Anca Ralescu, 2019. "Schedule optimization under fuzzy constraints of vehicle capacity," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 131-150, June.
    3. Jie Tang & Fanyong Meng & Francisco Javier Cabrerizo & Enrique Herrera-Viedma, 2019. "A procedure for group decision making with interval-valued intuitionistic linguistic fuzzy preference relations," Fuzzy Optimization and Decision Making, Springer, vol. 18(4), pages 493-527, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Durbach, Ian N. & Stewart, Theodor J., 2012. "Modeling uncertainty in multi-criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 223(1), pages 1-14.
    2. Grošelj, Petra & Hodges, Donald G. & Zadnik Stirn, Lidija, 2016. "Participatory and multi-criteria analysis for forest (ecosystem) management: A case study of Pohorje, Slovenia," Forest Policy and Economics, Elsevier, vol. 71(C), pages 80-86.
    3. Wu, Zhibin & Huang, Shuai & Xu, Jiuping, 2019. "Multi-stage optimization models for individual consistency and group consensus with preference relations," European Journal of Operational Research, Elsevier, vol. 275(1), pages 182-194.
    4. Mohamed Hanine & Omar Boutkhoum & Abderrafie El Maknissi & Abdessadek Tikniouine & Tarik Agouti, 2016. "Decision making under uncertainty using PEES–fuzzy AHP–fuzzy TOPSIS methodology for landfill location selection," Environment Systems and Decisions, Springer, vol. 36(4), pages 351-367, December.
    5. María Carmen Carnero & Andrés Gómez, 2019. "Optimization of Decision Making in the Supply of Medicinal Gases Used in Health Care," Sustainability, MDPI, vol. 11(10), pages 1-31, May.
    6. Yibin Zhang & Kevin W. Li & Zhou-Jing Wang, 2017. "Prioritization and Aggregation of Intuitionistic Preference Relations: A Multiplicative-Transitivity-Based Transformation from Intuitionistic Judgment Data to Priority Weights," Group Decision and Negotiation, Springer, vol. 26(2), pages 409-436, March.
    7. María Carmen Carnero, 2020. "Fuzzy Multicriteria Models for Decision Making in Gamification," Mathematics, MDPI, vol. 8(5), pages 1-23, May.
    8. Calabrese, Armando & Costa, Roberta & Levialdi, Nathan & Menichini, Tamara, 2019. "Integrating sustainability into strategic decision-making: A fuzzy AHP method for the selection of relevant sustainability issues," Technological Forecasting and Social Change, Elsevier, vol. 139(C), pages 155-168.
    9. Ilić, Damir & Milošević, Isidora & Ilić-Kosanović, Tatjana, 2022. "Application of Unmanned Aircraft Systems for smart city transformation: Case study Belgrade," Technological Forecasting and Social Change, Elsevier, vol. 176(C).
    10. Jana Krejčí & Ondřej Pavlačka & Jana Talašová, 2017. "A fuzzy extension of Analytic Hierarchy Process based on the constrained fuzzy arithmetic," Fuzzy Optimization and Decision Making, Springer, vol. 16(1), pages 89-110, March.
    11. Fujun Hou, 2016. "Market Competitiveness Evaluation of Mechanical Equipment with a Pairwise Comparisons Hierarchical Model," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-18, January.
    12. Rezaei, Jafar & Ortt, Roland, 2013. "Multi-criteria supplier segmentation using a fuzzy preference relations based AHP," European Journal of Operational Research, Elsevier, vol. 225(1), pages 75-84.
    13. Zhang, Long & Bai, Wuliyasu & Xiao, Huijuan & Ren, Jingzheng, 2021. "Measuring and improving regional energy security: A methodological framework based on both quantitative and qualitative analysis," Energy, Elsevier, vol. 227(C).
    14. Lidan Pei & Feifei Jin & Zhiwei Ni & Huayou Chen & Zhifu Tao, 2017. "An automatic iterative decision-making method for intuitionistic fuzzy linguistic preference relations," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(13), pages 2779-2793, October.
    15. Zhü, Kèyù, 2014. "Fuzzy analytic hierarchy process: Fallacy of the popular methods," European Journal of Operational Research, Elsevier, vol. 236(1), pages 209-217.
    16. Vassiliki Kazana & Angelos Kazaklis & Dimitrios Raptis & Christos Stamatiou, 2020. "A combined multi-criteria approach to assess forest management sustainability: an application to the forests of Eastern Macedonia & Thrace Region in Greece," Annals of Operations Research, Springer, vol. 294(1), pages 321-343, November.
    17. Caprioli, Caterina & Bottero, Marta, 2021. "Addressing complex challenges in transformations and planning: A fuzzy spatial multicriteria analysis for identifying suitable locations for urban infrastructures," Land Use Policy, Elsevier, vol. 102(C).
    18. Paweł Karczmarek & Witold Pedrycz & Adam Kiersztyn, 2021. "Fuzzy Analytic Hierarchy Process in a Graphical Approach," Group Decision and Negotiation, Springer, vol. 30(2), pages 463-481, April.
    19. Jana Krejčí & Alessio Ishizaka, 2018. "FAHPSort: A Fuzzy Extension of the AHPSort Method," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1119-1145, July.
    20. Satish Tyagi, 2016. "An improved fuzzy-AHP (IFAHP) approach to compare SECI modes," International Journal of Production Research, Taylor & Francis Journals, vol. 54(15), pages 4520-4536, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:fuzodm:v:17:y:2018:i:2:d:10.1007_s10700-017-9267-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.