IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i10p914-d272720.html
   My bibliography  Save this article

Deriving Fuzzy Weights of the Fuzzy Analytic Network Process via Fuzzy Inverse Matrix

Author

Listed:
  • Chin-Yi Chen

    (Department of Business Administration, Chung Yuan Christian University, Taoyuan 32023, Taiwan)

  • Jih-Jeng Huang

    (Department of Computer Science & Information Management, SooChow University, Taipei 100, Taiwan)

Abstract

The analytic hierarchical process/network process (AHP/ANP) is a popular multi-criteria decision making approach for determining the optimal alternative or weights of criteria. Many papers have extended the AHP/ANP to consider the fuzzy environment to reflect the subjective uncertainty of decision-makers. However, the fuzzy ANP (FANP) is not as popular as the fuzzy AHP (FAHP), because the calculation of the fuzzy supermatrix results in the divergence of the steady-state. In this paper, we provide a novel mathematical programming model to calculate the limiting distribution of the fuzzy supermatrix by considering a fuzzy inverse matrix rather than directly calculate the fuzzy supermatrix by limiting powers. In addition, we use a numerical example to illustrate the proposed method and compare the results with the previous method. The numerical results indicate the proposed method has the least spread of the fuzzy weights, thus justifying the usefulness of the proposed method.

Suggested Citation

  • Chin-Yi Chen & Jih-Jeng Huang, 2019. "Deriving Fuzzy Weights of the Fuzzy Analytic Network Process via Fuzzy Inverse Matrix," Mathematics, MDPI, vol. 7(10), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:914-:d:272720
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/10/914/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/10/914/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Thomas L. Saaty, 2013. "The Modern Science of Multicriteria Decision Making and Its Practical Applications: The AHP/ANP Approach," Operations Research, INFORMS, vol. 61(5), pages 1101-1118, October.
    2. Alessio Ishizaka & Markus Lusti, 2006. "How to derive priorities in AHP: a comparative study," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(4), pages 387-400, December.
    3. 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.
    4. 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.
    5. Kone, Aylin Cigdem & Buke, Tayfun, 2007. "An Analytical Network Process (ANP) evaluation of alternative fuels for electricity generation in Turkey," Energy Policy, Elsevier, vol. 35(10), pages 5220-5228, October.
    6. Paweł Ziemba, 2019. "Inter-Criteria Dependencies-Based Decision Support in the Sustainable wind Energy Management," Energies, MDPI, vol. 12(4), pages 1-29, February.
    7. Kirytopoulos, Konstantinos & Voulgaridou, Dimitra & Platis, Agapios & Leopoulos, Vrassidas, 2011. "An effective Markov based approach for calculating the Limit Matrix in the analytic network process," European Journal of Operational Research, Elsevier, vol. 214(1), pages 85-90, October.
    Full references (including those not matched with items on IDEAS)

    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. Ishizaka, Alessio & Siraj, Sajid & Nemery, Philippe, 2016. "Which energy mix for the UK (United Kingdom)? An evolutive descriptive mapping with the integrated GAIA (graphical analysis for interactive aid)–AHP (analytic hierarchy process) visualization tool," Energy, Elsevier, vol. 95(C), pages 602-611.
    2. Jelena Lukić & Mirjana Misita & Dragan D. Milanović & Ankica Borota-Tišma & Aleksandra Janković, 2022. "Determining the Risk Level in Client Analysis by Applying Fuzzy Logic in Insurance Sector," Mathematics, MDPI, vol. 10(18), pages 1-17, September.
    3. Aleksandar Aleksić & Danijela Tadić, 2023. "Industrial and Management Applications of Type-2 Multi-Attribute Decision-Making Techniques Extended with Type-2 Fuzzy Sets from 2013 to 2022," Mathematics, MDPI, vol. 11(10), pages 1-24, May.
    4. Kaytez, Fazıl, 2022. "Evaluation of priority strategies for the expansion of installed wind power capacity in Turkey using a fuzzy analytic network process analysis," Renewable Energy, Elsevier, vol. 196(C), pages 1281-1293.
    5. Hisham Alidrisi, 2021. "Measuring the Environmental Maturity of the Supply Chain Finance: A Big Data-Based Multi-Criteria Perspective," Logistics, MDPI, vol. 5(2), pages 1-24, April.
    6. Sanja Puzović & Jasmina Vesić Vasović & Dragan D. Milanović & Vladan Paunović, 2023. "A Hybrid Fuzzy MCDM Approach to Open Innovation Partner Evaluation," Mathematics, MDPI, vol. 11(14), pages 1-26, July.
    7. Mohsen Ahmadi, 2021. "A Computational Approach to Uncovering Economic Growth Factors," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1051-1076, December.
    8. Irina Vinogradova-Zinkevič, 2023. "Comparative Sensitivity Analysis of Some Fuzzy AHP Methods," Mathematics, MDPI, vol. 11(24), pages 1-41, December.
    9. 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.
    10. Javier Reig-Mullor & David Pla-Santamaria & Ana Garcia-Bernabeu, 2020. "Extended Fuzzy Analytic Hierarchy Process (E-FAHP): A General Approach," Mathematics, MDPI, vol. 8(11), pages 1-14, November.
    11. Mateusz Piwowarski & Mariusz Borawski & Kesra Nermend, 2021. "The Problem of Non-Typical Objects in the Multidimensional Comparative Analysis of the Level of Renewable Energy Development," Energies, MDPI, vol. 14(18), pages 1-24, September.
    12. Liu, Qizhi, 2022. "Identifying and correcting the defects of the Saaty analytic hierarchy/network process: A comparative study of the Saaty analytic hierarchy/network process and the Markov chain-based analytic network ," Operations Research Perspectives, Elsevier, vol. 9(C).
    13. 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.
    14. Ozgur Demirta, 2013. "Evaluating the Best Renewable Energy Technology for Sustainable Energy Plannin," International Journal of Energy Economics and Policy, Econjournals, vol. 3(Special), pages 23-33.
    15. Liu, Fang & Zou, Shu-Cai & Li, Qing, 2020. "Deriving priorities from pairwise comparison matrices with a novel consistency index," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    16. Matteo Brunelli, 2017. "Studying a set of properties of inconsistency indices for pairwise comparisons," Annals of Operations Research, Springer, vol. 248(1), pages 143-161, January.
    17. Bice Cavallo, 2019. "Coherent weights for pairwise comparison matrices and a mixed-integer linear programming problem," Journal of Global Optimization, Springer, vol. 75(1), pages 143-161, September.
    18. Benyou Jia & Slobodan P. Simonovic & Pingan Zhong & Zhongbo Yu, 2016. "A Multi-Objective Best Compromise Decision Model for Real-Time Flood Mitigation Operations of Multi-Reservoir System," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(10), pages 3363-3387, August.
    19. Pasura Aungkulanon & Walailak Atthirawong & Pongchanun Luangpaiboon & Wirachchaya Chanpuypetch, 2024. "Navigating Supply Chain Resilience: A Hybrid Approach to Agri-Food Supplier Selection," Mathematics, MDPI, vol. 12(10), pages 1-42, May.
    20. Juan Carlos Martín & Veronika Rudchenko & María-Victoria Sánchez-Rebull, 2020. "The Role of Nationality and Hotel Class on Guests’ Satisfaction. A Fuzzy-TOPSIS Approach Applied in Saint Petersburg," Administrative Sciences, MDPI, vol. 10(3), pages 1-24, September.

    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:gam:jmathe:v:7:y:2019:i:10:p:914-:d:272720. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.