IDEAS home Printed from https://ideas.repec.org/a/wut/journl/v2y2020p91-114id1486.html
   My bibliography  Save this article

The extention rank ordering criteria weighting methods in fuzzy enviroment

Author

Listed:
  • Ewa Roszkowska

Abstract

Weight elicitation is an important part of multi-criteria decision analysis. In real-life decisionmaking problems precise information is seldom available, and providing weights is often cognitively demanding as well as very time- and effort-consuming. The judgment of decision-makers (DMs) depends on their knowledge, skills, experience, personality, and available information. One of the weights determination approaches is ranking the criteria and converting the resulting ranking into numerical values. The best known and most widely used are rank sum, rank reciprocal and centroid weights techniques. The goal of this paper is to extend rank ordering criteria weighting methods for imprecise data, especially fuzzy data. Since human judgments, including preferences, are often vague and cannot be expressed by exact numerical values, the application of fuzzy concepts in elicitation weights is deemed relevant. The methods built on the ideas of rank order techniques take into account imprecise information about rank. The fuzzy rank sum, fuzzy rank reciprocal, and fuzzy centroid weights techniques are proposed. The weights obtained for each criterion are triangular fuzzy numbers. The proposed fuzzy rank ordering criteria weighting methods can be easily implemented into decision support systems. Numerical examples are provided to illustrate the practicality and validity of the proposed methods.

Suggested Citation

  • Ewa Roszkowska, 2020. "The extention rank ordering criteria weighting methods in fuzzy enviroment," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(2), pages 91-114.
    • Handle: RePEc:wut:journl:v:2:y:2020:p:91-114:id:1486
    DOI: 10.37190/ord200206
    as

    Download full text from publisher

    File URL: https://ord.pwr.edu.pl/assets/papers_archive/1486%20-%20published.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.37190/ord200206?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
    ---><---

    References listed on IDEAS

    as
    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Dan Horsky & M. R. Rao, 1984. "Estimation of Attribute Weights from Preference Comparisons," Management Science, INFORMS, vol. 30(7), pages 801-822, July.
    3. Takeda, E. & Cogger, K. O. & Yu, P. L., 1987. "Estimating criterion weights using eigenvectors: A comparative study," European Journal of Operational Research, Elsevier, vol. 29(3), pages 360-369, June.
    4. de Almeida, Jonatas Araujo & Costa, Ana Paula Cabral Seixas & de Almeida-Filho, Adiel Teixeira, 2016. "A new method for elicitation of criteria weights in additive models: Flexible and interactive tradeoffAuthor-Name: de Almeida, Adiel Teixeira," European Journal of Operational Research, Elsevier, vol. 250(1), pages 179-191.
    5. Xu, Xiaozhan, 2004. "A note on the subjective and objective integrated approach to determine attribute weights," European Journal of Operational Research, Elsevier, vol. 156(2), pages 530-532, July.
    6. A Morton & B Fasolo, 2009. "Behavioural decision theory for multi-criteria decision analysis: a guided tour," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(2), pages 268-275, February.
    7. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    8. Olson, D. L. & Dorai, V. K., 1992. "Implementation of the centroid method of Solymosi and Dombi," European Journal of Operational Research, Elsevier, vol. 60(1), pages 117-129, July.
    9. F. Hutton Barron & Bruce E. Barrett, 1996. "Decision Quality Using Ranked Attribute Weights," Management Science, INFORMS, vol. 42(11), pages 1515-1523, November.
    10. Edwards, Ward & Barron, F. Hutton, 1994. "SMARTS and SMARTER: Improved Simple Methods for Multiattribute Utility Measurement," Organizational Behavior and Human Decision Processes, Elsevier, vol. 60(3), pages 306-325, December.
    11. Ma, Jian & Fan, Zhi-Ping & Huang, Li-Hua, 1999. "A subjective and objective integrated approach to determine attribute weights," European Journal of Operational Research, Elsevier, vol. 112(2), pages 397-404, January.
    12. Mats Danielson & Love Ekenberg, 2017. "A Robustness Study of State-of-the-Art Surrogate Weights for MCDM," Group Decision and Negotiation, Springer, vol. 26(4), pages 677-691, July.
    13. Katrin Borcherding & Thomas Eppel & Detlof von Winterfeldt, 1991. "Comparison of Weighting Judgments in Multiattribute Utility Measurement," Management Science, INFORMS, vol. 37(12), pages 1603-1619, December.
    14. Weber, Martin & Borcherding, Katrin, 1993. "Behavioral influences on weight judgments in multiattribute decision making," European Journal of Operational Research, Elsevier, vol. 67(1), pages 1-12, May.
    15. C. West Churchman & Russell L. Ackoff, 1954. "An Approximate Measure of Value," Operations Research, INFORMS, vol. 2(2), pages 172-187, May.
    16. Srivastava, Joydeep & Connolly, Terry & Beach, Lee Roy, 1995. "Do Ranks Suffice? A Comparison of Alternative Weighting Approaches in Value Elicitation," Organizational Behavior and Human Decision Processes, Elsevier, vol. 63(1), pages 112-116, July.
    17. Doyle, John R. & Green, Rodney H. & Bottomley, Paul A., 1997. "Judging Relative Importance: Direct Rating and Point Allocation Are Not Equivalent," Organizational Behavior and Human Decision Processes, Elsevier, vol. 70(1), pages 65-72, April.
    18. Bottomley, Paul A. & Doyle, John R., 2001. "A comparison of three weight elicitation methods: good, better, and best," Omega, Elsevier, vol. 29(6), pages 553-560, December.
    19. Agata Sielska, 2015. "The impact of weights on the quality of agricultural producers' multicriteria decision models," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 25(4), pages 51-69.
    20. Saaty, Thomas L. & Vargas, Luis G., 1987. "Uncertainty and rank order in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 32(1), pages 107-117, October.
    21. Wang, Ying-Ming & Elhag, Taha M.S., 2007. "A goal programming method for obtaining interval weights from an interval comparison matrix," European Journal of Operational Research, Elsevier, vol. 177(1), pages 458-471, February.
    22. Roszkowska, Ewa & Wachowicz, Tomasz, 2015. "Application of fuzzy TOPSIS to scoring the negotiation offers in ill-structured negotiation problems," European Journal of Operational Research, Elsevier, vol. 242(3), pages 920-932.
    23. Gilberto Montibeller & Detlof von Winterfeldt, 2015. "Cognitive and Motivational Biases in Decision and Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 35(7), pages 1230-1251, July.
    24. Tzeng, Gwo-Hshiung & Chen, Ting-Yu & Wang, Jih-Chang, 1998. "A weight-assessing method with habitual domains," European Journal of Operational Research, Elsevier, vol. 110(2), pages 342-367, 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. Adiel T. Almeida-Filho & Adiel T. Almeida & Ana Paula C. S. Costa, 2017. "A flexible elicitation procedure for additive model scale constants," Annals of Operations Research, Springer, vol. 259(1), pages 65-83, December.
    2. Roger Chapman Burk & Richard M. Nehring, 2023. "An Empirical Comparison of Rank-Based Surrogate Weights in Additive Multiattribute Decision Analysis," Decision Analysis, INFORMS, vol. 20(1), pages 55-72, March.
    3. Rađenović Žarko & Veselinović Ivana, 2017. "Integrated AHP-TOPSIS Method for the Assessment of Health Management Information Systems Efficiency," Economic Themes, Sciendo, vol. 55(1), pages 121-142, March.
    4. Lienert, Judit & Duygan, Mert & Zheng, Jun, 2016. "Preference stability over time with multiple elicitation methods to support wastewater infrastructure decision-making," European Journal of Operational Research, Elsevier, vol. 253(3), pages 746-760.
    5. Poyhonen, Mari & Hamalainen, Raimo P., 2001. "On the convergence of multiattribute weighting methods," European Journal of Operational Research, Elsevier, vol. 129(3), pages 569-585, March.
    6. Eduarda Asfora Frej & Adiel Teixeira Almeida & Ana Paula Cabral Seixas Costa, 2019. "Using data visualization for ranking alternatives with partial information and interactive tradeoff elicitation," Operational Research, Springer, vol. 19(4), pages 909-931, December.
    7. Yang, Guo-liang & Yang, Jian-Bo & Xu, Dong-Ling & Khoveyni, Mohammad, 2017. "A three-stage hybrid approach for weight assignment in MADM," Omega, Elsevier, vol. 71(C), pages 93-105.
    8. Aron Larsson & Mona Riabacke & Mats Danielson & Love Ekenberg, 2015. "Cardinal and Rank Ordering of Criteria — Addressing Prescription within Weight Elicitation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 1299-1330, November.
    9. Guitouni, Adel & Martel, Jean-Marc, 1998. "Tentative guidelines to help choosing an appropriate MCDA method," European Journal of Operational Research, Elsevier, vol. 109(2), pages 501-521, September.
    10. Adiel Teixeira Almeida & Eduarda Asfora Frej & Lucia Reis Peixoto Roselli, 2021. "Combining holistic and decomposition paradigms in preference modeling with the flexibility of FITradeoff," 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. 29(1), pages 7-47, March.
    11. Amelia Bilbao-Terol & Mar Arenas-Parra & Raquel Quiroga-García & Celia Bilbao-Terol, 2022. "An extended best–worst multiple reference point method: application in the assessment of non-life insurance companies," Operational Research, Springer, vol. 22(5), pages 5323-5362, November.
    12. Hsu-Shih Shih, 2016. "A Mixed-Data Evaluation in Group TOPSIS with Differentiated Decision Power," Group Decision and Negotiation, Springer, vol. 25(3), pages 537-565, May.
    13. Hocine, Amine & Kouaissah, Noureddine, 2020. "XOR analytic hierarchy process and its application in the renewable energy sector," Omega, Elsevier, vol. 97(C).
    14. Suk, Kwanho & Yoon, Song-Oh, 2012. "The moderating role of decision task goals in attribute weight convergence," Organizational Behavior and Human Decision Processes, Elsevier, vol. 118(1), pages 37-45.
    15. Eduarda Asfora Frej & Danielle Costa Morais & Adiel Teixeira de Almeida, 2022. "Negotiation Support Through Interactive Dominance Relationship Specification," Group Decision and Negotiation, Springer, vol. 31(3), pages 591-620, June.
    16. Jiménez, Antonio & Mateos, Alfonso & Sabio, Pilar, 2013. "Dominance intensity measure within fuzzy weight oriented MAUT: An application," Omega, Elsevier, vol. 41(2), pages 397-405.
    17. John R. Doyle, 1999. "Elicitation and Context Effects in Judgments: Fixed Sum Versus Fixed Scale Frames," Management Science, INFORMS, vol. 45(7), pages 972-979, July.
    18. de Almeida, Jonatas Araujo & Costa, Ana Paula Cabral Seixas & de Almeida-Filho, Adiel Teixeira, 2016. "A new method for elicitation of criteria weights in additive models: Flexible and interactive tradeoffAuthor-Name: de Almeida, Adiel Teixeira," European Journal of Operational Research, Elsevier, vol. 250(1), pages 179-191.
    19. Dong, Yucheng & Liu, Yating & Liang, Haiming & Chiclana, Francisco & Herrera-Viedma, Enrique, 2018. "Strategic weight manipulation in multiple attribute decision making," Omega, Elsevier, vol. 75(C), pages 154-164.
    20. Ahn, Byeong Seok, 2017. "Approximate weighting method for multiattribute decision problems with imprecise parameters," Omega, Elsevier, vol. 72(C), pages 87-95.

    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:wut:journl:v:2:y:2020:p:91-114:id:1486. 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: Adam Kasperski (email available below). General contact details of provider: https://edirc.repec.org/data/iopwrpl.html .

    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.