IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v6y2018i9p172-d170909.html
   My bibliography  Save this article

Optimizing Three-Dimensional Constrained Ordered Weighted Averaging Aggregation Problem with Bounded Variables

Author

Listed:
  • Hui-Chin Tang

    (Department of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan)

  • Shen-Tai Yang

    (Department of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan)

Abstract

A single constrained ordered weighted averaging aggregation (COWA) problem is of considerable importance in many disciplines. Two models are considered: the maximization COWA problem with lower bounded variables and the minimization COWA problem with upper bounded variables. For a three-dimensional case of these models, we present the explicitly optimal solutions theoretically and empirically. The bounds and weights can affect the optimal solution of the three-dimensional COWA problem with bounded variables.

Suggested Citation

  • Hui-Chin Tang & Shen-Tai Yang, 2018. "Optimizing Three-Dimensional Constrained Ordered Weighted Averaging Aggregation Problem with Bounded Variables," Mathematics, MDPI, vol. 6(9), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:9:p:172-:d:170909
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/6/9/172/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/6/9/172/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. José M. Merigó & Anna M. Gil-Lafuente & Li-Gang Zhou & Hua-You Chen, 2012. "Induced and Linguistic Generalized Aggregation Operators and Their Application in Linguistic Group Decision Making," Group Decision and Negotiation, Springer, vol. 21(4), pages 531-549, July.
    2. Ligang Zhou & Huayou Chen & Jinpei Liu, 2013. "Generalized Multiple Averaging Operators and their Applications to Group Decision Making," Group Decision and Negotiation, Springer, vol. 22(2), pages 331-358, March.
    3. Yager, Ronald R., 1997. "On the analytic representation of the Leximin ordering and its application to flexible constraint propagation," European Journal of Operational Research, Elsevier, vol. 102(1), pages 176-192, October.
    4. Ogryczak, Wlodzimierz & Sliwinski, Tomasz, 2003. "On solving linear programs with the ordered weighted averaging objective," European Journal of Operational Research, Elsevier, vol. 148(1), pages 80-91, July.
    5. Fernández, Elena & Pozo, Miguel A. & Puerto, Justo & Scozzari, Andrea, 2017. "Ordered Weighted Average optimization in Multiobjective Spanning Tree Problem," European Journal of Operational Research, Elsevier, vol. 260(3), pages 886-903.
    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. Violet Xinying Chen & J. N. Hooker, 2023. "A guide to formulating fairness in an optimization model," Annals of Operations Research, Springer, vol. 326(1), pages 581-619, July.
    2. Chassein, André & Goerigk, Marc & Kasperski, Adam & Zieliński, Paweł, 2020. "Approximating combinatorial optimization problems with the ordered weighted averaging criterion," European Journal of Operational Research, Elsevier, vol. 286(3), pages 828-838.
    3. Kostreva, Michael M. & Ogryczak, Wlodzimierz & Wierzbicki, Adam, 2004. "Equitable aggregations and multiple criteria analysis," European Journal of Operational Research, Elsevier, vol. 158(2), pages 362-377, October.
    4. Włodzimierz Ogryczak & Bartosz Kozłowski, 2011. "Reference point method with importance weighted ordered partial achievements," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 380-401, December.
    5. Pingtao Yi & Qiankun Dong & Weiwei Li, 2021. "A family of IOWA operators with reliability measurement under interval-valued group decision-making environment," Group Decision and Negotiation, Springer, vol. 30(3), pages 483-505, June.
    6. Mi Jung Son & Jin Han Park & Ka Hyun Ko, 2019. "Some Hesitant Fuzzy Hamacher Power-Aggregation Operators for Multiple-Attribute Decision-Making," Mathematics, MDPI, vol. 7(7), pages 1-33, July.
    7. Merigó, José M. & Palacios-Marqués, Daniel & Ribeiro-Navarrete, Belén, 2015. "Aggregation systems for sales forecasting," Journal of Business Research, Elsevier, vol. 68(11), pages 2299-2304.
    8. Merigó, José M. & Palacios-Marqués, Daniel & del Mar Benavides-Espinosa, María, 2015. "Aggregation methods to calculate the average price," Journal of Business Research, Elsevier, vol. 68(7), pages 1574-1580.
    9. Guillaume, Romain & Houé, Raymond & Grabot, Bernard, 2014. "Robust competence assessment for job assignment," European Journal of Operational Research, Elsevier, vol. 238(2), pages 630-644.
    10. Baak, Werner & Goerigk, Marc & Hartisch, Michael, 2024. "A preference elicitation approach for the ordered weighted averaging criterion using solution choice observations," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1098-1110.
    11. Mut, Murat & Wiecek, Margaret M., 2011. "Generalized equitable preference in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 212(3), pages 535-551, August.
    12. Ligang Zhou & Zhifu Tao & Huayou Chen & Jinpei Liu, 2014. "Intuitionistic Fuzzy Ordered Weighted Cosine Similarity Measure," Group Decision and Negotiation, Springer, vol. 23(4), pages 879-900, July.
    13. Weijun Xu & Xin Chen & Yucheng Dong & Francisco Chiclana, 2021. "Impact of Decision Rules and Non-cooperative Behaviors on Minimum Consensus Cost in Group Decision Making," Group Decision and Negotiation, Springer, vol. 30(6), pages 1239-1260, December.
    14. Ljubić, Ivana & Pozo, Miguel A. & Puerto, Justo & Torrejón, Alberto, 2024. "Benders decomposition for the discrete ordered median problem," European Journal of Operational Research, Elsevier, vol. 317(3), pages 858-874.
    15. Weinand, Jann Michael & Kleinebrahm, Max & McKenna, Russell & Mainzer, Kai & Fichtner, Wolf, 2019. "Developing a combinatorial optimisation approach to design district heating networks based on deep geothermal energy," Applied Energy, Elsevier, vol. 251(C), pages 1-1.
    16. Bashir Bashir & Özlem Karsu, 2022. "Solution approaches for equitable multiobjective integer programming problems," Annals of Operations Research, Springer, vol. 311(2), pages 967-995, April.
    17. Jörg Kalcsics & Stefan Nickel & Justo Puerto & Antonio Rodríguez-Chía, 2010. "The ordered capacitated facility location problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 203-222, July.
    18. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    19. Argyris, Nikolaos & Karsu, Özlem & Yavuz, Mirel, 2022. "Fair resource allocation: Using welfare-based dominance constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 560-578.
    20. Junling Zhang & Xiaowen Qi & Changyong Liang, 2018. "Tackling Complexity in Green Contractor Selection for Mega Infrastructure Projects: A Hesitant Fuzzy Linguistic MADM Approach with considering Group Attitudinal Character and Attributes’ Interdependen," Complexity, Hindawi, vol. 2018, pages 1-31, December.

    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:6:y:2018:i:9:p:172-:d:170909. 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.