IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v243y2015i1p258-270.html
   My bibliography  Save this article

Generalized ordered weighted utility averaging-hyperbolic absolute risk aversion operators and their applications to group decision-making

Author

Listed:
  • Gao, Jianwei
  • Li, Ming
  • Liu, Huihui

Abstract

This paper develops a new class of aggregation operator based on utility function, which introduces the risk attitude of decision makers (DMs) in the aggregation process. First, under the general framework of utility function, we provide a new operator called the generalized ordered weighted utility averaging (GOWUA) operator, and study its properties which are suitable for any utility function. Then, under the hyperbolic absolute risk aversion (HARA) utility function, we propose another new operator named as the generalized ordered weighted utility averaging-hyperbolic absolute risk aversion (GOWUA-HARA) operator, and further investigate its families including a wide range of aggregation operators. To determine the GOWUA-HARA operator weights, we put forward an orness measure of the GOWUA-HARA operator and analyze its properties. Considering that different DMs may have different opinions toward decision-making and their opinions can be characterized by different orness measures, we construct a new optimization model to determine the optimal weights which can aggregate all the individual sets of weights into an overall set of weights. Furthermore, based on the GOWUA-HARA operator, a method for the multiple attribute group decision-making (MAGDM) is developed. Finally, an example is given to illustrate the application of the GOWUA-HARA operator to the MAGDM.

Suggested Citation

  • Gao, Jianwei & Li, Ming & Liu, Huihui, 2015. "Generalized ordered weighted utility averaging-hyperbolic absolute risk aversion operators and their applications to group decision-making," European Journal of Operational Research, Elsevier, vol. 243(1), pages 258-270.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:1:p:258-270
    DOI: 10.1016/j.ejor.2014.11.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171400962X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.11.039?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. Merigó, José M. & Casanovas, Montserrat & Yang, Jian-Bo, 2014. "Group decision making with expertons and uncertain generalized probabilistic weighted aggregation operators," European Journal of Operational Research, Elsevier, vol. 235(1), pages 215-224.
    2. Llamazares, Bonifacio, 2004. "Simple and absolute special majorities generated by OWA operators," European Journal of Operational Research, Elsevier, vol. 158(3), pages 707-720, November.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    4. Grasselli, Martino, 2003. "A stability result for the HARA class with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 611-627, December.
    5. Maes, Koen C. & Saminger, Susanne & De Baets, Bernard, 2007. "Representation and construction of self-dual aggregation operators," European Journal of Operational Research, Elsevier, vol. 177(1), pages 472-487, February.
    6. Mesiar, R., 2007. "Fuzzy set approach to the utility, preference relations, and aggregation operators," European Journal of Operational Research, Elsevier, vol. 176(1), pages 414-422, January.
    7. Jung, Eun Ju & Kim, Jai Heui, 2012. "Optimal investment strategies for the HARA utility under the constant elasticity of variance model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 667-673.
    8. Yang, Jian-Bo, 2001. "Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties," European Journal of Operational Research, Elsevier, vol. 131(1), pages 31-61, May.
    9. Yang, Guo-liang & Yang, Jian-bo & Liu, Wen-bin & Li, Xiao-xuan, 2013. "Cross-efficiency aggregation in DEA models using the evidential-reasoning approach," European Journal of Operational Research, Elsevier, vol. 231(2), pages 393-404.
    10. Ribeiro, Rita Almeida & Marques Pereira, Ricardo Alberto, 2003. "Generalized mixture operators using weighting functions: A comparative study with WA and OWA," European Journal of Operational Research, Elsevier, vol. 145(2), pages 329-342, March.
    11. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    12. Xu, Dong-Ling & Yang, Jian-Bo & Wang, Ying-Ming, 2006. "The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1914-1943, November.
    13. Canós, L. & Liern, V., 2008. "Soft computing-based aggregation methods for human resource management," European Journal of Operational Research, Elsevier, vol. 189(3), pages 669-681, September.
    14. G R Amin & A Emrouznejad, 2010. "Finding relevant search engines results: a minimax linear programming approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(7), pages 1144-1150, July.
    15. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi & Feng, Bo, 2010. "The OWA-based consensus operator under linguistic representation models using position indexes," European Journal of Operational Research, Elsevier, vol. 203(2), pages 455-463, June.
    16. Chiclana, F. & Herrera-Viedma, E. & Herrera, F. & Alonso, S., 2007. "Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 182(1), pages 383-399, October.
    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. Rodrigo Gómez Monge & Evaristo Galeana Figueroa & Víctor G. Alfaro-García & José M. Merigó & Ronald R. Yager, 2021. "Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    2. Gao, Jianwei & Guo, Fengjia & Ma, Zeyang & Huang, Xin & Li, Xiangzhen, 2020. "Multi-criteria group decision-making framework for offshore wind farm site selection based on the intuitionistic linguistic aggregation operators," Energy, Elsevier, vol. 204(C).
    3. Liu, Peide & Li, Ying, 2021. "An improved failure mode and effect analysis method for multi-criteria group decision-making in green logistics risk assessment," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    4. Taylan G. Topcu & Konstantinos Triantis, 2022. "An ex-ante DEA method for representing contextual uncertainties and stakeholder risk preferences," Annals of Operations Research, Springer, vol. 309(1), pages 395-423, February.
    5. Fu, Chao & Yang, Jian-Bo & Yang, Shan-Lin, 2015. "A group evidential reasoning approach based on expert reliability," European Journal of Operational Research, Elsevier, vol. 246(3), pages 886-893.
    6. Homenda, Wladyslaw & Jastrzebska, Agnieszka & Pedrycz, Witold, 2016. "Multicriteria decision making inspired by human cognitive processes," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 392-411.
    7. Merigó, José M. & Palacios-Marqués, Daniel & Zeng, Shouzhen, 2016. "Subjective and objective information in linguistic multi-criteria group decision making," European Journal of Operational Research, Elsevier, vol. 248(2), pages 522-531.
    8. Li, Ying & Liu, Peide & Li, Gang, 2023. "An asymmetric cost consensus based failure mode and effect analysis method with personalized risk attitude information," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    9. Min Jiang & Rui Shen & Zhiqing Meng, 2019. "A Concession Equilibrium Solution Method without Weighted Aggregation Operators for Multiattribute Group Decision-Making Problems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-10, January.
    10. Jianwei Gao & Huihui Liu, 2017. "Generalized Ordered Weighted Reference Dependent Utility Aggregation Operators and Their Applications to Group Decision-Making," Group Decision and Negotiation, Springer, vol. 26(6), pages 1173-1207, November.
    11. Shouzhen Zeng & Jianping Chen & Xingsen Li, 2016. "A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 403-422, March.

    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. Gao, Jianwei & Li, Ming & Liu, Huihui, 2015. "Generalized ordered weighted utility proportional averaging-hyperbolic absolute risk aversion operators and their applications to group decision-making," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 114-132.
    2. Fu, Chao & Yang, Jian-Bo & Yang, Shan-Lin, 2015. "A group evidential reasoning approach based on expert reliability," European Journal of Operational Research, Elsevier, vol. 246(3), pages 886-893.
    3. Merigó, José M. & Casanovas, Montserrat & Yang, Jian-Bo, 2014. "Group decision making with expertons and uncertain generalized probabilistic weighted aggregation operators," European Journal of Operational Research, Elsevier, vol. 235(1), pages 215-224.
    4. Jianwei Gao & Huihui Liu, 2017. "Generalized Ordered Weighted Reference Dependent Utility Aggregation Operators and Their Applications to Group Decision-Making," Group Decision and Negotiation, Springer, vol. 26(6), pages 1173-1207, November.
    5. Hong‐Chih Huang, 2010. "Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 451-472, June.
    6. Fu, Chao & Yang, Shanlin, 2012. "An evidential reasoning based consensus model for multiple attribute group decision analysis problems with interval-valued group consensus requirements," European Journal of Operational Research, Elsevier, vol. 223(1), pages 167-176.
    7. Chang, Hao & Chang, Kai, 2017. "Optimal consumption–investment strategy under the Vasicek model: HARA utility and Legendre transform," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 215-227.
    8. Fu, Chao & Yang, Shanlin, 2011. "An attribute weight based feedback model for multiple attributive group decision analysis problems with group consensus requirements in evidential reasoning context," European Journal of Operational Research, Elsevier, vol. 212(1), pages 179-189, July.
    9. Alain Bensoussan & Ka Chun Cheung & Yiqun Li & Sheung Chi Phillip Yam, 2022. "Inter‐temporal mutual‐fund management," Mathematical Finance, Wiley Blackwell, vol. 32(3), pages 825-877, July.
    10. Munk, Claus, 2008. "Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3560-3589, November.
    11. Auffret, Philippe, 2001. "An alternative unifying measure of welfare gains from risk-sharing," Policy Research Working Paper Series 2676, The World Bank.
    12. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    13. Detemple, Jerome & Sundaresan, Suresh, 1999. "Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 835-872.
    14. Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2022. "Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 101-140, February.
    15. Carole Bernard & Franck Moraux & Ludger R�schendorf & Steven Vanduffel, 2015. "Optimal payoffs under state-dependent preferences," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1157-1173, July.
    16. Roche, Hervé & Tompaidis, Stathis & Yang, Chunyu, 2013. "Why does junior put all his eggs in one basket? A potential rational explanation for holding concentrated portfolios," Journal of Financial Economics, Elsevier, vol. 109(3), pages 775-796.
    17. J-B Yang & D-L Xu & X Xie & A K Maddulapalli, 2011. "Multicriteria evidential reasoning decision modelling and analysis—prioritizing voices of customer," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1638-1654, September.
    18. Gerrard, Russell & Kyriakou, Ioannis & Nielsen, Jens Perch & Vodička, Peter, 2023. "On optimal constrained investment strategies for long-term savers in stochastic environments and probability hedging," European Journal of Operational Research, Elsevier, vol. 307(2), pages 948-962.
    19. Munk, Claus & Sorensen, Carsten, 2004. "Optimal consumption and investment strategies with stochastic interest rates," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1987-2013, August.
    20. Bernard, Carole & Chen, Jit Seng & Vanduffel, Steven, 2015. "Rationalizing investors’ choices," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 10-23.

    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:eee:ejores:v:243:y:2015:i:1:p:258-270. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.