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

Author

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  • 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 proportional averaging (GOWUPA) 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 proportional averaging-hyperbolic absolute risk aversion (GOWUPA-HARA) operator, and further investigate its families including a wide range of aggregation operators. To determine the GOWUPA-HARA operator weights, we put forward an orness measure of the GOWUPA-HARA operator and analyze its properties. Considering that different DMs may have different opinions towards decision-making and their opinions can be characterized by different orness measures, we construct a new nonlinear 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 GOWUPA-HARA operator, a method for multiple attribute group decision- making (MAGDM) is developed. Finally, an example is given to illustrate the application of the GOWUPA-HARA operator to the MAGDM.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:252:y:2015:i:c:p:114-132
    DOI: 10.1016/j.amc.2014.12.009
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    References listed on IDEAS

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    1. 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.
    2. repec:spr:grdene:v:22:y:2013:i:2:d:10.1007_s10726-011-9267-1 is not listed on IDEAS
    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. 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.
    5. Kim, Soung Hie & Choi, Sang Hyun & Kim, Jae Kyeong, 1999. "An interactive procedure for multiple attribute group decision making with incomplete information: Range-based approach," European Journal of Operational Research, Elsevier, vol. 118(1), pages 139-152, October.
    6. 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.
    7. repec:pal:jorsoc:v:61:y:2010:i:7:d:10.1057_jors.2009.53 is not listed on IDEAS
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    1. repec:spr:grdene:v:26:y:2017:i:6:d:10.1007_s10726-017-9535-9 is not listed on IDEAS
    2. 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.

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