Skip to main content
SpringerLink
Log in

Changing criteria weights to achieve fair VIKOR ranking: a postprocessing reranking approach

  • Published:
Autonomous Agents and Multi-Agent Systems Aims and scope Submit manuscript

Abstract

Ranking is a prerequisite for making decisions, and therefore it is a very responsible and frequently applied activity. This study considers fairness issues in a multi-criteria decision-making (MCDM) method called VIKOR (in Serbian language—VIšekriterijumska optimizacija i KOmpromisno Rešenje, which means Multiple Criteria Optimization and Compromise Solution). The method is specific because of its original property to search for the first-ranked compromise solutions based on the parameter v. The VIKOR method was modified in this paper to rank all the alternatives and find compromise solutions for each rank. Then, the obtained ranks were used to satisfy fairness constraints (i.e., the desired level of disparate impact) by criteria weights optimization. We built three types of mathematical models depending on decision makers’ (DMs’) preferences regarding the definition of the compromise parameter v. Metaheuristic optimization algorithms were explored in order to minimize the differences in VIKOR ranking prior to and after optimization. The proposed postprocessing reranking approach ensures fair ranking (i.e., the ranking without discrimination). The conducted experiments involve three real-life datasets of different sizes, well-known in the literature. The comparisons of the results with popular fair ranking algorithms include a comparative examination of several rank-based metrics intended to measure accuracy and fairness that indicate a high-quality competence of the suggested approach. The most significant contributions include developing automated and adaptive optimization procedures with the possibility of further adjustments following DMs’ preferences and matching fairness metrics with traditional MCDM goals in a comprehensive full VIKOR ranking.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Agarwal, A., Agarwal, S., Khanna, S., & Patil, P. (2020). Rank aggregation from pairwise comparisons in the presence of adversarial corruptions. In International Conference on Machine Learning International conference on machine learning (pp. 85–95).

  2. Alidrisi, H. (2021). An innovative job evaluation approach using the VIKOR algorithm. Journal of Risk and Financial Management, 14(6), 271. https://doi.org/10.3390/jrfm14060271

    Article  Google Scholar 

  3. Anvari, A., Zulkifli, N., & Arghish, O. (2014). Application of a modified VIKOR method for decision-making problems in lean tool selection. The International Journal of Advanced Manufacturing Technology, 71(5), 829–841. https://doi.org/10.1007/s00170-013-5520-x.

    Article  Google Scholar 

  4. Asudeh, A., Jagadish, H., Stoyanovich, J., Das, G. (2019). Designing fair ranking schemes. In Proceedings of the 2019 international conference on management of data (pp. 1259–1276). https://doi.org/10.1145/3299869.3300079.

  5. Barocas, S., & Selbst, A. D. (2016). Big data’s disparate impact. California Law Review, 104, 671.

    Google Scholar 

  6. Behzadian, M., Kazemzadeh, R. B., Albadvi, A., & Aghdasi, M. (2010). PROMETHEE: A comprehensive literature review on methodologies and applications. European Journal of Operational research, 200(1), 198–215. https://doi.org/10.1016/j.ejor.2009.01.021.

    Article  MATH  Google Scholar 

  7. Behzadian, M., Otaghsara, S. K., Yazdani, M., & Ignatius, J. (2012). A state-of the-art survey of TOPSIS applications. Expert Systems with applications, 39(17), 13051–13069. https://doi.org/10.1016/j.eswa.2012.05.056

    Article  Google Scholar 

  8. Beutel, A., Chen, J., Doshi, T., Qian, H., Wei, L., & Wu, Y., ... others (2019). Fairness in recommendation ranking through pairwise comparisons. In: Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining (pp. 2212–2220). https://doi.org/10.1145/3292500.3330745.

  9. Bozorg-Haddad, O., Solgi, M., & Loáiciga, H. A. (2017). Meta-heuristic and evolutionary algorithms for engineering optimization. Wiley.

    Book  Google Scholar 

  10. Burke, R. (2017). Multisided fairness for recommendation. arXiv preprint arXiv:1707.00093.

  11. Büyüközkan, G., & Ruan, D. (2008). Evaluation of software development projects using a fuzzy multi-criteria decision approach. Mathematics and Computers in Simulation, 77(5–6), 464–475. https://doi.org/10.1016/j.matcom.2007.11.015

    Article  MathSciNet  MATH  Google Scholar 

  12. Cao, Z., Zou, Y., Zhao, X., Hong, K., & Zhang, Y. (2021). Multidimensional fairness equilibrium evaluation of urban housing expropriation compensation based on VIKOR. Mathematics, 9(4), 430. https://doi.org/10.3390/math9040430

    Article  Google Scholar 

  13. Castillo, C. (2019). Fairness and transparency in ranking. ACM SIGIR forum (Vol. 52, pp. 64–71). https://doi.org/10.1145/3308774.3308783.

  14. Caton, S. & Haas, C. (2020). Fairness in machine learning: A survey. arXiv preprint arXiv:2010.04053.

  15. Chang, C.-L., & Hsu, C.-H. (2011). Applying a modified VIKOR method to classify land subdivisions according to watershed vulnerability. Water Resources Management, 25(1), 301–309. https://doi.org/10.1007/s11269-010-9700-2

    Article  Google Scholar 

  16. Chen, C., Cook, W. D., Imanirad, R., & Zhu, J. (2020). Balancing fairness and efficiency: Performance evaluation with disadvantaged units in non-homogeneous environments. European Journal of Operational Research, 287(3), 1003–1013. https://doi.org/10.1016/j.ejor.2020.05.015.

    Article  MathSciNet  MATH  Google Scholar 

  17. Chen, V.X. & Hooker, J. (2020). Balancing fairness and efficiency in an optimization model. arXiv preprint arXiv:2006.05963.

  18. Corbett-Davies, S. & Goel, S. (2018). The measure and mismeasure of fairness: A critical review of fair machine learning. arXiv preprint arXiv:1808.00023.

  19. Devi, K. (2011). Extension of VIKOR method in intuitionistic fuzzy environment for robot selection. Expert Systems with Applications, 38(11), 14163–14168. https://doi.org/10.1016/j.eswa.2011.04.227

    Article  Google Scholar 

  20. do Carmo Silva, M., Gavião, L. O., Gomes, C. F. S., & Lima, G. B. A. (2017). A proposal for the application of multicriteria analysis to rank countries according to innovation using the indicators provided by the world intellectual property organization. RAI Revista de Administração e Inovação, 14(3), 188–198. https://doi.org/10.1016/j.rai.2017.05.003

    Article  Google Scholar 

  21. Dodevska, Z., Delibašić, B., Radovanović, S., Suknović, M., & Marković. (2022). Prevention of discrimination in ranking using modified TOPSIS method (in Serbian). Proceedings of the 28th ICT conference “YU INFO 2022” (pp. 30–35).

  22. Dutta, S., Lanvin, B., & Wunsch-Vincent, S. (2015). The global innovation index 2015: Effective innovation policies for development. Cornell University, INSEAD, and WIPO.

  23. Fei, L., Deng, Y., & Hu, Y. (2019). DS-VIKOR: A new multi-criteria decision-making method for supplier selection. International Journal of Fuzzy Systems, 21(1), 157–175. https://doi.org/10.1007/s40815-018-0543-y

    Article  MathSciNet  Google Scholar 

  24. Feldman, M., Friedler, S.A., Moeller, J., Scheidegger, C., & Venkatasubramanian, S. (2015). Certifying and removing disparate impact. In: Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining (pp. 259–268). https://doi.org/10.1145/2783258.2783311

  25. Freimer, M., & Yu, P.-L. (1976). Some new results on compromise solutions for group decision problems. Management Science, 22(6), 688–693. https://doi.org/10.1287/mnsc.22.6.688

    Article  MathSciNet  MATH  Google Scholar 

  26. Fu, H.-P., Chu, K.-K., Chao, P., Lee, H.-H., & Liao, Y.-C. (2011). Using fuzzy AHP and VIKOR for benchmarking analysis in the hotel industry. The Service Industries Journal, 31(14), 2373–2389. https://doi.org/10.1080/02642069.2010.503874

    Article  Google Scholar 

  27. Gajane, P. & Pechenizkiy, M. (2017). On formalizing fairness in prediction with machine learning. arXiv preprint arXiv:1710.03184.

  28. Gandomi, A. H., & Deb, K. (2020). Implicit constraints handling for efficient search of feasible solutions. Computer Methods in Applied Mechanics and Engineering, 363, 112917. https://doi.org/10.1016/j.cma.2020.112917

    Article  MathSciNet  MATH  Google Scholar 

  29. Gao, R., & Shah, C. (2020). Toward creating a fairer ranking in search engine results. Information Processing & Management, 57(1), 102138. https://doi.org/10.1016/j.ipm.2019.102138

    Article  Google Scholar 

  30. Ghorabaee, M. K. (2016). Developing an MCDM method for robot selection with interval type-2 fuzzy sets. Robotics and Computer-Integrated Manufacturing, 37, 221–232. https://doi.org/10.1016/j.rcim.2015.04.007

    Article  Google Scholar 

  31. Ghosh, A., Dutt, R., & Wilson, C. (2021). When fair ranking meets uncertain inference. In: Proceedings of the 44th international ACM SIGIR conference on research and development in information retrieval (pp. 1033–1043). https://doi.org/10.1145/3404835.3462850

  32. Goraya, M. S., Singh, D., et al. (2021). A comparative analysis of prominently used MCDM methods in cloud environment. The Journal of Supercomputing, 77(4), 3422–3449. https://doi.org/10.1007/s11227-020-03393-w

    Article  Google Scholar 

  33. Govindan, K., & Jepsen, M. B. (2016). ELECTRE: A comprehensive literature review on methodologies and applications. European Journal of Operational Research, 250(1), 1–29. https://doi.org/10.1016/j.ejor.2015.07.019

    Article  MathSciNet  MATH  Google Scholar 

  34. Hajian, S., Bonchi, F., & Castillo, C. (2016). Algorithmic bias: From discrimination discovery to fairness-aware data mining. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining (pp. 2125–2126). https://doi.org/10.1145/2939672.2945386

  35. Hardt, M., Price, E., Price, E., & Srebro, N. (2016). Equality of opportunity in supervised learning. D. Lee, M. Sugiyama, U. Luxburg, I. Guyon, & R. Garnett (Eds.), Advances in neural information processing systems (Vol. 29). Curran Associates, Inc.

  36. Hofmann, H. (n.d.). UCI machine learning repository: Statlog (german credit data) data set. Retrieved from https://archive.ics.uci.edu/ml/datasets/statlog+(german+credit+data)

  37. Jahan, A., & Edwards, K. L. (2015). A state-of-the-art survey on the influence of normalization techniques in ranking: Improving the materials selection process in engineering design. Materials & Design (1980–2015), 65, 335–342. https://doi.org/10.1016/j.matdes.2014.09.022

    Article  Google Scholar 

  38. Jahan, A., Mustapha, F., Ismail, M. Y., Sapuan, S., & Bahraminasab, M. (2011). A comprehensive VIKOR method for material selection. Materials & Design, 32(3), 1215–1221. https://doi.org/10.1016/j.matdes.2010.10.015

    Article  Google Scholar 

  39. Jiang, W. (2016). Limited public resources allocation model based on social fairness using an extended VIKOR method. Kybernetes. https://doi.org/10.1108/K-05-2014-0108

    Article  Google Scholar 

  40. Karaboğa, D., & Ökdem, S. (2004). A simple and global optimization algorithm for engineering problems: Differential evolution algorithm. Turkish Journal of Electrical Engineering and Computer Sciences, 12(1), 53–60.

    Google Scholar 

  41. Katoch, S., Chauhan, S. S., & Kumar, V. (2021). A review on genetic algorithm: Past, present, and future. Multimedia Tools and Applications, 80(5), 8091–8126. https://doi.org/10.1007/s11042-020-10139-6.

    Article  Google Scholar 

  42. Kermany, N.R., Zhao, W., Yang, J., Wu, J., & Pizzato, L. (2020). An ethical multi-stakeholder recommender system based on evolutionary multi-objective optimization. In 2020 IEEE international conference on services computing (SCC) (pp. 478–480). https://doi.org/10.1109/SCC49832.2020.00074.

  43. Köchling, A., & Wehner, M. C. (2020). Discriminated by an algorithm: a systematic review of discrimination and fairness by algorithmic decision-making in the context of HR recruitment and HR development. Business Research, 13(3), 795–848. https://doi.org/10.1007/s40685-020-00134-w

    Article  Google Scholar 

  44. Kou, G., Olgu Akdeniz, Ö., Dinçer, H., & Yüksel, S. (2021). Fintech investments in European banks: A hybrid IT2 fuzzy multidimensional decision-making approach. Financial Innovation, 7(1), 1–28. https://doi.org/10.1186/s40854-021-00256-y.

    Article  Google Scholar 

  45. Kuhlman, C., VanValkenburg, M., & Rundensteiner, E. (2019). FARE: Diagnostics for fair ranking using pairwise error metrics. The world wide web conference (pp. 2936–2942). https://doi.org/10.1145/3308558.3313443.

  46. Kulkarni, A. J., & Siarry, P. (2021). Handbook of AI-based metaheuristics. CRC Press.

  47. Kusner, M.J., Loftus, J., Russell, C., & Silva, R. (2017). Counterfactual fairness. I. Guyon et al. (Eds.), Advances in neural information processing systems (Vol. 30). Curran Associates, Inc.

  48. Lahoti, P., Gummadi, K. P., & Weikum, G. (2019). iFair: Learning individually fair data representations for algorithmic decision making. In 2019 IEEE 35th international conference on data engineering (ICDE) (pp. 1334–1345). https://doi.org/10.1109/ICDE.2019.00121.

  49. Lee, C. K. H. (2018). A review of applications of genetic algorithms in operations management. Engineering Applications of Artificial Intelligence, 76, 1–12. https://doi.org/10.1016/j.engappai.2018.08.011

    Article  Google Scholar 

  50. Lee, H.-C., & Chang, C.-T. (2018). Comparative analysis of MCDM methods for ranking renewable energy sources in Taiwan. Renewable and Sustainable Energy Reviews, 92, 883–896. https://doi.org/10.1016/j.rser.2018.05.007

    Article  Google Scholar 

  51. Liou, J. J., Tsai, C.-Y., Lin, R.-H., & Tzeng, G.-H. (2011). A modified VIKOR multiple-criteria decision method for improving domestic airlines service quality. Journal of Air Transport Management, 17(2), 57–61. https://doi.org/10.1016/j.jairtraman.2010.03.004

    Article  Google Scholar 

  52. Luo, X., Chang, X., & Ban, X. (2016). Regression and classification using extreme learning machine based on L1-norm and L2-norm. Neurocomputing, 174, 179–186. https://doi.org/10.1016/j.neucom.2015.03.112

    Article  Google Scholar 

  53. Luo, X., & Wang, X. (2017). Extended VIKOR method for intuitionistic fuzzy multiattribute decision-making based on a new distance measure. Mathematical Problems in Engineering. https://doi.org/10.1155/2017/4072486.

  54. Mardani, A., Zavadskas, E. K., Govindan, K., Amat Senin, A., & Jusoh, A. (2016). VIKOR technique: A systematic review of the state of the art literature on methodologies and applications. Sustainability, 8(1), 37. https://doi.org/10.3390/su8010037

    Article  Google Scholar 

  55. Marini, F., & Walczak, B. (2015). Particle swarm optimization (PSO). a tutorial. Chemometrics and Intelligent Laboratory Systems, 149, 153–165. https://doi.org/10.1016/j.chemolab.2015.08.020

    Article  Google Scholar 

  56. Mehbodniya, A., Kaleem, F., Yen, K. K., & Adachi, F. (2013). A fuzzy extension of VIKOR for target network selection in heterogeneous wireless environments. Physical Communication, 7, 145–155. https://doi.org/10.1016/j.phycom.2013.02.002

    Article  Google Scholar 

  57. Mehrabi, N., Morstatter, F., Saxena, N., Lerman, K., & Galstyan, A. (2021). A survey on bias and fairness in machine learning. ACM Computing Surveys (CSUR), 54(6), 1–35.

    Article  Google Scholar 

  58. Meksavang, P., Shi, H., Lin, S.-M., & Liu, H.-C. (2019). An extended picture fuzzy VIKOR approach for sustainable supplier management and its application in the beef industry. Symmetry, 11(4), 468. https://doi.org/10.3390/sym11040468

    Article  Google Scholar 

  59. Meng, Y., Wu, H., Zhao, W., Chen, W., Dinçer, H., & Yüksel, S. (2021). A hybrid heterogeneous Pythagorean fuzzy group decision modelling for crowdfunding development process pathways of fintech-based clean energy investment projects. Financial Innovation, 7(1), 1–34. https://doi.org/10.1186/s40854-021-00250-4

    Article  Google Scholar 

  60. Moreno, L., Blanco, D., Muñoz, M. L., & Garrido, S. (2011). L1–L2-norm comparison in global localization of mobile robots. Robotics and Autonomous Systems, 59(9), 597–610. https://doi.org/10.1016/j.robot.2011.04.006

    Article  Google Scholar 

  61. Naeem, K., Riaz, M., & Karaaslan, F. (2021). A mathematical approach to medical diagnosis via pythagorean fuzzy soft TOPSIS, VIKOR and generalized aggregation operators. Complex & Intelligent Systems, 7(5), 2783–2795. https://doi.org/10.1007/s40747-021-00458-y

    Article  Google Scholar 

  62. Opara, K. R., & Arabas, J. (2019). Differential evolution: A survey of theoretical analyses. Swarm and Evolutionary Computation, 44, 546–558. https://doi.org/10.1016/j.swevo.2018.06.010.

    Article  Google Scholar 

  63. Opricovic, S. (1998). Multicriteria optimization in civil engineering (in Serbian). Belgrade: Faculty of Civil Engineering.

    Google Scholar 

  64. Opricovic, S., & Tzeng, G.-H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156(2), 445–455. https://doi.org/10.1016/S0377-2217(03)00020-1.

    Article  MATH  Google Scholar 

  65. Opricovic, S., & Tzeng, G.-H. (2007). Extended VIKOR method in comparison with outranking methods. European Journal of Operational Research, 178(2), 514–529. https://doi.org/10.1016/j.ejor.2006.01.020.

    Article  MATH  Google Scholar 

  66. Pandey, A. & Caliskan, A. (2021). Disparate impact of artificial intelligence bias in ridehailing economy’s price discrimination algorithms. In Proceedings of the 2021 AAAI/ACM conference on AI, Ethics, and Society (pp. 822–833). https://doi.org/10.1145/3461702.3462561.

  67. Pant, M., Zaheer, H., Garcia-Hernandez, L., Abraham, A., et al. (2020). Differential evolution: A review of more than two decades of research. Engineering Applications of Artificial Intelligence, 90, 103479. https://doi.org/10.1016/j.engappai.2020.103479

    Article  Google Scholar 

  68. Persson, A. (2016). Implicit bias in predictive data profiling within recruitments. In IFIP international summer school on privacy and identity management (pp. 212–230). https://doi.org/10.1007/978-3-319-55783-0_15

  69. PSO (n.d.). Particle swarm optimization (PSO) with constraint support. Retrieved from https://pythonhosted.org/pyswarm/ (BSD License)

  70. Rawls, J. (1999). A theory of justice (Revised). Cambridge, Massachusetts: The belknap press of Harvard University Press.

    Book  Google Scholar 

  71. Riaz, M., Hamid, M. T., Athar Farid, H. M., & Afzal, D. (2020). TOPSIS, VIKOR and aggregation operators based on \(q\)-rung orthopair fuzzy soft sets and their applications. Journal of Intelligent & Fuzzy Systems, 39(5), 6903–6917. https://doi.org/10.3233/JIFS-192175

    Article  Google Scholar 

  72. Riaz, M., & Tehrim, S. T. (2021). A robust extension of VIKOR method for bipolar fuzzy sets using connection numbers of SPA theory based metric spaces. Artificial Intelligence Review, 54(1), 561–591. https://doi.org/10.1007/s10462-020-09859-w.

    Article  Google Scholar 

  73. Roy, P. K., & Shaw, K. (2021). A multicriteria credit scoring model for SMEs using hybrid BWM and TOPSIS. Financial Innovation, 7(1), 1–27. https://doi.org/10.1186/s40854-021-00295-5

    Article  Google Scholar 

  74. Saaty, T. L. (2008). Relative measurement and its generalization in decision making why pairwise comparisons are central in mathematics for the measurement of intangible factors the analytic hierarchy/network process. RACSAM-Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 102(2), 251–318. https://doi.org/10.1007/BF03191825

    Article  MathSciNet  MATH  Google Scholar 

  75. Sacharidis, D., Mouratidis, K., & Kleftogiannis, D. (2019). A common approach for consumer and provider fairness in recommendations.

  76. Sayadi, M. K., Heydari, M., & Shahanaghi, K. (2009). Extension of VIKOR method for decision making problem with interval numbers. Applied Mathematical Modelling, 33(5), 2257–2262. https://doi.org/10.1016/j.apm.2008.06.002

    Article  MathSciNet  MATH  Google Scholar 

  77. SciPy community. (2022). SciPy Reference Guide. Release, 1.8.1.

  78. Shemshadi, A., Shirazi, H., Toreihi, M., & Tarokh, M. J. (2011). A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting. Expert Systems with Applications, 38(10), 12160–12167. https://doi.org/10.1016/j.eswa.2011.03.027.

    Article  Google Scholar 

  79. Solgi, R.M. (2020). Geneticalgorithm 1.0.2. MIT Licence https://pypi.org/project/geneticalgorithm/.

  80. Speicher, T., Heidari, H., Grgic-Hlaca, N., Gummadi, K.P., Singla, A., Weller, A., & Zafar, M.B. (2018). A unified approach to quantifying algorithmic unfairness: Measuring individual &group unfairness via inequality indices. In Proceedings of the 24th ACM SIGKDD international conference on knowledge discovery & data mining (pp. 2239–2248). https://doi.org/10.1145/3219819.3220046.

  81. Tehrim, S. T., & Riaz, M. (2020). An interval-valued bipolar fuzzy linguistic VIKOR method using connection numbers of SPA theory and its application to decision support system. Journal of Intelligent & Fuzzy Systems, 39(3), 3931–3948. https://doi.org/10.3233/JIFS-200038

    Article  Google Scholar 

  82. Tsoukalas, A., Parpas, P., & Rustem, B. (2009). A smoothing algorithm for finite min-max-min problems. Optimization Letters, 3(1), 49–62. https://doi.org/10.1007/s11590-008-0090-9

    Article  MathSciNet  MATH  Google Scholar 

  83. United Nations DESA. (2016). Transforming our world: The 2030 agenda for sustainable development, A/RES/70/1.

  84. Vahdani, B., Hadipour, H., Sadaghiani, J. S., & Amiri, M. (2010). Extension of VIKOR method based on interval-valued fuzzy sets. The International Journal of Advanced Manufacturing Technology, 47(9), 1231–1239. https://doi.org/10.1007/s00170-009-2241-2

    Article  Google Scholar 

  85. Vinogradova, I., Podvezko, V., & Zavadskas, E. K. (2018). The recalculation of the weights of criteria in MCDM methods using the Bayes approach. Symmetry, 10(6), 205. https://doi.org/10.3390/sym10060205

    Article  Google Scholar 

  86. Vogel, R., Bellet, A., & Clémençon, S. (2021). Learning fair scoring functions: Bipartite ranking under ROC-based fairness constraints. In International conference on artificial intelligence and statistics (pp. 784–792).

  87. Wang, D., Tan, D., & Liu, L. (2018). Particle swarm optimization algorithm: An overview. Soft Computing, 22(2), 387–408. https://doi.org/10.1007/s00500-016-2474-6.

    Article  Google Scholar 

  88. Webber, W., Moffat, A., & Zobel, J. (2010). A similarity measure for indefinite rankings. ACM Transactions on Information Systems (TOIS), 28(4), 1–38. https://doi.org/10.1145/1852102.1852106

    Article  Google Scholar 

  89. Yang, K. & Stoyanovich, J. (2017). Measuring fairness in ranked outputs. In Proceedings of the 29th international conference on scientific and statistical database management (pp. 1–6). https://doi.org/10.1145/3085504.3085526.

  90. Yang, W., & Wu, Y. (2020). A new improvement method to avoid rank reversal in VIKOR. IEEE Access, 8, 21261–21271. https://doi.org/10.1109/ACCESS.2020.2969681

    Article  Google Scholar 

  91. You, X.-Y., You, J.-X., Liu, H.-C., & Zhen, L. (2015). Group multi-criteria supplier selection using an extended VIKOR method with interval 2-tuple linguistic information. Expert Systems with Applications, 42(4), 1906–1916. https://doi.org/10.1016/j.eswa.2014.10.004

    Article  Google Scholar 

  92. Yu, D., Kou, G., Xu, Z., & Shi, S. (2021). Analysis of collaboration evolution in AHP research: 1982–2018. International Journal of Information Technology & Decision Making, 20(01), 7–36. https://doi.org/10.1142/S0219622020500406

    Article  Google Scholar 

  93. Yu, P.-L. (1973). A class of solutions for group decision problems. Management Science, 19(8), 936–946. https://doi.org/10.1287/mnsc.19.8.936.

    Article  MathSciNet  MATH  Google Scholar 

  94. Yu, P.-L. & Leitmann, G. (1976). Compromise solutions, domination structures, and salukvadze’s solution. Multicriteria decision making and differential games (pp. 85–101). Springer. https://doi.org/10.1007/BF00934871.

  95. Zajac, E. E. (1996). Political economy of fairness. MIT Press.

  96. Zehlike, M., Bonchi, F., Castillo, C., Hajian, S., Megahed, M., & Baeza-Yates, R. (2017). FA*IR: A fair top-k ranking algorithm. In Proceedings of the 2017 ACM on conference on information and knowledge management (pp. 1569–1578). https://doi.org/10.1145/3132847.3132938.

  97. Zehlike, M. & Castillo, C. (2020). Reducing disparate exposure in ranking: A learning to rank approach. In Proceedings of the web conference 2020 (pp. 2849–2855). https://doi.org/10.1145/3366424.3380048.

  98. Zehlike, M., Sühr, T., Baeza-Yates, R., Bonchi, F., Castillo, C., & Hajian, S. (2022). Fair top-\(k\) ranking with multiple protected groups. Information Processing & Management, 59(1), 102707. https://doi.org/10.1016/j.ipm.2021.102707

    Article  Google Scholar 

  99. Zehlike, M., Sühr, T., Castillo, C., &tanovski, I. (2020). FairSearch: A tool for fairness in ranked search results. In Companion proceedings of the web conference 2020 (pp. 172–175). https://doi.org/10.1145/3366424.3383534

  100. Zehlike, M., Yang, K., & Stoyanovich, J. (2021). Fairness in ranking: A survey. arXiv preprint arXiv:2103.14000.

  101. Zelany, M. (1974). A concept of compromise solutions and the method of the displaced ideal. Computers & Operations Research, 1(3–4), 479–496. https://doi.org/10.1016/0305-0548(74)90064-1

    Article  Google Scholar 

  102. Zeleny, M. (1975). Games with multiple payoffs. International Journal of Game Theory, 4(4), 179–191. https://doi.org/10.1007/BF01769266.

    Article  MathSciNet  MATH  Google Scholar 

  103. Zeng, Q.-L., Li, D.-D., & Yang, Y.-B. (2013). VIKOR method with enhanced accuracy for multiple criteria decision making in healthcare management. Journal of Medical Systems, 37(2), 1–9. https://doi.org/10.1007/s10916-012-9908-1.

    Article  Google Scholar 

  104. Zhang, J., Kou, G., Peng, Y., & Zhang, Y. (2021). Estimating priorities from relative deviations in pairwise comparison matrices. Information Sciences, 552, 310–327. https://doi.org/10.1016/j.ins.2020.12.008

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This paper is the result of the project ONR - N62909-19-1-2008 supported by the Office of Naval Research, the United States: Aggregating computational algorithms and human decision-making preferences in multi-agent settings, and realized by the University of Belgrade, Faculty of Organizational Sciences.

Author information

Author notes

  1. A. Petrović, S. Radovanović, and B. Delibašić contributed to this work according to the reported order.

Authors and Affiliations

  1. The Institute for Artificial Intelligence Research and Development of Serbia, 1 Fruškogorska, Novi Sad, 21000, Serbia

    Zorica Dodevska

  2. The University of Belgrade, Faculty of Organizational Sciences, 154 Jove Ilića, Belgrade, 11000, Serbia

    Andrija Petrović, Sandro Radovanović & Boris Delibašić

Authors
  1. Zorica Dodevska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrija Petrović
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sandro Radovanović
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Boris Delibašić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zorica Dodevska.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A: Lexicon of abbreviations and mathematical symbols

Appendix A: Lexicon of abbreviations and mathematical symbols

All abbreviations (mostly acronyms) are defined in the paper (when first-time usage). To facilitate the reading of the paper, Table 13 contains an alphabetically sorted list of repetitively used abbreviations, along with their meaning.

Table 13 List of repeating abbreviations
Full size table

Table 14 summarizes and explains the mathematical symbols used in the paper.

Table 14 List of mathematical symbols
Full size table

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dodevska, Z., Petrović, A., Radovanović, S. et al. Changing criteria weights to achieve fair VIKOR ranking: a postprocessing reranking approach. Auton Agent Multi-Agent Syst 37, 9 (2023). https://doi.org/10.1007/s10458-022-09591-5

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10458-022-09591-5

Keywords

Search

Navigation