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Normal Fuzzy Three-Way Decision Based on Prospect Theory

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Rough Sets (IJCRS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14481))

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Abstract

Prospect theory-based three-way decision has been successfully applied in various fuzzy information systems owing to its excellent performance in expressing the risk attitude of decision makers. However, the current prospect theory-based three-way decisions have two following limitations. On the one hand, they are constrained in processing uncertain continuous data or neglecting the distribution of uncertain fuzzy numbers. On the other hand, the risk attitudes of decision-makers are not considered when calculating the conditional probability. To address the two issues, we propose a normal fuzzy prospect theory-based three-way decision model and a normal fuzzy ideal solution method. First, since normal fuzzy numbers can describe the continuous uncertain data subjected to the normal distribution, we use it to represent the uncertain decision information, i.e., normal fuzzy outcome matrix, normal fuzzy reference points. Then, by integrating prospect theory and TOPSIS, we propose a normal fuzzy ideal solution method to calculate conditional probability, which considers the risk attitudes of decision-makers. Finally, the comparative experiments demonstrate the effectiveness and superiority of our proposal.

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References

  1. Gao, Y., Li, D.S., Zhong, H.: A novel target threat assessment method based on three-way decisions under intuitionistic fuzzy multi-attribute decision making environment. Eng. Appl. Artif. Intell. 87, 103276 (2020)

    Article  Google Scholar 

  2. Gu, C.-L., Wang, W., Wei, H.-Y.: Regression analysis model based on normal fuzzy numbers. In: Fan, T.-H., Chen, S.-L., Wang, S.-M., Li, Y.-M. (eds.) Quantitative Logic and Soft Computing 2016. AISC, vol. 510, pp. 487–504. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-46206-6_46

    Chapter  Google Scholar 

  3. Gu, J., Wang, Z., Xu, Z., Chen, X.: A decision-making framework based on the prospect theory under an intuitionistic fuzzy environment. Technol. Econ. Dev. Econ. 24(6), 2374–2396 (2018)

    Article  Google Scholar 

  4. Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47(2), 363–391 (1979)

    Article  MathSciNet  Google Scholar 

  5. Li, A.G., Zhang, Z.H., Meng, Y.: Fuzzy Mathematics and Its Application. Metallurgical Industry Press, Dongcheng (2005)

    Google Scholar 

  6. Liang, D.C., Xu, Z.S., Liu, D., Wu, Y.: Method for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy information. Inf. Sci. 435, 282–295 (2018)

    Article  MathSciNet  Google Scholar 

  7. Peng, Z.Z., Sun, Y.Y.: The Fuzzy Mathematics and Its Application. Wuhan University Press, Wuhan (2007)

    Google Scholar 

  8. Sang, G., Wu, T.: Normal fuzzy number multi-attribute decision making model and its application. J. Shanxi Univ. (Nat. Sci. Ed.) 36(1), 34–39 (2013)

    Google Scholar 

  9. Tian, X.L., Xu, Z.S., Gu, J., Herrera-Viedma, E.: How to select a promising enterprise for venture capitalists with prospect theory under intuitionistic fuzzy circumstance? Appl. Soft Comput. 67, 756–763 (2018)

    Article  Google Scholar 

  10. Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertain. 5(4), 297–323 (1992)

    Article  Google Scholar 

  11. Wang, T.X., Li, H.X., Zhou, X.Z., Huang, B., Zhu, H.B.: A prospect theory-based three-way decision model. Knowl.-Based Syst. 203, 106129 (2020)

    Article  Google Scholar 

  12. Wang, T.X., Li, H.X., Zhou, X.Z., Liu, D., Huang, B.: Three-way decision based on third-generation prospect theory with z-numbers. Inf. Sci. 569, 13–38 (2021)

    Article  MathSciNet  Google Scholar 

  13. Yang, M.S., Ko, C.H.: On a class of fuzzy c-numbers clustering procedures for fuzzy data. Fuzzy Sets Syst. 84(1), 49–60 (1996)

    Article  MathSciNet  Google Scholar 

  14. Yang, X.P., Yao, J.T.: Modelling multi-agent three-way decisions with decision-theoretic rough sets. Fund. Inform. 115(2–3), 157–171 (2012)

    MathSciNet  Google Scholar 

  15. Yang, X., Li, Y.H., Li, T.R.: A review of sequential three-way decision and multi-granularity learning. Int. J. Approx. Reason. 152, 414–433 (2022)

    Article  MathSciNet  Google Scholar 

  16. Yang, Z.L., Chang, J.P.: Interval-valued Pythagorean normal fuzzy information aggregation operators for multi-attribute decision making. IEEE Access 8, 51295–51314 (2020)

    Article  Google Scholar 

  17. Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180(3), 341–353 (2010)

    Article  MathSciNet  Google Scholar 

  18. Yao, Y.Y.: The superiority of three-way decisions in probabilistic rough set models. Inf. Sci. 181(6), 1080–1096 (2011)

    Article  MathSciNet  Google Scholar 

  19. Yao, Y.Y.: Interval sets and three-way concept analysis in incomplete contexts. Int. J. Mach. Learn. Cybernet. 8(1), 3–20 (2017)

    Article  MathSciNet  Google Scholar 

  20. Zhan, J.M., Wang, J.J., Ding, W.P., Yao, Y.Y.: Three-way behavioral decision making with hesitant fuzzy information systems: survey and challenges. IEEE/CAA J. Automatica Sinica (2022)

    Google Scholar 

  21. Zhang, S.C.: Cost-sensitive classification with respect to waiting cost. Knowl.-Based Syst. 23(5), 369–378 (2010)

    Article  Google Scholar 

  22. Zhong, Y., Li, Y., Yang, Y., Li, T., Jia, Y.: An improved three-way decision model based on prospect theory. Int. J. Approx. Reason. 142, 109–129 (2022)

    Article  MathSciNet  Google Scholar 

  23. Zhou, B., Yao, Y., Luo, J.: A three-way decision approach to email spam filtering. In: Farzindar, A., Kešelj, V. (eds.) AI 2010. LNCS (LNAI), vol. 6085, pp. 28–39. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13059-5_6

    Chapter  Google Scholar 

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Acknowledgements

This work was supported by the Natural Science Foundation of Sichuan Province (No. 2022NSFSC0528), the Sichuan Science and Technology Program (No. 2022ZYD0113), Jiaozi Institute of Fintech Innovation, Southwestern University of Finance and Economics (Nos. kjcgzh20230103, kjcgzh20230201), the Fundamental Research Funds for the Central Universities (No. JBK2307055).

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Authors and Affiliations

  1. School of Computing and Artificial Intelligence, Southwestern University of Finance and Economics, Chengdu, 611130, China

    Yanhua Li, Jiafen Liu & Xin Yang

  2. School of Sciences, Southwest Petroleum University, Chengdu, 610500, China

    Yihua Zhong

Authors
  1. Yanhua Li
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  2. Jiafen Liu
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  3. Yihua Zhong
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  4. Xin Yang
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Corresponding author

Correspondence to Xin Yang .

Editor information

Editors and Affiliations

  1. IRCCS Istituto Ortopedico Galeazzi, Milano, Italy

    Andrea Campagner

  2. Ghent University, Ghent, Belgium

    Oliver Urs Lenz

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Shuyin Xia

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. AGH University of Science and Technology, KrakĂłw, Poland

    Jarosław Wąs

  6. University of Regina, Regina, SK, Canada

    JingTao Yao

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Li, Y., Liu, J., Zhong, Y., Yang, X. (2023). Normal Fuzzy Three-Way Decision Based on Prospect Theory. In: Campagner, A., Urs Lenz, O., Xia, S., Ślęzak, D., Wąs, J., Yao, J. (eds) Rough Sets. IJCRS 2023. Lecture Notes in Computer Science(), vol 14481. Springer, Cham. https://doi.org/10.1007/978-3-031-50959-9_32

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  • DOI: https://doi.org/10.1007/978-3-031-50959-9_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-50958-2

  • Online ISBN: 978-3-031-50959-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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