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A Quantum Probabilistic Linguistic Term Framework to Multi-attribute Decision-Making for Battlefield Situation Assessment

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Abstract

The decision-making process is always associated with uncertainty and vagueness because of the incomplete decision data and unpredictable decision-making behavior. The concurrence of the epistemic uncertainty and the aleatory uncertainty, especially when only the qualitative data are accessible, poses more challenges to the decision-making. The probabilistic linguistic term set provides a flexible tool for data representation in such an environment. However, most of the existing decision-making methods for the probabilistic linguistic term sets depend on the aggregation operator. The subjectivity of the decision-makers and the decision-making behaviors are not fully considered. To solve this problem, a quantum-like probabilistic linguistic term decision-making framework is proposed, in which the quantum state, quantum data processing, and quantum interference effect are analyzed in detail. The decision-making beliefs of decision-makers are in a superposition state and their subjective relationships are depicted in the interference term. A multi-attribute decision-making method in this framework is then proposed for practical applications. Then the applications for sea-battlefield situation assessment are presented as the illustration and validation. A comparative analysis is also provided to depict the advantages of the proposed method, based on which appropriate conclusions and remarks are drawn.

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References

  1. Zadeh, L.A.: Concept of a linguistic variable and its application to approximate reasoning. 1. Inf. Sci. 8, 199–249 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  2. Degani, R., Bortolan, G.: The problem of linguistic approximation in clinical decision making. Int. J. Approximate Reason. 2, 143–162 (1988)

    Article  Google Scholar 

  3. R.R. Yager, A new methodology for ordinal multiobjective decisions based on fuzzy sets, in: Readings in Fuzzy Sets for Intelligent Systems, Morgan Kaufmann, 1993, pp. 751–756.

  4. Xu, Z.S.: A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf. Sci. 166, 19–30 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Xu, Z.S., Wang, H.: On the syntax and semantics of virtual linguistic terms for information fusion in decision making. Inf. Fusion 34, 43–48 (2017)

    Article  Google Scholar 

  6. Wang, H., Xu, Z.S., Zeng, X.J.: Modeling complex linguistic expressions in qualitative decision making: An overview. Knowl.-Based Syst. 144, 174–187 (2018)

    Article  Google Scholar 

  7. Yao, X., Wang, H., Xu, Z.S.: Probabilistic linguistic term envelopment analysis model. Int. J. Fuzzy Syst. 23, 262–279 (2021)

    Article  Google Scholar 

  8. Rodriguez, R.M., Martinez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20, 109–119 (2012)

    Article  Google Scholar 

  9. He, Y., Xu, Z.S.: An overview on recent researches of uncertain group decision making: Methodology, framework and development. Int. J. Inf. Technol. Decis. Mak. 20, 165–198 (2021)

    Article  Google Scholar 

  10. Hao, Z.N., Xu, Z.S., Zhao, H., Su, Z.: Probabilistic dual hesitant fuzzy set and its application in risk evaluation. Knowl.-Based Syst. 127, 16–28 (2017)

    Article  Google Scholar 

  11. Pang, Q., Wang, H., Xu, Z.S.: Probabilistic linguistic term sets in multi-attribute group decision making. Inf. Sci. 369, 128–143 (2016)

    Article  Google Scholar 

  12. Gu, J., Zheng, Y., Tian, X.L., Xu, Z.S.: A decision-making framework based on prospect theory with probabilistic linguistic term sets. J. Oper. Res. Soc. 72, 879–888 (2021)

    Article  Google Scholar 

  13. Tian, X.L., Xu, Z.S., Gu, J., Herrera, F.: A consensus process based on regret theory with probabilistic linguistic term sets and its application in venture capital. Inf. Sci. 562, 347–369 (2021)

    Article  MathSciNet  Google Scholar 

  14. Jiang, L.S., Liao, H.C.: A nondominated selection procedure with partially consistent non-reciprocal probabilistic linguistic preference relations and its application in social donation channel selection under the COVID-19 outbreaks. Inf. Sci. 564, 416–429 (2021)

    Article  MathSciNet  Google Scholar 

  15. Lin, M.W., Huang, C., Xu, Z.S., Chen, R.Q.: Evaluating IoT platforms using integrated probabilistic linguistic MCDM method. IEEE Internet Things J. 7, 11195–11208 (2020)

    Article  Google Scholar 

  16. Wen, Z., Liao, H.C., Emrouznejad, A.: Information representation of blockchain technology: Risk evaluation of investment by personalized quantifier with cubic spline interpolation. Inf. Process. Manage. 58, 1 (2021)

    Article  Google Scholar 

  17. Liao, H.C., Mi, X.M., Xu, Z.S.: A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions. Fuzzy Optim. Decis. Making 19, 81–134 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  18. Ali, J., Bashir, Z., Rashid, T.: WASPAS-based decision making methodology with unknown weight information under uncertain evaluations. Expert Syst. Appl. 168, 114143 (2021)

    Article  Google Scholar 

  19. Jiang, L.S., Liao, H.C.: A linear programming method based on probabilistic linguistic kolmogorov-smirnov distance for hospital service quality evaluation, in. IEEE Symp. Ser. Comput. Intell. 2019, 3195–3200 (2019)

    Google Scholar 

  20. Zhang, X.L., Liao, H.C., Xu, B., Xiong, M.F.: A probabilistic linguistic-based deviation method for multi-expert qualitative decision making with aspirations. Appl. Soft Comput. J. 93, 106362 (2020)

    Article  Google Scholar 

  21. Zhang, Y.X., Xu, Z.S., Hao, Z.N., Liao, H.C.: Dynamic assessment of Internet public opinions based on the probabilistic linguistic Bayesian network and prospect theory. Appl. Soft Comput. 106, 107359 (2021)

    Article  Google Scholar 

  22. Xue, W.T., Xu, Z.S., Mi, X.S., Ren, Z.L.: Dynamic reference point method with probabilistic linguistic information based on the regret theory for public health emergency decision-making. Econ. Res.-Ekonomska Istrazivanja 1, 1–35 (2021)

    Google Scholar 

  23. Ma, Z., Zhu, J., Zhang, S.: Probabilistic-based expressions in behavioral multi-attribute decision making considering pre-evaluation. Fuzzy Optim. Decis. Making 20, 145–173 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  24. Busemeyer, J.R., Bruza, P.D.: Quantum Models of Cognition and Decision. Cambridge University Press, Cambridge (2012)

    Book  Google Scholar 

  25. Ishwarya, M.S., Cherukuri, A.K.: Quantum-inspired ensemble approach to multi-attributed and multi-agent decision-making. Appl. Soft Comput. 106, 107283 (2021)

    Article  Google Scholar 

  26. Moreira, C., Wichert, A.: Interference effects in quantum belief networks. Appl. Soft Comput. 25, 64–85 (2014)

    Article  Google Scholar 

  27. Brandenburger, A., Mura, P.L.: Team decision problems with classical and quantum signals. Philos. Trans. R. Soc. A 374, 20150096 (2016)

    Article  Google Scholar 

  28. Yearsley, J.M.: Advanced tools and concepts for quantum cognition: A tutorial. J. Math. Psychol. 78, 24–39 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  29. Herrera, F., Herrera-Viedma, E.: Choice functions and mechanisms for linguistic preference relations. Eur. J. Oper. Res. 120, 144–161 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  30. Lin, M.W., Chen, Z.Y., Xu, Z.S., Gou, X.J., Herrera, F.: Score function based on concentration degree for probabilistic linguistic term sets: An application to TOPSIS and VIKOR. Inf. Sci. 551, 270–290 (2021)

    Article  MathSciNet  Google Scholar 

  31. Wang, H., Liao, H., Xu, Z.S.: Order relations and operations on the set of probabilistic linguistic term sets. IEEE Trans. Fuzzy Syst. 1, 1 (2021)

    Google Scholar 

  32. Nielsen, M.A., Chuang, I.: Quantum computation and quantum information. Am. J. Phys. 70, 558–559 (2002)

    Article  Google Scholar 

  33. Lee, J.S., Bang, J., Lee, J., Lee, K.G.: Experimental demonstration on quantum sensitivity to available information in decision making. Sci. Rep. 9, 8 (2019)

    Google Scholar 

  34. Koksalmis, E., Kabak, Ö.: Deriving decision makers’ weights in group decision making: An overview of objective methods. Information Fusion 49, 146–160 (2019)

    Article  Google Scholar 

  35. Chao, X.R., Kou, G., Peng, Y., Viedma, E.H.: Large-scale group decision-making with non-cooperative behaviors and heterogeneous preferences: An application in financial inclusion. Eur. J. Oper. Res. 288, 271–293 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  36. Liu, Y., Eckert, C.M., Earl, C.: A review of fuzzy AHP methods for decision-making with subjective judgements. Exp. Syst. Appl. 161, 113738 (2020)

    Article  Google Scholar 

  37. Xia, M.M., Xu, Z.S.: Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment. Inf. Fusion 13, 31–47 (2012)

    Article  Google Scholar 

  38. Xu, Z.S.: Approaches to multi-stage multi-attribute group decision making. Int. J. Inf. Technol. Decis. Mak. 10, 121–146 (2011)

    Article  MATH  Google Scholar 

  39. Jolliffe, I.T., Cadima, J.: Principal component analysis: a review and recent developments. Philos. Trans. R. Soc. A 374, 20150202 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  40. Hao, Z.N., Xu, Z.S., Li, J.Y., Zhao, H.: A quantum-like intuitionistic fuzzy decision-making framework with applications to multi-attribute decision-making Problem, Technique report (2021).

  41. Moreira, C., Wichert, A.: Quantum-like bayesian networks for modeling decision making. Front. Psychol. 7, 20 (2016)

    Article  Google Scholar 

  42. He, Z.C., Chan, F.T.S., Jiang, W.: A quantum framework for modelling subjectivity in multi-attribute group decision making. Comput. Ind. Eng. 124, 560–572 (2018)

    Article  Google Scholar 

  43. 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 

  44. Ma, S.D., Zhang, H.Z., Yang, G.Q.: Target threat level assessment based on cloud model under fuzzy and uncertain conditions in air combat simulation. Aerosp. Sci. Technol. 67, 49–53 (2017)

    Article  Google Scholar 

  45. Yu, P., Liu, G., Wei, W., Tang, Z.: Research on airspace target threat assessment model in sea battlefield based on GA-RBF. In: 2nd IEEE International Conference on Automation, Electronics and Electrical Engineering, 2019, pp. 428–432.

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Funding

Funding was provided by University Natural Science Research Project of Jiangsu Province(CN) (Grant No. 19KJD510002).

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Authors and Affiliations

  1. Jiangsu Police Institute, Nanjing, 210031, China

    Junyao Li

  2. Unit 31431 of PLA, Shenyang, 110001, China

    Zhinan Hao

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  1. Junyao Li
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  2. Zhinan Hao
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Correspondence to Zhinan Hao.

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Li, J., Hao, Z. A Quantum Probabilistic Linguistic Term Framework to Multi-attribute Decision-Making for Battlefield Situation Assessment. Int. J. Fuzzy Syst. 24, 495–507 (2022). https://doi.org/10.1007/s40815-021-01151-5

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  • DOI: https://doi.org/10.1007/s40815-021-01151-5

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