Stochastic Multiple Criteria Comprehensive Evaluation Based on Probabilistic Linguistic Preference Relations: A Case Study of Healthcare Insurance Audits in China


As a typical multiple criteria comprehensive evaluation (MCCE) problem, healthcare insurance audits (HIA) play a vital role in governmental audits. To handle the HIA in an autonomous region in China, a systematic methodology in the framework of MCCE is presented. An evaluation system is constructed at first based on the specific auditing objective. The group of individual preferences is collected by a probabilistic linguistic preference relation (PLPR). Its consistency and prioritization are handled based on the idea of stochastic analysis and the widely acknowledged techniques of linguistic preference relations (LPRs). Specifically, the consistency degree is measured by the probability of stochastically generated LPRs being with acceptable consistency, and then improved by revising the probabilistic distributions involved in the PLPR. The priority is derived by the expected value of priorities of the stochastically generated LPRs. Moreover, the comprehensive evaluation is conducted based on aspiration-based utility functions. The proposed methodology enables decision makers to determine parameters intuitively, and presents interpretable and admissible results. It is effective even if the original individual preferences are with low consistency degree. Finally, the focused HIA problem is solved based on the proposed methodology.

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  1. 1.

    Cabrerizo, F.J., Alonso, S., Herrera-Viedma, E.: A consensus model for group decision making problems with unbalanced fuzzy linguistic information. Int. J. Inf. Technol. Decis. Mak. 8(01), 109–131 (2009)

    MATH  Article  Google Scholar 

  2. 2.

    Feng, B., Lai, F.J.: Multi-attribute group decision making with aspirations: a case study. Omega 44, 136–147 (2014)

    Article  Google Scholar 

  3. 3.

    Fu, H.H., Lin, D.K., Tsai, H.T., Wei, D.: Applying lot-by-lot double sampling plan to reform Taiwan national health insurance auditing system. Qual. Quant. 43(4), 571–584 (2009)

    Article  Google Scholar 

  4. 4.

    Fu, H.H., Tsai, H.T., Lin, C.W., Wei, D.: Application of a single sampling plan for auditing medical-claim payments made by Taiwan national health insurance. Health Policy 70(2), 185–195 (2004)

    Article  Google Scholar 

  5. 5.

    Gao, J., Xu, Z.S., Ren, P.J., Liao, H.C.: An emergency decision making method based on the multiplicative consistency of probabilistic linguistic preference relations. Int. J. Mach. Learn. Cybern. 10(7), 1613–1629 (2019)

    Article  Google Scholar 

  6. 6.

    He, J.H.: Reorganization of anti-corruption agencies in China. J. Money Laund. Control 19(2), 106–108 (2016)

    Article  Google Scholar 

  7. 7.

    Lahdelma, R., Salminen, P.: SMAA-2: stochastic multicriteria acceptability analysis for group decision making. Oper. Res. 49(3), 444–454 (2001)

    MATH  Article  Google Scholar 

  8. 8.

    Li, C.C., Dong, Y.C., Xu, Y.J., Chiclana, F., Herrera-Viedma, E., Herrera, F.: An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and fusion: taxonomy and future directions. Inf. Fusion 52, 143–156 (2019)

    Article  Google Scholar 

  9. 9.

    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. Mak. 19(1), 81–134 (2020)

    MathSciNet  MATH  Article  Google Scholar 

  10. 10.

    Liu, G., Gong, K.: State Auditing and Anticorruption Campaign: Evidence from China, pp. 117–139. Springer Singapore, Singapore (2018)

  11. 11.

    Luo, S.Z., Zhang, H.Y., Wang, J.Q., Li, L.: Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations. J. Oper. Res. Soc. 70(12), 2039–2055 (2019)

    Article  Google Scholar 

  12. 12.

    Macharis, C., Milan, L., Verlinde, S.: A stakeholder-based multicriteria evaluation framework for city distribution. Res. Transp. Bus. Manag. 11, 75–84 (2014)

    Article  Google Scholar 

  13. 13.

    Martinez-Alier, J., Munda, G., O’Neill, J.: Weak comparability of values as a foundation for ecological economics. Ecol. Econ. 26(3), 277–286 (1998)

    Article  Google Scholar 

  14. 14.

    Munda, G.: Social multi-criteria evaluation: methodological foundations and operational consequences. Eur. J. Oper. Res. 158(3), 662–677 (2004)

    MathSciNet  MATH  Article  Google Scholar 

  15. 15.

    Orlovsky, S.: Decision-making with a fuzzy preference relation. Fuzzy Sets Syst. 1(3), 155–167 (1978)

    MathSciNet  MATH  Article  Google Scholar 

  16. 16.

    Paim, CdRP, Zucchi, P.: Evaluation auditing of the quality of health care in accreditation of health facilities. Ciencia & Saude Coletiva 16, 1163–1171 (2011)

    Article  Google Scholar 

  17. 17.

    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 

  18. 18.

    Rosen, R.: Complexity as a system property\(\dagger\). Int. J. Gen. Syst. 3(4), 227–232 (1977)

    MATH  Google Scholar 

  19. 19.

    Saaty, T.L.: A scaling method for priorities in hierarchical structures. J. Math. Psychol. 15(3), 234–281 (1977)

    MathSciNet  MATH  Article  Google Scholar 

  20. 20.

    Saaty, T.L.: Axiomatic foundation of the analytic hierarchy process. Manag. Sci. 32(7), 841–855 (1986)

    MathSciNet  MATH  Article  Google Scholar 

  21. 21.

    Saaty, T.L.: How to make a decision: the analytic hierarchy process. J. Oper. Res. Soc. 48(1), 9–26 (1990)

    MATH  Article  Google Scholar 

  22. 22.

    Saaty, T.L.: A ratio scale metric and the compatibility of ratio scales: the possibility of arrow’s impossibility theorem. Appl. Math. Lett. 7(6), 45–49 (1994)

    MathSciNet  MATH  Article  Google Scholar 

  23. 23.

    Schneider, T., Sommerfeld, W., Möller, J.: Audits across state borders for medical consulting agencies within the german healthcare insurance system. Gesundheitswesen 65(6), 365–370 (2003)

    Article  Google Scholar 

  24. 24.

    Shaikh, M., Woodward, M., Rahimi, K., Patel, A., Rath, S., MacMahon, S., Jha, V.: Use of major surgery in south india: a retrospective audit of hospital claim data from a large, community health insurance program. Surgery 157(5), 865–873 (2015)

    Article  Google Scholar 

  25. 25.

    Simon, H.A.: Rational choice and the structure of the environment. Psychol. Rev. 63(2), 129–138 (1956)

    Article  Google Scholar 

  26. 26.

    Sinha, P.C., Ghosh, S.K.: Determination of sample size for auditing medical insurance claims. J. Commer. Account. Res. 1(4), 24–32 (2012)

    Google Scholar 

  27. 27.

    Song, Y.M.: Deriving the priority weights from probabilistic linguistic preference relation with unknown probabilities. PLoS ONE 13(12), e0208855 (2018)

    Article  Google Scholar 

  28. 28.

    Tervonen, T., Lahdelma, R.: Implementing stochastic multicriteria acceptability analysis. Eur. J. Oper. Res. 178(2), 500–513 (2007)

    MATH  Article  Google Scholar 

  29. 29.

    Ureña, R., Chiclana, F., Morente-Molinera, J., Herrera-Viedma, E.: Managing incomplete preference relations in decision making: a review and future trends. Inf. Sci. 302, 14–32 (2015)

    MathSciNet  MATH  Article  Google Scholar 

  30. 30.

    Vetter, S., Studier-Fischer, S., Wentzensen, A., Frank, C.: The challenge of auditing by medical health insurance inspectors: development of individual case inspections according to 275ff SGB V. Der Unfallchirurg 112(8), 756–758 (2009)

    Article  Google Scholar 

  31. 31.

    Wang, H.: Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making. Int. J. Comput. Intell. Syst. 8(1), 14–33 (2015)

    Article  Google Scholar 

  32. 32.

    Wang, H., Xu, C., Xu, Z.S.: An approach to evaluate the methods of determining experts’ objective weights based on evolutionary game theory. Knowl.-Based Syst. 182, 104862 (2019)

    Article  Google Scholar 

  33. 33.

    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 

  34. 34.

    Wu, X.L., Liao, H.C., Xu, Z.S., Hafezalkotob, A., Herrera, F.: Probabilistic linguistic MULTIMOORA: a multicriteria decision making method based on the probabilistic linguistic expectation function and the improved Borda rule. IEEE Trans. Fuzzy Syst. 26(6), 3688–3702 (2018)

    Article  Google Scholar 

  35. 35.

    Wu, Z.B., Xu, J.P.: A consistency and consensus based decision support model for group decision making with multiplicative preference relations. Decis. Support Syst. 52(3), 757–767 (2012)

    Article  Google Scholar 

  36. 36.

    Xu, Z.S.: Deviation measures of linguistic preference relations in group decision making. Omega 33(3), 249–254 (2005)

    Article  Google Scholar 

  37. 37.

    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 

  38. 38.

    Yan, H.B., Ma, T., Sriboonchitta, S., Huynh, V.N.: A stochastic dominance based approach to consumer-oriented kansei evaluation with multiple priorities. Ann. Oper. Res. 256, 329–357 (2017)

    MathSciNet  MATH  Article  Google Scholar 

  39. 39.

    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8(3), 199–249 (1975)

    MathSciNet  MATH  Article  Google Scholar 

  40. 40.

    Zhang, Y.X., Xu, Z.S., Wang, H., Liao, H.C.: Consistency-based risk assessment with probabilistic linguistic preference relation. Appl. Soft Comput. 49, 817–833 (2016)

    Article  Google Scholar 

  41. 41.

    Zhu, B., Xu, Z.S., Zhang, R., Hong, M.: Generalized analytic network process. Eur. J. Oper. Res. 244(1), 277–288 (2015)

    MathSciNet  MATH  Article  Google Scholar 

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This work was supported in part by the National Natural Science Foundation of China (Nos. 71971119, 71972102), the social science foundation of Jiangsu Province (No. 19GLC009), the Key University Science Research Project of Jiangsu Province (No. 18KJB413006), and the 2018 Youth Teacher Research Project of Nanjing Audit University.

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Correspondence to Hai Wang.

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Xu, C., Qian, G. & Wang, H. Stochastic Multiple Criteria Comprehensive Evaluation Based on Probabilistic Linguistic Preference Relations: A Case Study of Healthcare Insurance Audits in China. Int. J. Fuzzy Syst. 22, 1607–1623 (2020).

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  • Multiple criteria analysis
  • Probabilistic linguistic preference relation
  • Complex linguistic expression
  • Aspiration
  • Healthcare insurance audit