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A distance measure based intuitionistic triangular fuzzy multi-criteria group decision making method and its application

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Abstract

This paper aims to offer a group decision making (GDM) method based on intuitionistic triangular fuzzy information. Toward this end, a new ranking method for intuitionistic triangular fuzzy numbers (ITFNs) is firstly introduced based on the credibility measure theory, which can provide a total order on ITFNs. In view of the condition that interactions exist among the decision makers (DMs) or the criteria, the 2-additive Shapley intuitionistic triangular fuzzy aggregation (2ASITFA) operator is further proposed. According to the Wasserstein distance, a new distance measure of intuitionistic triangular fuzzy sets (ITFSs) is defined. Moreover, under the partial weak order information on the importance and interaction among the DMs and the criteria, the programming models are constructed to obtain the optimal 2-additive measure of the DMs and criteria respectively. Then, an intuitionistic triangular fuzzy multi-criteria GDM (ITFMCGDM) method is developed. At length, a practical example for evaluating the service quality of medical and nursing institutions (MNIs) is offered to illustrate the application of the proposed method.

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References

  1. Hirakawa Y, Chiang C, Aoyama A (2017) A qualitative study on barriers to achieving high-quality, community-based integrated dementia care. J Rural Med 12(1):28–32

    Article  Google Scholar 

  2. Heckman GA, Crutchlow L, Boscart V, Hillier L, Franco B, Lee L, Molnar F, Seitz D, Stolee P (2019) Quality assurance as a foundational element for an integrated system of dementia care: perspectives from physicians and geriatricians. Int J Health Care Qual Assur 32(6):978–990

    Article  Google Scholar 

  3. Tang ZH, Yu WH, Rao XL, Luo ZQ, Wang L (2017) The building of the “treatment-care and four linkage combination” integrated care model. Chin J Nurs 52(1):40–43

    Google Scholar 

  4. Fang JY, Zhang HC, Chen WQ, Shen Y, Wang SS, Ju CH, Guo Q (2020) Study on the establishment of health service quality evaluation index system of the pension institutions combined with medical service. Chin J Health Policy 13(4):24–30

    Google Scholar 

  5. Faul AC, D’Ambrosio JG, Yankeelov PA, Cotton SG, Furman CD, Hall-Faul M, Gordon B, Wright RB (2019) Human flourishing and integrated care models: the development of the flourish index. Gerontologist 59(6):653–663

    Article  Google Scholar 

  6. Segelman M, Szydlowski J, Kinosian B, McNabney M, Raziano DB, Eng C, van Reenen C, Greener HT (2014) Hospitalizations in the program of all-inclusive care for the elderly. J Am Geriatr Soc 62(2):320–324

    Article  Google Scholar 

  7. Deschodt M, Laurent G, Cornelissen L, Yip O, Zúñiga F, Denhaerynck K, Briel M, Karabegovic A, Geest SD (2020) Core components and impact of nurse-led integrated care models for home-dwelling older people: a systematic review and meta-analysis. Int J Nurs Stud 105:103552

    Article  Google Scholar 

  8. Tang J, Meng FY, Zhang YL (2021) Common probability-based interactive algorithms for group decision making with normalized probability linguistic preference relations. Fuzzy Optim Decis Mak 21:99–136. https://doi.org/10.1007/s10700-021-09360-1

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu F, Yuan XH (2007) Fuzzy number intuitionistic fuzzy set. Fuzzy Syst Math 21(1):88–91

    MATH  Google Scholar 

  10. Wang XF (2008) Fuzzy number intuitionistic fuzzy arithmetic aggregation operators. Int J Fuzzy Syst 10(2):104–111

    MathSciNet  Google Scholar 

  11. Chen K, Wang M (2017) Research on performance evaluation of projects loaned by international financial organizations with fuzzy number intuitionistic fuzzy information. J Intell Fuzzy Syst 33:3505–3514

    Article  Google Scholar 

  12. Chen DF, Zhang L, Jiao JS (2010) Triangle fuzzy number intuitionistic fuzzy aggregation operators and their application to group decision making. In: Wang FL, Deng H, Gao Y, Lei J (eds) Artificial Intelligence and Computational Intelligence. AICI 2010. Lecture notes in computer science, Vol 6320. Springer, Berlin

    Google Scholar 

  13. Yu DJ (2013) Prioritized information fusion method for triangular intuitionistic fuzzy set and its application to teaching quality evaluation. Int J Intell Syst 28:411–435

    Article  Google Scholar 

  14. Xia MM, Xu ZS, Zhu B (2012) Generalized intuitionistic fuzzy Bonferroni means. Int J Intell Syst 27(1):23–47

    Article  Google Scholar 

  15. Verma R (2015) Generalized bonferroni mean operator for fuzzy number intuitionistic fuzzy sets and its application to multiattribute decision making. Int J Intell Syst 30(5):499–519

    Article  Google Scholar 

  16. Mahmood T, Liu PD, Ye J, Khan Q (2018) Several hybrid aggregation operators for triangular intuitionistic fuzzy set and their application in multi-criteria decision making. Granul Comput 3(2):153–168

    Article  Google Scholar 

  17. Zhang QL, Liu F, Fan CQ, Xie WH (2018) Fuzzy numbers intuitionistic fuzzy descriptor systems. Inf Sci 469:44–59

    Article  MathSciNet  MATH  Google Scholar 

  18. Wu D, Yan XB, Peng R, Ma XY (2019) Multi-criteria decision making based on correlation coefficient of triangular intuitionistic fuzzy numbers. J Shanghai Jiaotong Univ (Sci) 24(4):480–484

    Article  Google Scholar 

  19. Xu J, Dong JY, Wan SP, Yang DY, Zeng YF (2019) A heterogeneous multiattribute group decision-making method based on intuitionistic triangular fuzzy information. Complexity. 2019:1–18. https://doi.org/10.1155/2019/9846582

    Article  MATH  Google Scholar 

  20. Zhang SL, Meng FY (2020) A group decision making method with intuitionistic triangular fuzzy preference relations and its application. Appl Intell 51:2556–2573

    Article  Google Scholar 

  21. Liu BD, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans Fuzzy Syst 10(4):445–450

    Article  Google Scholar 

  22. Liu BD (2002) Theory and practice of uncertain programming. Physica-Verlag, Heidelberg

    Book  MATH  Google Scholar 

  23. Zhang X, Liu PD (2010) Method for aggregating triangular fuzzy intuitionistic fuzzy information and its application to decision making. Technol Econ Dev Econ 16(2):280–290

    Article  Google Scholar 

  24. Lee ES, Li RL (1988) Comparison of fuzzy numbers based on the probability measure of fuzzy events. Comput Math Appl 15:887–896

    MathSciNet  MATH  Google Scholar 

  25. Liu YJ, Wu J, Liang CY (2015) Attitudinal ranking and correlated aggregating methods for multiple attribute group decision making with triangular intuitionistic fuzzy Choquet integral. Kybernetes 44(10):1437–1454

    Article  MathSciNet  Google Scholar 

  26. Wang W, Mendel JM (2019) Interval-valued intuitionistic fuzzy aggregation methodology for decision making with a prioritization of criteria. Iran J Fuzzy Syst 16(4):115–127

    MathSciNet  MATH  Google Scholar 

  27. Sugeno M (1974) Theory of fuzzy integral and its application, Ph.D. dissertation. Tokyo, Japan: Tokyo Institute of Technology

  28. Grabisch M (1996) The application of fuzzy integrals in multi-criteria decision making. Eur J Operat Res 89:445–456

    Article  MATH  Google Scholar 

  29. Grabisch M (1997) K-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst 92:167–189

    Article  MathSciNet  MATH  Google Scholar 

  30. Shapley LS (1953) A value for n-person game. In: Kuhn H, Tucker A (eds) Contributions to the theory of games, vol 2. Princeton Unversity Press, Princeton, pp 307–317

    Google Scholar 

  31. Meng FY, Tang J (2013) Interval-valued intuitionistic fuzzy multiattribute group decision making based on cross entropy measure and Choquet integral. Int J Intell Syst 28:1172–1195

    Article  Google Scholar 

  32. Nayagam V, Ponnialagan D, Jeevaraj S (2020) Similarity measure on incomplete imprecise interval information and its applications. Neural Comput Appl 32(8):3749–3761

    Article  Google Scholar 

  33. Irpino A, Verde R (2008) Dynamic clustering of interval data using a Wasserstein-based distance. Patt Rec Lett 29:1648–1658

    Article  MATH  Google Scholar 

  34. Grabisch M, Kojadinovic I, Meyer P (2008) A review of methods for capacity identification in Choquet integral based multi-attribute utility theory applications of the Kappalab R package. Eur J Operat Res 186:766–785

    Article  MathSciNet  MATH  Google Scholar 

  35. Wu JZ, Zhang Q, Du QJ, Dong ZL (2014) Compromise principle based methods of identifying capacities in the framework of multicriteria decision analysis. Fuzzy Sets Syst 246:91–106

    Article  MathSciNet  MATH  Google Scholar 

  36. Zhou XH, Yao J (2014) Triangular fuzzy number intuitionistic fuzzy power averaging operator and its application. Acta Anal Funct Appl 16(4):308–314

    MathSciNet  MATH  Google Scholar 

  37. Liu NN, Xu ZS, He Y, Zeng XJ (2020) An inverse prospect theory-based algorithm in extended incomplete additive probabilistic linguistic preference relation environment and its application in financial products selection. Fuzzy Optim Decis Ma 20:397–428. https://doi.org/10.1007/s10700-020-09348-3

    Article  MathSciNet  MATH  Google Scholar 

  38. Valipour A, Sarvari H, Tamosaitiene J (2018) Risk assessment in PPP projects by applying different MCDM methods and comparative results analysis. Adm Sci 8(4):80

    Article  Google Scholar 

  39. Zhang SL, Tang J, Meng FY, Yuan RP (2021) A group decision making method with interval-valued intuitionistic fuzzy preference relations and its application in the selection of cloud computing vendors for SMEs. Informatica 32(1):163–193

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No.71571192), the Innovation-Driven Project of Central South University (No. 2019KF-09), and the Major Project for National Natural Science Foundation of China (No. 71790615).

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Authors and Affiliations

  1. Business College, Qingdao Preschool Education College, Qingdao, 266318, China

    ShaoLin Zhang & FanYong Meng

  2. Archives, Qingdao Agricultural University, Qingdao, 266109, China

    Xia Li

  3. School of Management Science and Engineering, Nanjing University of Information Science & Technology, Nanjing, 210044, China

    FanYong Meng

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  1. ShaoLin Zhang
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  2. Xia Li
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Correspondence to FanYong Meng.

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Zhang, S., Li, X. & Meng, F. A distance measure based intuitionistic triangular fuzzy multi-criteria group decision making method and its application. Appl Intell 53, 9463–9482 (2023). https://doi.org/10.1007/s10489-022-04009-x

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