Cloud-based ERP system selection based on extended probabilistic linguistic MULTIMOORA method and Choquet integral operator

  • Shui-xia Chen
  • Jian-qiang WangEmail author
  • Tie-li Wang


Cloud-based enterprise resource planning (ERP) is a combination of standard ERP system and cloud flexibility. Adopting a suitable cloud-based ERP system is an uncertain multi-criteria decision-making problem. Probabilistic linguistic term sets (PLTSs) can be used to address the uncertainty in such problem. On the basis of PLTSs, we introduce an innovative two-step comparative method for the evaluation of cloud-based ERP systems. The extended multiple multi-objective optimisations by ratio analysis method within PLTSs are proposed to obtain the class of cloud-based ERP vendors. Two classes, namely, accepted and rejected, are obtained. Then, we select the suitable cloud-based ERP packages in the accepted class. We put forward the probabilistic linguistic Choquet integral operator to aggregate the ERP package evaluation matrices given the interrelationships between criteria. Subsequently, a new comparison method is introduced to obtain the final results. We conduct an illustrative example to prove the rationality of the presented method. The feasibility of this model is verified by comparative analysis and validity test.


Cloud-based ERP system selection Multi-criteria decision-making Probabilistic linguistic term sets MULTIMOORA method Choquet integral operator 

Mathematics Subject Classification




The authors would like to thank the editors and anonymous reviewers for their great help on this study. This work was supported by the National Natural Science Foundation of China (No. 71571193) and Postgraduate Survey Project of Central South University (No. 2018dcyj035).

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interests regarding the publication of this paper.


  1. Al-Ghofaili AA, Al-Mashari MA (2014) ERP system adoption traditional ERP systems vs. cloud-based ERP systems. In: Fourth edition of the international conference on the innovative computing technology (INTECH 2014), Luton, UKGoogle Scholar
  2. Bai C, Zhang R, Qian L, Wu Y (2017) Comparisons of probabilistic linguistic term sets for multi-criteria decision making. Knowl Based Syst 119:284–291CrossRefGoogle Scholar
  3. Bao G-Y, Lian X-L, He M, Wang L-L (2010) Improved two-tuple linguistic representation model based on new linguistic evaluation scale. Control Decis 25(5):780–784MathSciNetGoogle Scholar
  4. Brauers WK, Zavadskas EK (2006) The MOORA method and its application to privatization in a transition economy. Control Cybern 35:445–469MathSciNetzbMATHGoogle Scholar
  5. Brauers WKM, Zavadskas EK (2011) MULTIMOORA optimization used to decide on a bank loan to buy property. Technol Econ Dev Econ 17(1):174–188CrossRefGoogle Scholar
  6. Brauers WKM, Zavadskas EK (2012) Robustness of MULTIMOORA: a method for multi-objective optimization. Informatica 23(1):1–25MathSciNetzbMATHGoogle Scholar
  7. Brauers WKM, Zavadskas EK, Kildienė S (2014) Was the construction sector in 20 European countries anti-cyclical during the recession years 2008–2009 as measured by multicriteria analysis (MULTIMOORA)? Procedia Comput Sci 31:949–956CrossRefGoogle Scholar
  8. Choquet G (1953) Theory of capacities. Ann Inst Fourier 5:131–295MathSciNetCrossRefGoogle Scholar
  9. Gürbüz T, Alptekin SE, Işıklar Alptekin G (2012) A hybrid MCDM methodology for ERP selection problem with interacting criteria. Decis Support Syst 54(1):206–214CrossRefGoogle Scholar
  10. Hafezalkotob A, Hafezalkotob A, Liao H, Herrera F (2019) An overview of MULTIMOORA for multi-criteria decision-making: theory, developments, applications, and challenges. Inf Fusion 51:145–177CrossRefGoogle Scholar
  11. Hao Z, Xu Z, Zhao H, Su Z (2017) Probabilistic dual hesitant fuzzy set and its application in risk evaluation. Knowl Based Syst 127:16–28CrossRefGoogle Scholar
  12. Hua G, Song XX (2010) Fuzzy comprehensive appraisal of ERP selection. In: Electrical and control engineering (ICECE), 2010 international conference, Wuhan, ChinaGoogle Scholar
  13. Joshi D, Kumar S (2016) Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making. Eur J Oper Res 248(1):183–191MathSciNetCrossRefGoogle Scholar
  14. Kilic HS, Zaim S, Delen D (2014) Development of a hybrid methodology for ERP system selection: the case of Turkish Airlines. Decis Support Syst 66(Supplement C):82–92CrossRefGoogle Scholar
  15. Kilic HS, Zaim S, Delen D (2015) Selecting “the best” ERP system for SMEs using a combination of ANP and PROMETHEE methods. Expert Syst Appl 42(5):2343–2352CrossRefGoogle Scholar
  16. Lee K-M, Leekwang H (1995) Identification of λ-fuzzy measure by genetic algorithms. Fuzzy Set Syst 75(3):301–309MathSciNetCrossRefGoogle Scholar
  17. Li J, Wang J-q (2018) Multi-criteria decision-making with probabilistic hesitant fuzzy information based on expected multiplicative consistency. Neural Comput Appl. CrossRefGoogle Scholar
  18. Li J, Wang JQ, Hu JH (2018) Multi-criteria decision-making method based on dominance degree and BWM with probabilistic hesitant fuzzy information. Int J Mach Learn Cybern. CrossRefGoogle Scholar
  19. Liang D, Kobina A, Quan W (2018) Grey relational analysis method for probabilistic linguistic multi-criteria group decision-making based on geometric Bonferroni mean. Int J Fuzzy Syst 20(7):2234–2244CrossRefGoogle Scholar
  20. Liao H, Xu Z, Zeng X-J (2014) Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf Sci 271:125–142MathSciNetCrossRefGoogle Scholar
  21. López C, Ishizaka A (2017) GAHPSort: a new group multi-criteria decision method for sorting a large number of the cloud-based ERP solutions. Comput Ind 92–93:12–24CrossRefGoogle Scholar
  22. Luo SZ, Zhang HY, Wang JQ (2018) Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations. J Oper Res Soc. CrossRefGoogle Scholar
  23. Moreira NJM, Duarte LT, Lavor C, Torezzan C (2017) A novel low-rank matrix completion approach to estimate missing entries in Euclidean distance matrix. Comput Appl Math 4:1–11zbMATHGoogle Scholar
  24. Nie R-X, Tian Z-P, Wang J-Q, Hu J-H (2019) Pythagorean fuzzy multiple criteria decision analysis based on Shapley fuzzy measures and partitioned normalized weighted Bonferroni mean operator. Int J Intell Syst 34(2):297–324CrossRefGoogle Scholar
  25. Ogunrinde RR, Jusoh YY, Pa NC, Ab Wan, Rahman WN, Abdullah A (2016) Cloud enterprise resource planning selection model for small and medium enterprises. Adv Sci Lett 22(8):1939–1943CrossRefGoogle Scholar
  26. Pang Q, Wang H, Xu Z (2016) Probabilistic linguistic term sets in multi-attribute group decision making. Inf Sci 369:128–143CrossRefGoogle Scholar
  27. Parthasarathy S, Sharma S (2014) Determining ERP customization choices using nominal group technique and analytical hierarchy process. Comput Ind 65(6):1009–1017CrossRefGoogle Scholar
  28. Peng H, Wang J (2018) A multicriteria group decision-making method based on the normal cloud model with Zadeh’s Z-numbers. IEEE Trans Fuzzy Syst 26(6):3246–3260CrossRefGoogle Scholar
  29. Peng H, Zhang H, Wang J (2018a) Cloud decision support model for selecting hotels on with probabilistic linguistic information. Int J Hosp Manag 68:124–138CrossRefGoogle Scholar
  30. Peng J, Wang J, Hu J (2018b) Multi-criteria decision-making approach based on single-valued neutrosophic hesitant fuzzy geometric weighted Choquet integral Heronian mean operator. J Intell Fuzzy Syst 35(3):3661–3674CrossRefGoogle Scholar
  31. Rodriguez RM, Martinez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119CrossRefGoogle Scholar
  32. Tan C, Chen X (2010) Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Syst Appl 37(1):149–157CrossRefGoogle Scholar
  33. Verville J, Halingten A (2002) An investigation of the decision process for selecting an ERP software: the case of ESC. Manag Decis 40(3):206–216CrossRefGoogle Scholar
  34. Wang X, Triantaphyllou E (2008) Ranking irregularities when evaluating alternatives by using some ELECTRE methods. Omega 36(1):45–63CrossRefGoogle Scholar
  35. Wang XK, Wang JQ, Zhang HY (2018) Distance-based multi-criteria group decision-making approach with probabilistic linguistic term sets. Expert Syst. CrossRefGoogle Scholar
  36. Wu X, Liao H, Xu Z, Hafezalkotob A, Herrera F (2018) Probabilistic linguistic MULTIMOORA: a multi-criteria decision making method based on the probabilistic linguistic expectation function and the improved borda rule. IEEE Trans Fuzzy Syst 26(6):3688–3702CrossRefGoogle Scholar
  37. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefGoogle Scholar
  38. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning—II. Inf Sci 8(4):301–357MathSciNetCrossRefGoogle Scholar
  39. Zhang S, Xu Z, He Y (2017) Operations and integrations of probabilistic hesitant fuzzy information in decision making. Inf Fusion 38:1–11CrossRefGoogle Scholar
  40. Zhang X, Zhang H, Wang J (2019) Discussing incomplete 2-tuple fuzzy linguistic preference relations in multi-granular linguistic MCGDM with unknown weight information. Soft Comput 23(6):2015–2032CrossRefGoogle Scholar
  41. Zhao H, You J-X, Liu H-C (2017) Failure mode and effect analysis using MULTIMOORA method with continuous weighted entropy under interval-valued intuitionistic fuzzy environment. Soft Comput 21(18):5355–5367CrossRefGoogle Scholar

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© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.School of BusinessCentral South UniversityChangshaPeople’s Republic of China
  2. 2.Management SchoolUniversity of South ChinaHengyangPeople’s Republic of China

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