Advertisement

Consistency Theory Framework of DHHFLPRs

  • Xunjie GouEmail author
  • Zeshui Xu
Chapter
  • 2 Downloads
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 396)

Abstract

In decision-making processes, preference relations are popular and powerful techniques for expert preference modeling (Ureña et al. in Inf Sci 302:14–32, 2015). Consistency measures of preference relations are the vital basis of group decision-making (GDM) and have been studied extensively, which show that the supplied preferences satisfy some transitive properties (Wu and Xu in Omega 65(3):28–40, 2016). Consistency measures mainly consist of two parts: (1) judging whether each preference relation is of acceptable consistency; (2) improving the preference relation with unacceptable consistency. Based on double hierarchy hesitant fuzzy linguistic preference information, Gou et al. (Inf Sci 489:93–112 2019), Gou et al. (Int J Strateg Prop Manag 42(1):1–23, 2020) discussed the additive consistency measures and multiplicative consistency measures for DHHFLPRs, respectively. In this chapter, we will deeply discuss these two consistency measures for DHHFLPRs.

References

  1. Alonso S, Herrera-Viedma E, Chiclana F, Herrera F (2010) A web based consensus support system for group decision making problems and incomplete preferences. Inf Sci 180:4477–4495MathSciNetCrossRefGoogle Scholar
  2. Baets BD, Meyer HD, Schuymer BD, Jenei S (2006) Cyclic evaluation of transitivity of reciprocal relations. Soc Choice Welf 26:217–238MathSciNetCrossRefGoogle Scholar
  3. Chen T, Liu L, Xiong W, Zhou LA (2018) Real estate boom and misallocation of capital in China (Working paper). Princeton UniversityGoogle Scholar
  4. Chiclana F, Herrera-Viedma E, Alonso S, Herrera F (2009) Cardinal consistency of reciprocal preference relations: a characterization of multiplicative transitivity. IEEE Trans Fuzzy Syst 17(1):14–23CrossRefGoogle Scholar
  5. Dong YC, Xu YF, Li HY (2008) On consistency measures of linguistic preference relations. Eur J Oper Res 189(2):430–444MathSciNetCrossRefGoogle Scholar
  6. Fu C, Yang SL (2010) The group consensus based evidential reasoning approach for multiple attributive group decision analysis. Eur J Oper Res 206(3):601–608MathSciNetCrossRefGoogle Scholar
  7. Gou XJ, Liao HC, Wang XX, Xu ZS, Herrera F (2020) Consensus based on multiplicative consistent double hierarchy linguistic preferences: Venture capital in real estate market. Int J Strateg Prop Manag 42(1):1–23Google Scholar
  8. Gou XJ, Liao HC, Xu ZS, Herrera F (2017) Double hierarchy hesitant fuzzy linguistic term set and multimoora method: A case of study to evaluate the implementation status of haze controlling measures. Inf Fusion 38:22–34CrossRefGoogle Scholar
  9. Gou XJ, Liao HC, Xu ZS, Min R, Herrera F (2019) Group decision making with double hierarchy hesitant fuzzy linguistic preference relations: consistency based measures, index and repairing algorithms and decision model. Inf Sci 489:93–112MathSciNetCrossRefGoogle Scholar
  10. Gou XJ, Xu ZS, Liao HC, Herrera F (2018) Multiple criteria decision making based on distance and similarity measures with double hierarchy hesitant fuzzy linguistic environment. Comput Ind Eng 126:516–530CrossRefGoogle Scholar
  11. Herrera-Viedma E, Alonso S, Chiclana F, Herrera F (2007) A consensus model for group decision making with incomplete fuzzy preference relations. IEEE Trans Fuzzy Syst 15(5):863–877CrossRefGoogle Scholar
  12. Li J, Wang JQ (2019) Multi-criteria decision making with probabilistic hesitant fuzzy information based on expected multiplicative consistency. Neural Comput Appl 31:8897–8915CrossRefGoogle Scholar
  13. Li J, Wang JQ, Hu JH (2019) Consensus building for hesitant fuzzy preference relations with multiplicative consistency. Comput Ind Eng 128:387–400CrossRefGoogle Scholar
  14. Liu C, Xiong W (2018) China’s real estate market (Working paper). National Bureau Econ Res.  https://doi.org/10.3386/w25297
  15. Sałabun W (2014) The Characteristic Objects Method: a new approach to identify a multi-criteria group decision-making model. Intl J Comput Tech Appl 5(5):1597–1602Google Scholar
  16. Sałabun W (2015) The Characteristic Objects Method: A new distance-based approach to multicriteria decision-making problems. J Multi-Criteria Decis Anal 22(1–2):37–50CrossRefGoogle Scholar
  17. Shang TZ, Lu SB, Li XF, Hei PY, Lei XH, Gong JG, Liu JH, Zhai JQ, Wang H (2017) Balancing development of major coal bases with available water resources in China through 2020. Appl Energy 194:735–750CrossRefGoogle Scholar
  18. Ureña R, Chiclana F, Morente-Molinera JA, Herrera-Viedma E (2015) Managing incomplete preference relations in decision making: are view and future trends. Inf Sci 302:14–32CrossRefGoogle Scholar
  19. Wang BL, Cai YP, Yin XA, Tan Q, Hao Y (2017) An integrated approach of system dynamics, orthogonal experimental design and inexact optimization for supporting water resources management under uncertainty. Water Resour Manag 31(5):1665–1694CrossRefGoogle Scholar
  20. Winz I, Brierley G, Trowsdale S (2009) The use of system dynamics simulation in water resources management. Water Resour Manag 23(7):1301–1323CrossRefGoogle Scholar
  21. Wu ZB, Xu JP (2016) Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations. Omega 65(3):28–40CrossRefGoogle Scholar
  22. Xia MM, Xu ZS (2011) Some issues on multiplicative consistency of interval reciprocal relations. Int J Inf Tech Decis Mak 10(6):1043–1065CrossRefGoogle Scholar
  23. Xia MM, Xu ZS, Chen J (2013) Algorithms for improving consistency or consensus of reciprocal [0,1]-valued preference relations. Fuzzy Sets Syst 216:108–133MathSciNetCrossRefGoogle Scholar
  24. Xia MM, Xu ZS, Wang Z (2014) Multiplicative consistency-based decision support system for incomplete linguistic preference relations. Int J Syst Sci 45(3):625–636MathSciNetCrossRefGoogle Scholar
  25. Xu ZS, Cai XQ, Szmidt E (2011) Algorithms for estimating missing elements of incomplete intuitionistic preference relations. Int J Intell Syst 26(9):787–813CrossRefGoogle Scholar
  26. Yu DJ, Xu ZS, Wang W (2018) Bibliometric analysis of fuzzy theory research in China: a 30-year perspective. Knowl-Based Syst 141:188–199CrossRefGoogle Scholar
  27. Zhu B, Xu ZS (2014) Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans Fuzzy Syst 22(1):35–45MathSciNetCrossRefGoogle Scholar
  28. Zhu B, Xu ZS, Xu JP (2014) Deriving a ranking from hesitant fuzzy preference relations under group decision making. IEEE Trans Cybern 44(8):1328–1337CrossRefGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.Business SchoolSichuan UniversityChengduChina

Personalised recommendations