Advertisement

Soft Computing

, Volume 23, Issue 2, pp 583–597 | Cite as

Exploiting the priority weights from interval linguistic fuzzy preference relations

  • Fanyong Meng
  • Jie Tang
  • Zeshui XuEmail author
Methodologies and Application

Abstract

Interval linguistic fuzzy preference relations (ILFPRs) are powerful tools to denote the decision makers’ uncertain qualitative preferences. To avoid the inconsistent ranking results, consistency analysis is very critical. This paper introduces a new additive consistency concept for ILFPRs, which satisfies all properties of the additive consistency concept for fuzzy preference relations. Then, a model to judging the additive consistency of ILFPRs is constructed. When ILFPRs are inconsistent, an approach to deriving additive consistent ILFPRs is presented. Considering the incomplete case, goal programming models to determining the missing values are established. Subsequently, a distance measure-based group consensus index is given to measuring the consensus of individual ILFPRs. Furthermore, a new method for group decision making with ILFPRs is developed, which is based on the additive consistency and consensus analysis. Finally, two numerical examples are offered to show the application of the developed procedure, and a comparison analysis is performed.

Keywords

Group decision making Interval linguistic fuzzy preference relation Additive consistency Consensus Programming model 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 71571192, 71571123, 71671188, and 71501189), the National Social Science Foundation of China (No. 16BJY119), the Innovation-Driven Planning Foundation of Central South University (No. 2016CXS027), the State Key Program of National Natural Science of China (No. 71431006), the Projects of Major International Cooperation NSFC (No. 71210003), the Hunan Province Foundation for Distinguished Young Scholars of China (No. 2016JJ1024), and the China Postdoctoral Science Foundation (No. 2016M602170).

Compliance with ethical standards

Conflict of interest

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

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Alonso S, Cabrerizo FJ, Chiclana F, Herrera F, Herrera-Viedma E (2009) Group decision-making with incomplete fuzzy linguistic preference relations. Int J Intell Syst 24(2):201–222CrossRefzbMATHGoogle Scholar
  2. Ben-Arieh D, Chen ZF (2006) Linguistic-labels aggregation and consensus measure for autocratic decision making using group recommendations. IEEE Trans Syst Man Cybern A 36(3):558–568CrossRefGoogle Scholar
  3. Büyüközkan G, Güleryüz S (2014) A new GDM based AHP framework with linguistic interval fuzzy preference relations for renewable energy planning. J Intell Fuzzy Syst 27(6):3181–3195MathSciNetGoogle Scholar
  4. Cabrerizo FJ, Heradio R, Pérez IJ, Herrera-Viedma E (2010) A selection process based on additive consistency to deal with incomplete fuzzy linguistic information. J Univ Comput Sci 16(1):62–81MathSciNetzbMATHGoogle Scholar
  5. Chen HY, Zhou LG, Han B (2011) On compatibility of uncertain additive linguistic preference relations and its application in the group decision making. Knowl Based Syst 24(24):816–823CrossRefGoogle Scholar
  6. Delgado M, Verdegay JL, Vila MA (1993) On aggregation operations of linguistic labels. Int J Intell Syst 8(3):351–370CrossRefzbMATHGoogle Scholar
  7. Dong YC, Xu YF, Li H (2008) On consistency measures of linguistic preference relations. Eur J Oper Res 189(2):430–444MathSciNetCrossRefzbMATHGoogle Scholar
  8. Dong YC, Xu YF, Li HY, Feng B (2010) The OWA-based consensus operator under linguistic representation models using position indexes. Eur J Oper Res 203(2):455–463CrossRefzbMATHGoogle Scholar
  9. Herrera F (1995) A sequential selection process in group decision making with linguistic assessment. Inf Sci 85(4):223–239CrossRefzbMATHGoogle Scholar
  10. Herrera F, Martínez L (2000) A 2-tuple linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752CrossRefGoogle Scholar
  11. Herrera F, Herrera-Viedma E, Verdegay JL (1996a) A model of consensus in group decision making under linguistic assessments. Fuzzy Set Syst 78(1):73–87MathSciNetCrossRefzbMATHGoogle Scholar
  12. Herrera F, Herrera-Viedma E, Verdegay JL (1996b) Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Set Syst 79(2):75–190MathSciNetCrossRefzbMATHGoogle Scholar
  13. Herrera F, Herrera-Viedma E, Verdegay JL (1997a) A rational consensus model in group decision making using linguistic assessments. Fuzzy Set Syst 88(1):31–49CrossRefzbMATHGoogle Scholar
  14. Herrera F, Herrera-Viedma E, Verdegay JL (1997b) Linguistic measures based on fuzzy coincidence for reaching consensus in group decision making. Int J Approx Reason 16(3–4):309–334CrossRefzbMATHGoogle Scholar
  15. Herrera-Viedma E, Chiclana F, Herrera F, Alonso S (2007) Group decision making model with incomplete fuzzy preference relations based on additive consistency. IEEE Trans Syst Man Cybern B 37(1):176–189CrossRefzbMATHGoogle Scholar
  16. Liu F (2009) Acceptable consistency analysis of interval reciprocal comparison matrices. Fuzzy Set Syst 160(18):2686–2700MathSciNetCrossRefzbMATHGoogle Scholar
  17. Meng FY, Zeng XL, Li ZY (2007) Research the priority methods of interval numbers complementary judgment matrix. In: International conference on grey systems and intelligent services, vol 1, pp 42–47Google Scholar
  18. Meng FY, An QX (2017) An approach for group decision making method with hesitant fuzzy preference relations. Knowl Based Syst 127:1–15CrossRefGoogle Scholar
  19. Meng FY, Chen XH (2016) A robust additive consistency-based method for decision making with triangular fuzzy reciprocal preference relations. Fuzzy Optim Decis Mak. doi: 10.1007/s10700-016-9262-8 zbMATHGoogle Scholar
  20. Meng FY, Chen XH (2017) A new method for triangular fuzzy compare wise judgment matrix process based on consistency analysis. Int J Fuzzy Syst 19:27–46MathSciNetCrossRefGoogle Scholar
  21. Meng FY, Tan CQ, Chen XH (2017a) Multiplicative consistency analysis for interval reciprocal preference relations: a comparative study. Omega 68:17–38CrossRefGoogle Scholar
  22. Meng FY, An QX, Tan CQ, Chen XH (2017b) An approach for group decision making with interval fuzzy preference relations based on additive consistency and consensus analysis. IEEE Trans Syst Man Cybern Syst 47:2069–2082CrossRefGoogle Scholar
  23. Sun BZ, Ma W (2015) An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application. Omega 51(2):83–92CrossRefGoogle Scholar
  24. Tang J, Meng FY (2017) A consistency-based method to decision making with triangular fuzzy multiplicative preference relations. Int J Fuzzy Syst. doi: 10.1007/s40815-017-0333-y Google Scholar
  25. Tanino T (1984) Fuzzy preference orderings in group decision making. Fuzzy Set Syst 12(2):117–131MathSciNetCrossRefzbMATHGoogle Scholar
  26. Tapia García JM, del Moral MJ, Martinez MA, Herrera-Viedma E (2012) A consensus model for group decision making problems with linguistic interval fuzzy preference relations. Expert Syst Appl 39(11):10022–10030CrossRefGoogle Scholar
  27. Xu ZS (2002) Research on compatibility and consistency of fuzzy complementary judgment matrices. J PLA Univ Sci Technol 3(2):94–96Google Scholar
  28. Xu ZS (2004a) A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf Sci 166(1–4):19–30MathSciNetCrossRefzbMATHGoogle Scholar
  29. Xu ZS (2004b) EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. Int J Uncertain Fuzziness Knowl Based Syst 12(6):791–810MathSciNetCrossRefzbMATHGoogle Scholar
  30. Xu ZS (2004c) Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf Sci 168(1–1):171–184CrossRefzbMATHGoogle Scholar
  31. Xu ZS (2006) An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations. Decis Support Syst 41(2):488–499CrossRefGoogle Scholar
  32. Xu ZS (2011) An approach to group decision making based on incomplete linguistic preference relations. Int J Inf Tech Decis Mak 1(4):631–634Google Scholar
  33. Xu JP, Wu ZB (2013) A maximizing consensus approach for object selection based on uncertain linguistic preference relations. Comput Ind Eng 64(4):999–1008CrossRefGoogle Scholar
  34. Xu YJ, Li KW, Wang HM (2014a) Incomplete interval fuzzy preference relations and their applications. Comput Ind Eng 67(1):93–103CrossRefGoogle Scholar
  35. Xu YJ, Ma F, Tao FF, Wang HM (2014b) Some methods to deal with unacceptable incomplete 2-tuple fuzzy linguistic preference relations in group decision making. Knowl Based Syst 56(3):179–190CrossRefGoogle Scholar
  36. Zadeh LA (1965) Fuzzy sets. Inf Control 8(65):338–353CrossRefzbMATHGoogle Scholar
  37. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-part I. Inf Sci 8(3):199–249CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of International AuditNanjing Audit UniversityNanjingChina
  2. 2.Business SchoolSichuan UniversityChengduChina
  3. 3.School of BusinessCentral South UniversityChangshaChina
  4. 4.School of Computer and SoftwareNanjing University of Information Science and TechnologyNanjingChina

Personalised recommendations