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A decision making model based on intuitionistic multiplicative preference relations with approximate consistency

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Abstract

Intuitionistic fuzzy numbers possess the ability to model the bipolarity of practical objects and phenomena. The positive and negative opinions of decision makers (DMs) could be captured by intuitionistic multiplicative preference relations (IMPRs). In this study, the known consistency definitions of IMPRs are reviewed and the underlying ideas are analyzed. By considering the uncertainty shown by IMPRs, the concept of approximate consistency (AC) is proposed. Then the AC and acceptable AC of IMPRs are defined by dividing the non-determinacy judgements of the DM with the introduction of an attitude factor. The methods of eliciting the priorities of alternatives from an IMPR with acceptable AC are studied. A decision making model is proposed by considering the acceptable AC of IMPRs. Numerical results are reported to demonstrate that the application of different attitude factors could lead to different optimal solutions. It is observed that the inherent property of IMPRs should be incorporated into theoretical and practical models under intuitionistic fuzzy environments.

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References

  1. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  MATH  Google Scholar 

  2. Atanassov KT (2012) On intuitionistic fuzzy sets theory. Springer-Verlag, Berlin

    Book  MATH  Google Scholar 

  3. Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York

    MATH  Google Scholar 

  4. Gong ZW, Li LS, Forrest J, Zhao Y (2011) The optimal priority models of the intuitionistic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity. Expert Syst Appl 38:4394–4402

    Article  Google Scholar 

  5. Gong ZW, Li LS, Zhou FX, Yao TX (2009) Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations. Comput Ind Eng 57:1187–1193

    Article  Google Scholar 

  6. Herrera-Viedma E, Herrera F, Chiclana F, Luque M (2004) Some issues on consistency of fuzzy preference relations. Eur J Oper Res 154:98–109

    Article  MathSciNet  MATH  Google Scholar 

  7. Jiang Y, Xu ZS, Yu XH (2015) Group decision making based on incomplete intuitionistic multiplicative preference relations. Inf Sci 295:33–52

    Article  MathSciNet  MATH  Google Scholar 

  8. Jiang Y, Xu ZS, Yu XH (2013) Compatibility measures and consensus models for group decision making with intuitionistic multiplicative preference relations. Appl Soft Comput 13:2075–2086

    Article  Google Scholar 

  9. Jin FF, Ni ZW, Pei LD, Chen HY, Li YP (2018) Goal programming approach to derive intuitionistic multiplicative weights based on intuitionistic multiplicative preference relations. Int J Mach Learn Cybernet 9:641–650

    Article  Google Scholar 

  10. Li DF (ed) (2014) Decision and game theory in management with intuitionistic fuzzy sets. In: Studies in fuzziness and soft computing, vol. 308. Springer

  11. Liao HC, Xu ZS (2014) Priorities of intuitionistic fuzzy preference relation based on multiplicative consistency. IEEE Trans Fuzzy Syst 22:1669–1681

    Article  Google Scholar 

  12. Lin L, Yuan XH, Xia ZQ (2007) Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets. J Comput Syst Sci 73:84–88

    Article  MathSciNet  MATH  Google Scholar 

  13. Liu BD (2010) Uncertainty theory: a branch of mathematics for modelling human uncertainty. Springer, Berlin

    Book  Google Scholar 

  14. Liu F (2009) Acceptable consistency analysis of interval reciprocal comparison matrices. Fuzzy Sets Syst 160:2686–2700

    Article  MathSciNet  MATH  Google Scholar 

  15. Liu PD, Cao H (2019) Some intuitionistic fuzzy power Bonferroni mean operators in the framework of Dempster-Shafer theory and their application to multicriteria decision making. Appl Soft Comput J 85:105790

    Article  Google Scholar 

  16. Liu F, Pedrycz W, Wang ZX, Zhang WG (2017) An axiomatic approach to approximation-consistency of triangular fuzzy reciprocal preference relations. Fuzzy Sets Syst 322:1–18

    Article  MathSciNet  MATH  Google Scholar 

  17. Liu F, Pedrycz W, Zhang WG (2017) Limited rationality and its quantification through the interval number judgments with permutations. IEEE Trans Cybernet 47(12):4025–4037

    Article  Google Scholar 

  18. Liu F, Tan X, Yang H, Zhao H (2020) Decision making based on intuitionistic fuzzy preference relations with additive approximate consistency. J Intell Fuzzy Syst 39:4041–4058

    Article  Google Scholar 

  19. Liu F, Zhang JW, Yu Q, Peng YN, Pedrycz W (2020) On weak consistency of interval additive reciprocal matrices. Fuzzy Opt Decis Making 19:153–175

    Article  MathSciNet  MATH  Google Scholar 

  20. Meng FY, Tang J, Xu ZS (2019) Deriving priority weights from intuitionistic fuzzy multiplicative preference relations. Int J Intell Syst 34:2937–2969

    Article  Google Scholar 

  21. Meng FY, Tang J, Xu ZS (2017) A 0–1 mixed programming model based method for group decision making with intuitionistic fuzzy preference relations. Comput Ind Eng 112:289–304

    Article  Google Scholar 

  22. Meng FY, Chen SM, Yuan RP (2020) Group decision making with heterogeneous intuitionistic fuzzy preference relations. Inf Sci 523:197–219

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  24. Pedrycz W, Chen SM (2015) Granular computing and decision-making: interactive and iterative approaches. Springer, New York

    Book  Google Scholar 

  25. Ren P, Xu ZS, Liao HC (2016) Intuitionistic multiplicative analytic hierarchy process in group decision making. Comput Ind Eng 101:513–524

    Article  Google Scholar 

  26. Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York

    MATH  Google Scholar 

  27. Saaty TL (2013) The modern science of multicriteria decision making and its practical applications: the AHP/ANP approach. Oper Res 61(5):1101–1118

    Article  MathSciNet  MATH  Google Scholar 

  28. Tang J, Meng FY, Zhang SL (2019) Consistency comparison analysis of decision making with intuitionistic fuzzy preference relations. IEEE Trans Eng Manag. https://doi.org/10.1109/TEM.2019.2919559

    Article  Google Scholar 

  29. Tanino T (1984) Fuzzy preference orderings in group decision making. Fuzzy Sets Syst 12:117–131

    Article  MathSciNet  MATH  Google Scholar 

  30. van Laarhoven PJM, Pedrycz W (1983) A fuzzy extension of Saaty's priority theory. Fuzzy Sets Syst 11(1–3):229–241

    Article  MathSciNet  MATH  Google Scholar 

  31. Wang ZJ (2015) A note on “A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making”. Eur J Oper Res 247:867–871

    Article  MathSciNet  MATH  Google Scholar 

  32. Wang P, Liu PD, Chiclana F (2020) Multi-stage consistency optimization algorithm for decision making with incomplete probabilistic linguistic preference relation. Inf Sci. https://doi.org/10.1016/j.ins.2020.10.004

    Article  Google Scholar 

  33. Xia MM, Xu ZS, Liao HC (2013) Preference relations based on intuitionistic multiplicative information. IEEE Trans Fuzzy Syst 21:113–133

    Article  Google Scholar 

  34. Xu ZS (2013) Priority weight intervals derived from intuitionistic multiplicative preference relations. IEEE Trans Fuzzy Syst 21:642–654

    Article  Google Scholar 

  35. Xu ZS (2007) Intuitionistic preference relations and their application in group decision making. Inf Sci 177:2363–2379

    Article  MathSciNet  MATH  Google Scholar 

  36. Xu ZS (2014) Intuitionistic preference modeling and interactive decision making. Springer-Verlag, Berlin

    Book  MATH  Google Scholar 

  37. Xu ZS (2007) A survey of preference relations. Int J Gener Syst 36:179–203

    Article  MathSciNet  MATH  Google Scholar 

  38. Xu ZS, Liao HC (2013) Intuitionistic fuzzy analytic hierarchy process. IEEE Trans Fuzzy Syst 22:749–761

    Article  Google Scholar 

  39. Xu ZS, Wei CP (1999) A consistency improving method in the analytic hierarchy process. Eur J Oper Res 116(2):443–449

    Article  MATH  Google Scholar 

  40. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MATH  Google Scholar 

  41. Zhang ZM, Chen SM, Wang C (2020) Group decision making with incomplete intuitionistic multiplicative preference relations. Inf Sci 516:560–571

    Article  MathSciNet  MATH  Google Scholar 

  42. Zhang Z, Guo CH (2017) Deriving priority weights from intuitionistic multiplicative preference relations under group decision-making settings. J Oper Res Soc 68:1582–1599

    Article  Google Scholar 

  43. Zhang C, Liao HC, Luo L, Xu ZS (2020) Distance-based consensus reaching process for group decision making with intuitionistic multiplicative preference relations. Appl Soft Comput J 88:106045

    Article  Google Scholar 

  44. Zhang ZM, Pedrycz W (2017) Models of mathematical programming for intuitionistic multiplicative preference relations. IEEE Trans Fuzzy Syst 25:945–957

    Article  Google Scholar 

  45. Zhang ZM, Pedrycz W (2018) Goal programming approaches to managing consistency and consensus for intuitionistic multiplicative preference relations in group decision-making. IEEE Trans Fuzzy Syst 26:3261–3275

    Article  Google Scholar 

  46. Zhang XM, Xu ZS (2012) A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making. Fuzzy Opt Decis Making 12:135–146

    Article  MathSciNet  MATH  Google Scholar 

  47. Zimmermann HJ (1987) Fuzzy sets, decision making, and expert systems. Springer Science & Business Media, New York

    Book  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Associate Editor and the anonymous reviewers for the valuable comments improving the quality of the paper. The work was supported by the National Natural Science Foundation of China (Nos. 71871072, 71571054), the Guangxi Natural Science Foundation for Distinguished Young Scholars (No. 2016GXNSFFA380004), 2017 Guangxi high school innovation team and outstanding scholars plan, and the Innovation Project of Guangxi Graduate Education (No. YCSW2021044).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangxi University, Nanning, 530004, Guangxi, China

    Xu Tan & Fang Liu

  2. China-ASEAN Research Institute, Guangxi University, Nanning, 530004, Guangxi, China

    Hui Zhao & Fang Liu

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  1. Hui Zhao
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  2. Xu Tan
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  3. Fang Liu
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Correspondence to Fang Liu.

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Zhao, H., Tan, X. & Liu, F. A decision making model based on intuitionistic multiplicative preference relations with approximate consistency. Int. J. Mach. Learn. & Cyber. 12, 2761–2775 (2021). https://doi.org/10.1007/s13042-021-01362-0

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  • DOI: https://doi.org/10.1007/s13042-021-01362-0

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