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Calculating priority weights from interval-valued multiplicative hesitant fuzzy preference relations

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Abstract

To denote the reciprocally uncertain hesitancy of decision makers, this paper introduces a new type of fuzzy sets called interval-valued multiplicative hesitant fuzzy variables (IVMHFVs), which is an extension of multiplicative hesitant fuzzy variables. On the basis of IVMHFVs, interval-valued multiplicative hesitant fuzzy preference relations (IVMHFPRs) are introduced. To rank objects based on IVMHFPRs reasonably, the consistency of IVMHFPRs is studied and a consistency definition is presented. Using this concept, a 0–1 mixed programming model for judging the consistency of IVMHFPRs is built, and a consistency-based programming model for deriving consistent IVMHFPRs is constructed. When the offered IVMHFPRs are incomplete, a model for determining missing values is established. In the setting of group decision making, a consensus index is defined and an interactive method for improving the consensus is offered. After that, an approach to group decision making with inconsistent and incomplete IVMHFPRs is developed. Meanwhile, a practical example is provided to show the application of the new method.

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References

  • Arbel A, Vargas LG (1990) The analytic hierarchy process with interval judgments. In: Proceedings of IXth international symposium on MCDM Fair fax

  • Cabrerizo FJ, Chiclana F, Ureña MR, Herrera-Viedma E (2013) Challenges and open questions in soft consensus models. In: Joint IFSA World Congress and NAFIPS annual meeting (IFSA/NAFIPS), Edmonton, AB, pp 944–949

  • Chandran B, Golden B, Wasil E (2005) Linear programming models for estimating weights in the analytic hierarchy process. Comput Oper Res 32(9):2235–2254

    Article  MATH  Google Scholar 

  • Chen N, Xu ZS, Xia MM (2013) Interval-valued hesitant preference relation relations and their applications to group decision making. Knowl Based Syst 37:528–540

    Article  Google Scholar 

  • Chen SM, Cheng SH, Lin TE (2015) Group decision making systems using group recommendations based on interval fuzzy preference relations and consistency matrices. Inf Sci 298:555–567

    Article  MathSciNet  MATH  Google Scholar 

  • Genç S, Boran FE, Akay D, Xu ZS (2010) Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations. Inf Sci 180(24):4877–4891

    Article  MathSciNet  MATH  Google Scholar 

  • Hua MM, Ren PY, Lan JB, Wang J, Zheng WM (2014) Note on “Some models for deriving the priority weights from interval fuzzy preference relations”. Eur J Oper Res 237(2):771–773

    Article  MathSciNet  MATH  Google Scholar 

  • Islam R, Biswal MP, Alam SS (1997) Preference programming and inconsistent interval judgments. Eur J Oper Res 97(1):53–62

    Article  MATH  Google Scholar 

  • Liu F (2009) Acceptable consistency analysis of interval reciprocal comparison matrices. Fuzzy Sets Syst 160(18):2686–2700

    Article  MathSciNet  MATH  Google Scholar 

  • Liu F, Zhang WG, Zhang LH (2014) A group decision making model based on a generalized ordered weighted geometric average operator with interval preference matrices. Fuzzy Sets Syst 246(1):1–18

    Article  MathSciNet  MATH  Google Scholar 

  • Meng FY, An QX (2017) An approach for group decision making method with hesitant fuzzy preference relations. Knowl Based Syst 127:1–15

    Article  Google Scholar 

  • Meng FY, Tan CQ (2017) A new consistency concept for interval multiplicative preference relations. Appl Soft Comput 52:262–276

    Article  Google Scholar 

  • Meng FY, Chen XH, Tan CQ (2016) Cooperative fuzzy games with interval characteristic functions. Oper Res 16(1):1–24

    Google Scholar 

  • Meng FY, An QX, Tan CQ, Chen XH (2017a) 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(8):2069–2082

    Article  Google Scholar 

  • Meng FY, Tan CQ, Chen XH (2017b) Multiplicative consistency analysis for interval reciprocal preference relations: a comparative study. Omega 68:17–38

    Article  Google Scholar 

  • Meng FY, Tang J, Xu ZS (2017c) Exploiting the priority weights from interval linguistic fuzzy preference relations. Soft Comput. https://doi.org/10.1007/s00500-017-2878-y

    Article  MATH  Google Scholar 

  • Meng FY, Tang J, An QX, Chen XH (2017d) Decision making with intuitionistic linguistic preference relations. Int Trans Oper Res. https://doi.org/10.1111/itor.12383

    Article  Google Scholar 

  • Orlovsky S (1978) Decision-making with a fuzzy preference relation. Fuzzy Sets Syst 1(3):155–167

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Saaty TL, Vargas LG (1987) Uncertainty and rank order in the analytic hierarchy process. Eur J Oper Res 32(1):107–117

    Article  MathSciNet  MATH  Google Scholar 

  • Tang J, An QX, Meng FY, Chen XH (2017) A natural method for ranking objects from hesitant fuzzy preference relations. Int J Inf Technol Decis Mak 16(4):1611–1646

    Article  Google Scholar 

  • Tang J, Meng FY, Li CL, Li CH (2018) A consistency-based approach to group decision making with uncertain multiplicative linguistic fuzzy preference relations. J Intell Fuzzy Syst 35(1):1037–1054

    Article  Google Scholar 

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539

    MATH  Google Scholar 

  • Ureña R, Chiclana F, Alonso S, Morente-Molinera JA, Herrera-Viedma E (2014) On incomplete fuzzy and multiplicative preference relations in multi-person decision making. Proc Comput Sci 31:793–801

    Article  Google Scholar 

  • Ureña R, Chiclana F, Fujita H, Herrera-Viedma E (2015a) Confidence-consistency driven group decision making approach with incomplete reciprocal intuitionistic preference relations. Knowl Based Syst 89:86–96

    Article  Google Scholar 

  • Ureña R, Chiclana F, Herrera-Viedma E (2015b) Consistency based completion approaches of incomplete preference relations in uncertain decision contexts. In: IEEE International Conference on Fuzzy Systems, Istanbul, Turkey, pp 1–6

  • Ureña R, Chiclana F, Morente-Molinera JA, Herrera-Viedma E (2015c) Managing incomplete preference relations in decision making: a review and future trends. Inf Sci 302:14–32

    Article  MathSciNet  MATH  Google Scholar 

  • Ureña R, Chiclana FJ, Morente-Molinera JA, Herrera-Viedma E (2016) GDM-R: a new framework in R to support fuzzy group decision making processes. Inf Sci 357:161–181

    Article  Google Scholar 

  • Ureña R, Chiclana F, Melançon G, Herrera-Viedma E (2019) A social network based approach for consensus achievement in multiperson decision making. Inf Fusion 47:72–87

    Article  Google Scholar 

  • 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 

  • Wang ZJ, Chen YG (2014) Logarithmic least squares prioritization and completion methods for interval fuzzy preference relations based on geometric transitivity. Inf Sci 289:59–75

    Article  MathSciNet  MATH  Google Scholar 

  • Wang ZJ, Li KW (2012) Goal programming approaches to deriving interval weights based on interval fuzzy preference relations. Inf Sci 193(193):180–198

    Article  MathSciNet  MATH  Google Scholar 

  • Wang ZJ, Li KW (2015) A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices. Eur J Oper Res 242(3):890–900

    Article  MathSciNet  MATH  Google Scholar 

  • Wang YM, Yang JB, Xu DL (2005a) Interval weight generation approaches based on consistency test and interval comparison matrices. Appl Math Comput 167(1):252–273

    MathSciNet  MATH  Google Scholar 

  • Wang YM, Yang JB, Xu DL (2005b) A two-stage logarithmic goal programming method for generating weights from interval comparison matrices. Fuzzy Sets Syst 152(3):475–498

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J, Lan JB, Ren PY, Luo YY (2012) Some programming models to derive priority weights from additive interval fuzzy preference relation. Knowl Based Syst 27(1):69–77

    Article  Google Scholar 

  • Wei YQ, Liu JS, Wang XZ (1994) Concept of consistence and weights of the judgement matrix in the uncertain type of AHP. Syst Engine Theory Prac 14(1):16–22

    Google Scholar 

  • Wu J, Chiclana F (2014) A social network analysis trust-consensus based approach to group decision-making problems with interval-valued fuzzy reciprocal preference relations. Knowl Based Syst 59:97–107

    Article  Google Scholar 

  • Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52(3):395–407

    Article  MathSciNet  MATH  Google Scholar 

  • Xia MM, Xu ZS (2014) Interval weight generation approaches for reciprocal relations. Appl Math Modell 38(3):828–838

    Article  MathSciNet  MATH  Google Scholar 

  • Xu ZS (2001) A practical method for priority of interval number complementary judgment matrix. Oper Res Manage Sci 10(1):16–19

    Google Scholar 

  • Xu ZS (2011) Consistency of interval fuzzy preference relations in group decision making. Appl Soft Comput 11(5):3898–3909

    Article  Google Scholar 

  • Xu ZS, Chen J (2008) Some models for deriving the priority weights from interval fuzzy preference relations. Eur J Oper Res 184(1):266–280

    Article  MathSciNet  MATH  Google Scholar 

  • Xu YJ, Chen L, Rodríguez RM, Herrera F, Wang HM (2016) Deriving the priority weights from incomplete hesitant fuzzy preference relations in group decision making. Knowl Based Syst 99:71–78

    Article  Google Scholar 

  • Xu YJ, Francisco JC, Herrera-Viedma E (2017) A consensus model for hesitant fuzzy preference relations and its application in water allocation management. Appl Soft Comput 58:265–284

    Article  Google Scholar 

  • Xu YJ, Li CY, Wen XW (2018) Missing values estimation and consensus building for incomplete hesitant fuzzy preference relations with multiplicative consistency. Int J Comput Intell Syst 11(1):101–119

    Article  Google Scholar 

  • Zhang ZM (2016) Deriving the priority weights from incomplete hesitant fuzzy preference relations based on multiplicative consistency. Appl Soft Comput 46:37–59

    Article  Google Scholar 

  • Zhang ZM (2017) A framework of group decision making with hesitant fuzzy preference relations based on multiplicative consistency. Int J Fuzzy Syst 19(4):982–996

    Article  MathSciNet  Google Scholar 

  • Zhang ZM, Wu C (2014a) Deriving the priority weights from hesitant multiplicative preference relations in group decision making. Appl Soft Comput 25:107–117

    Article  Google Scholar 

  • Zhang ZM, Wu C (2014b) A decision support model for group decision making with hesitant multiplicative preference relations. Inf Sci 282:136–166

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang ZM, Wang C, Tian XD (2015a) A decision support model for group decision making with hesitant fuzzy preference relations. Knowl Based Syst 86:77–101

    Article  Google Scholar 

  • Zhang ZM, Wang C, Tian XD (2015b) Multi-criteria group decision making with incomplete hesitant fuzzy preference relations. Appl Soft Comput 36:1–23

    Article  Google Scholar 

  • Zhang Z, Kou XY, Dong QX (2018a) Additive consistency analysis and improvement for hesitant fuzzy preference relations. Expert Syst Appl 98:118–128

    Article  Google Scholar 

  • Zhang Z, Kou XY, Yu WY, Guo CH (2018b) On priority weights and consistency for incomplete hesitant fuzzy preference relations. Knowl Based Syst 143:115–126

    Article  Google Scholar 

  • Zhu B, Xu ZS (2014a) Regression methods for hesitant fuzzy preference relations. Tech Econ Develop Econ 19(sup1):S214–S227

    Article  Google Scholar 

  • Zhu B, Xu ZS (2014b) Analytic hierarchy process-hesitant group decision making. Eur J Oper Res 239(3):794–801

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu B, Xu ZS, Xu JP (2014) Deriving a ranking from hesitant fuzzy preference relations under group decision making. IEEE Trans Cybern 44(8):1328–1337

    Article  Google Scholar 

  • Zhu B, Xu ZS, Zhang R, Hong M (2016) Hesitant analytic hierarchy process. Eur J Oper Res 250(2):602–614

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 71571192, 71601049, and 71671188), the Innovation-Driven Project of Central South University (No. 2018CX039), the Fundamental Research Funds for the Central Universities of Central South University (No. 2018zzts094), the Major Project for National Natural Science Foundation of China (No. 71790615), and the State Key Program of National Natural Science of China (No. 71431006).

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Authors and Affiliations

  1. School of Business, Central South University, Changsha, 410083, China

    Jie Tang & Fanyong Meng

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

    Fanyong Meng

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  1. Jie Tang
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  2. Fanyong Meng
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Correspondence to Fanyong Meng.

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Tang, J., Meng, F. Calculating priority weights from interval-valued multiplicative hesitant fuzzy preference relations. Soft Comput 23, 11573–11592 (2019). https://doi.org/10.1007/s00500-018-03698-2

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