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Determining decision makers’ weights in group ranking: a granular computing method

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Abstract

Deriving the consensus ranking(s) from a set of rankings plays an important role in group decision making. However, the relative importance, i.e. weight of a decision maker, is ignored in most of the ordinal ranking methods. This paper aims to determine the weights of decision makers by measuring the support degree of each pair of ordinal rankings. We first define the similarity degree of dominance granular structures to depict the mutual relations of the ordinal rankings. Then, the support degree, which is obtained from similarity degree, is presented to determine weights of decision makers. Finally, an improved programming model is proposed to compute the consensus rankings by minimizing the violation with the weighted ranking(s). Two examples are given to illustrate the rationality of the proposed model.

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References

  1. Bogart KP (1973) Preference structures I distance between transitive prefernce relations. J Math Soci 3:49–67

    Article  MATH  MathSciNet  Google Scholar 

  2. Bogart KP (1975) Preference structures II: distance between asymmetric relations. SIAM J Appl Math 29:254–262

    Article  MATH  MathSciNet  Google Scholar 

  3. Brüggemann R, Sørensen PB (2004) Estimation of averaged ranks by a local partial order model. J Chem Inf Comput Sci 44:618–625

    Article  Google Scholar 

  4. Chen HY, Zhou LG (2011) An approach to group decision making with interval fuzzy preference relations based on induced generalized continuous ordered weighted averaging operator. Expert Syst Appl 38:13432–13440

    Article  Google Scholar 

  5. Chen TY, Li CH (2010) Determining objective weights with intuitionistic fuzzy entropy measures: a comparative analysis. Inf Sci 180:4207–4222

    Article  Google Scholar 

  6. Chen YL, Cheng LC (2010) An approach to group ranking decisions in a dynamic environment. Decis Support Syst 48:622–634

    Article  Google Scholar 

  7. Cook WD, Seiford LM (1982) On the Borda-Kendall consensus method for priority ranking problems. Manag Sci 28(6):621–637

    Article  MATH  MathSciNet  Google Scholar 

  8. Cook WD, Kress M (1985) Ordinal ranking with intensity of preference. Manag Sci 31(1):26–32

    Article  MATH  MathSciNet  Google Scholar 

  9. Cook WD, Kress M, Seiford LM (1986) Information and preference in partial orders: a bimatrix representation. Psychometrika 51(2):197–207

    Article  MATH  MathSciNet  Google Scholar 

  10. Cook WD, Kress M, Seiford LM (1986) An axiomatic approach to distance on partial orderings. Oper Res 20(2):115–122

    MATH  MathSciNet  Google Scholar 

  11. Cook WD, Kress M, Seiford LM (1996) A general framework for distance-based consensus in ordinal ranking models. Eur J Oper Res 96:392–397

    Article  Google Scholar 

  12. Cook WD (2006) Distance-based and ad hoc consensus models in ordinal preference ranking. Eur J Oper Res 172:369–385

    Article  MATH  Google Scholar 

  13. Cook WD, Golany B, Penn M, Raviv T (2007) Creating a consensus ranking of proposals from reviewers’ partial ordinal rankings. Comput Oper Res 34:954–65

    Article  MATH  Google Scholar 

  14. Emond EJ, Mason D (2002) A new rank correlation coefficient with application to the consensus ranking problem. J Mult Crit Decis Anal 11(1):17–28

    Article  MATH  Google Scholar 

  15. Fan ZP, Liu Y (2010) A method for group decison-making based on multi-granularity uncertain linguistic information. Expert Syst Appl 37:4000–4008

    Article  Google Scholar 

  16. Hu QH, Yu DR, Guo MZ (2011) Fuzzy preference based on rough sets. Inf Sci 180:2003–2022

    Article  MathSciNet  Google Scholar 

  17. Hu QH, Che XJ, Zhang L, Zhang D, Guo MZ, Yu DR (2012) Rank entropy-based decision trees for monotonic classification. IEEE T Knowl Data En 24:2052–2064

    Article  Google Scholar 

  18. Jabeur K, Martel JM, Ben Khélifa S (2004) A distance based collective pre-order integrating the relative importance of the group’s members. Group Decis Negot 13(4):327–49

    Article  Google Scholar 

  19. Jabeur K, Martel JM (2005) A collective choice method based on individual preferences relational systems(p.r.s). Eur J Oper Res 177(3):469–485

    MathSciNet  Google Scholar 

  20. Jabeur K, Martel JM (2007) An ordinal sorting method for group decision-making. Eur J Oper Res 180:1272–1289

    Article  MATH  MathSciNet  Google Scholar 

  21. Jabeur K, Martel JM (2010) An agreement index with respect to a consensus preorder. Group Decis Negot 19:571–590

    Article  Google Scholar 

  22. Jabeur K, Martel JM, Guitouni A (2012) Deriving a minimum distance-based collective preorder: a binary mathematical programming approach. OR Spectr 34:23–42

    Article  MATH  MathSciNet  Google Scholar 

  23. Jiang XH, Lim LH, Yao Y, Ye YY (2011) Statistical ranking and combinatorial Hodge theory. Math Program (Ser. B) 127: 203–244.

    Article  MATH  MathSciNet  Google Scholar 

  24. Jiang JL (2007) An approach to group decision making based on interval fuzzy preference relations. J Syst Sci Sys Eng 16(1):113–120

    Article  Google Scholar 

  25. Kemeny JG, Snell JL (1962) Preference ranking: an axiomatic approach. Math Models Soc Sci 1962:9–23

    Google Scholar 

  26. Kendall M (1962) Rank correlation methods. Hafner, New York

    Google Scholar 

  27. Li JH, Mei CL et al (2013) On rule acquisition in decision formal contexts. Int J Mach Learn Cybern 4:721–731

    Article  Google Scholar 

  28. Liang JY, Chin KS, Dang CY (2004) A new method for measuring uncertainty and fuzzyiness in rough set theory. Int J Gen Syst 31(4):331–342

    Article  MathSciNet  Google Scholar 

  29. Liang JY, Shi ZZ (2004) The information entropy, rough entropy and knowledge granulation in rough set theory. Int J Uncertain Fuzz 12(1):37–46

    Article  MATH  MathSciNet  Google Scholar 

  30. Liang X, Wei CP (2014) An Atanassov’s intuitionistic fuzzy multi-attribute group decision making based on entropy and similarity measure. Int J Mach Learn Cybern 5:435–444

    Article  Google Scholar 

  31. Lipschutz S, Lipson ML, (1997) Schaum’s outline of theory and problems of discrete mathematics, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  32. Morais DC, Almeida ATd (2012) Group decision making on water resources based on analysis of individual rankings. OMEGA 40(1):42–45

    Article  Google Scholar 

  33. Pang JF, Liang JY (2012) Evaluation of the results of multi-attribute group decison-making with linguistic information. OMEGA 40(3):294–301

    Article  Google Scholar 

  34. Qian YH, Liang JY, Dang CY (2009) Knowdedge structure, knowledge granulation and knowledge distance in a knowledge base. Int J Approx Reason 50:174–188

    Article  MATH  MathSciNet  Google Scholar 

  35. Qian YH, Liang JY, Wu WZ, Dang CY (2011) Information granularity in fuzzy binary GrC model. IEEE T Fuzzy Syst 19:253–264

    Article  Google Scholar 

  36. Ramanathan R, Ganesh LS (1994) Group preference aggregation methods employed in AHP: an evaluation and an intrinsic process for deriving members’ weightages. Eur J Oper Res 79(2):249–265

    Article  MATH  Google Scholar 

  37. Saaty TL (1990) How to make a decision: the analytic hierarchy process. Eur J Oper Res 48(1):9–26

    Article  MATH  Google Scholar 

  38. Saaty TL, Shang JS (2011) An innovative orders-of-magnitude approach to AHP-based multi-criteria decision making: prioritizing divergent intangible humane acts. Eur J Oper Res 214:703–715

    Article  MathSciNet  Google Scholar 

  39. Song P, Liang JY, Qian YH (2012) A two-grade approach to ranking interval data. Knowl Based Syst 27:234–244

    Article  Google Scholar 

  40. Wang YM (1998) Using the method of maximizing deviations to make decision for multi-indices. J Syst Eng Electron 7:24–26

    Google Scholar 

  41. Wu WZ, Leung Y (2011) Theory and applications of granular labelled partitions in multi-scale decision tables. Inf Sci 181:3878–3897

    Article  MATH  Google Scholar 

  42. Wu WZ, Leung Y (2013) Optimal scale selection for multi-scale decision tables. Int J Approx Reason 54:1107–1129

    Article  MathSciNet  Google Scholar 

  43. Xu WH, Zhang XY, Zhang WX (2009) Knowledge entropy and knowledge measure in ordered information systems. Appl soft Comput 9:1244–1251

    Article  Google Scholar 

  44. Xu WH, Liu H, Zhang WX (2011) On granularity in information systems based on binary relation. Intell Inf Manag 3(3):75–86

    Google Scholar 

  45. Yager RR (2001) The power average operator. IEEE T Syst Man Cy A 31(6):724–731

    Article  MathSciNet  Google Scholar 

  46. Yao YY (1995) Measuring retrieval effectiveness based on user preference of documents. J Am Soc Inf Sci 46(2):133–145

    Article  Google Scholar 

  47. Yao YY (2009) Interpreting concept learning in cognitive informatics and granular computing. IEEE T Syst Man Cy B 39(4):855–866

    Article  Google Scholar 

  48. Yeung D, Wang XZ (2002) Improving performance of similarity-based clustering by feature weight learning. IEEE T Pattern Anal 24(4):556–561

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 71031006), the Shanxi Provincial Foundation for Returned Scholars (No. 2013-101), the Construction Project of the Science and Technology Basic Condition Platform of Shanxi Province (No. 2012091002-0101) and the Research Projects in Education Teaching of Yuncheng University (No. JY2011025).

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Authors and Affiliations

  1. Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information Technology, Shanxi University, Taiyuan, 030006, Shanxi, China

    Baoli Wang, Jiye Liang & Yuhua Qian

  2. Department of Applied Mathematics, Yuncheng University, Yuncheng, 044000, Shanxi, China

    Baoli Wang

  3. Department of Computer Science and Technology, Taiyuan Normal University, Taiyuan, 030012, Shanxi, China

    Jiye Liang

Authors
  1. Baoli Wang
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  2. Jiye Liang
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  3. Yuhua Qian
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Correspondence to Jiye Liang.

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Wang, B., Liang, J. & Qian, Y. Determining decision makers’ weights in group ranking: a granular computing method. Int. J. Mach. Learn. & Cyber. 6, 511–521 (2015). https://doi.org/10.1007/s13042-014-0278-5

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  • DOI: https://doi.org/10.1007/s13042-014-0278-5

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