HodgeRank Is the Limit of Perron Rank

Published Online:https://doi.org/10.1287/moor.2015.0744

References

  • Akian M, Bapat R, Gaubert S (1998) Asymptotics of the Perron eigenvalue and eigenvector using max-algebra. Comptes Rendus de l’Académie des Sciences—Series I—Math. 327(11):927–932.CrossrefGoogle Scholar
  • Bai Z, Silverstein JW (2010) Spectral Analysis of Large Dimensional Random Matrices, Springer Series in Statistics (Springer, New York).CrossrefGoogle Scholar
  • Crawford GB (1987) The geometric mean procedure for estimating the scale of a judgement matrix. Math. Modelling 9(3):327–334.CrossrefGoogle Scholar
  • Dahl G (2005) A method for approximating symmetrically reciprocal matrices by transitive matrices. Linear Algebra Appl. 403:207–215.CrossrefGoogle Scholar
  • Dong Y, Zhang G, Hong W, Xu Y (2010) Consensus models for AHP group decision making under row geometric mean prioritization method. Decision Support Systems 49(3):281–289.CrossrefGoogle Scholar
  • Elsner L, van den Driessche P (2004) Max-algebra and pairwise comparison matrices. Linear Algebra Appl. 385:47–62.CrossrefGoogle Scholar
  • Farkas A (2007) The analysis of the principal eigenvector of pairwise comparison matrices. Acta Polytechnica Hungarica 4(2):99–115.Google Scholar
  • Fürnkranz J, Hüllermeier E (2010) Preference Learning (Springer, Berlin).Google Scholar
  • Hochbaum DS (2006) Ranking sports teams and the inverse equal paths problem. Internet Network Economics (Springer, Berlin),307–318.CrossrefGoogle Scholar
  • Jiang X, Lim L-H, Yao Y, Ye Y (2011) Statistical ranking and combinatorial Hodge theory. Math. Programming 127(1):203–244.CrossrefGoogle Scholar
  • Saari DG (2014) A new way to analyze paired comparison rules. Math. Oper. Res. 39(3):647–655.LinkGoogle Scholar
  • Saaty TL (1980) The Analytic Hierarchy Process (McGrawHill, New York).Google Scholar
  • Saaty TL (2006) Rank from comparisons and from ratings in the analytic hierarchy/network processes. Eur. J. Oper. Res. 168(2):557–570.CrossrefGoogle Scholar
  • Stewart GW, Sun J (1990) Matrix Perturbation Theory (Academic Press, New York).Google Scholar
  • Tran NM (2013) Pairwise ranking: Choice of method can produce arbitrarily different rank order. Linear Algebra Appl. 438(3):1012–1024.CrossrefGoogle Scholar
  • Yin YQ, Bai ZD, Krishnaiah PR (1988) On the limit of the largest eigenvalue of the large dimensional sample covariance matrix. Probability Theory and Related Fields 78(4):509–521.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.