Least-square method to priority of the fuzzy preference relations with incomplete information

The priority problem of incomplete preference relations is investigated. Using the transformation relation between multiplicative preference relation and fuzzy preference relation, we develop a least-square model to obtain the collective priority vector of the incomplete preference relations presented by multiple decision makers, with the existence condition of the solution being developed. Meanwhile, we extend this model to the cases of the fuzzy preference relations with complete information presented by multiple decision makers and the fuzzy preference relation with complete information presented by one decision maker. Finally, it is illustrated by a numerical example that the method proposed is feasible and effective.

[1]  XU Ze-shui,et al.  Group Decision Making Method Based on Different Types of Incomplete Judgment Matrices , 2006 .

[2]  W. Pedrycz,et al.  A fuzzy extension of Saaty's priority theory , 1983 .

[3]  M. Kwiesielewicz,et al.  A note on the fuzzy extension of Saaty's priority theory , 1998, Fuzzy Sets Syst..

[4]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[5]  M. Kwiesielewicz.  The logarithmic least squares and the generalized pseudoinverse in estimating ratios , 1996 .

[6]  Thomas O. Boucher,et al.  Strong transitivity, rationality and weak monotonicity in fuzzy pairwise comparisons , 1998, Fuzzy Sets Syst..

[7]  Z. S. Xu,et al.  Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation , 2004, Int. J. Approx. Reason..

[8]  XU Ze-shui.  Interactive Approach Based on Incomplete Complementary Judgement Matrices to Group Decision Making , 2005 .

[9]  Jian Ma,et al.  A method for repairing the inconsistency of fuzzy preference relations , 2006, Fuzzy Sets Syst..

[10]  Z. Xu.  Generalized chi square method for the estimation of weights , 2000 .

[11]  T. Saaty,et al.  The Analytic Hierarchy Process , 1985 .

[12]  Zeshui Xu,et al.  A least deviation method to obtain a priority vector of a fuzzy preference relation , 2005, Eur. J. Oper. Res..

[13]  Xu Ze.  Two Methods for Priorities of Complementary Judgement Matrices ——Weighted Least-square Method and Eigenvector Method , 2002 .

[14]  MaoJi-Ye,et al.  A method for repairing the inconsistency of fuzzy preference relations , 2006 .

[15]  G. Crawford,et al.  A note on the analysis of subjective judgment matrices , 1985 .