Building Consistent Pairwise Comparison Matrices over Abelian Linearly Ordered Groups

In the paper, algorithms are provided to check the consistency of pairwise comparison matrices and to build consistent matrices over abelian linearly ordered groups. A measure of consistency is also given; this measure improves a consistent index provided in a previous paper.

[1]  Francisco Herrera,et al.  Cardinal Consistency of Reciprocal Preference Relations: A Characterization of Multiplicative Transitivity , 2009, IEEE Transactions on Fuzzy Systems.

[2]  T. L. Saaty.  A Scaling Method for Priorities in Hierarchical Structures , 1977 .

[3]  Massimo Squillante,et al.  Generalized consistency and intensity vectors for comparison matrices: Research Articles , 2007 .

[4]  Livia D’Apuzzo,et al.  Ranking and weak consistency in the A.H.P. context , 1997 .

[5]  T. Saaty.  Axiomatic foundation of the analytic hierarchy process , 1986 .

[6]  Francisco Herrera,et al.  Some issues on consistency of fuzzy preference relations , 2004, Eur. J. Oper. Res..

[7]  Livia D'Apuzzo,et al.  Weak Consistency and Quasi-Linear Means Imply the Actual Ranking , 2002, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[8]  Ronald R. Yager,et al.  Structure of Uninorms , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[9]  Livia D'Apuzzo,et al.  Transitive Matrices, Strict Preference Order and Ordinal Evaluation Operators , 2006, Soft Comput..

[10]  Massimo Squillante,et al.  Generalized consistency and intensity vectors for comparison matrices , 2007, Int. J. Intell. Syst..

[11]  J. Barzilai.  Consistency Measures for Pairwise Comparison Matrices , 1998 .

[12]  L. Basile,et al.  Transitive matrices, strict preference and intensity operators , 2006 .

[13]  L. D'Apuzzo,et al.  A general unified framework for pairwise comparison matrices in multicriterial methods , 2009 .

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