Comparing inconsistency of pairwise comparison matrices depending on entries

Abstract Pairwise comparisons have been a long-standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision-making methods. Since several types of pairwise comparison matrices (e.g., multiplicative, additive, fuzzy) are proposed in literature, in this paper, we investigate, for which type of matrix, decision-makers are more coherent when they express their subjective preferences. By performing an experiment, we found that the additive approach provides the worst level of coherence.

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

[2]  Fujun Hou,et al.  A Multiplicative Alo-group Based Hierarchical Decision Model and Application , 2016, Commun. Stat. Simul. Comput..

[3]  A. Greenwald Within-subjects designs: To use or not to use? , 1976 .

[4]  W. Cook,et al.  Deriving weights from pairwise comparison ratio matrices: An axiomatic approach , 1988 .

[5]  L. Thurstone A law of comparative judgment. , 1994 .

[6]  Boaz Golany,et al.  Deriving weights from pairwise comparison matrices: The additive case , 1990 .

[7]  Alessio Ishizaka,et al.  Mapping verbal AHP scale to numerical scale for cloud computing strategy selection , 2017, Appl. Soft Comput..

[8]  Bice Cavallo,et al.  A further discussion of "A Semiring-based study of judgment matrices: properties and models" [Information Sciences 181 (2011) 2166-2176] , 2014, Inf. Sci..

[9]  David V. Budescu,et al.  Eliciting Subjective Probabilities through Pair‐wise Comparisons , 2017 .

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

[11]  Jian Chen,et al.  Consistency and consensus improving methods for pairwise comparison matrices based on Abelian linearly ordered group , 2015, Fuzzy Sets Syst..

[12]  B. John,et al.  A First Course In Abstract Algebra , 7 th By , 2019 .

[13]  Alessio Ishizaka,et al.  How to derive priorities in AHP: a comparative study , 2006, Central Eur. J. Oper. Res..

[14]  Bice Cavallo,et al.  Deriving weights from a pairwise comparison matrix over an alo-group , 2011, Soft Computing.

[15]  Bice Cavallo,et al.  Investigating Properties of the ⊙-Consistency Index , 2012, IPMU.

[16]  Tetsuzo Tanino,et al.  Fuzzy Preference Relations in Group Decision Making , 1988 .

[17]  Eelko Huizingh,et al.  A comparison of verbal and numerical judgments in the analytic hierarchy process , 1997 .

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

[19]  Pedro Linares,et al.  Are inconsistent decisions better? An experiment with pairwise comparisons , 2009, Eur. J. Oper. Res..

[20]  Matteo Brunelli,et al.  Studying a set of properties of inconsistency indices for pairwise comparisons , 2015, Ann. Oper. Res..

[21]  Kevin Kam Fung Yuen,et al.  Important Facts and Observations about Pairwise Comparisons (the special issue edition) , 2016, Fundam. Informaticae.

[22]  Jaroslav Ramík,et al.  Pairwise comparison matrix with fuzzy elements on alo-group , 2015, Inf. Sci..

[23]  Gary Charness,et al.  Journal of Economic Behavior & Organization , 2022 .

[24]  E. Poulton Unwanted range effects from using within-subject experimental designs. , 1973 .

[25]  Alessio Ishizaka,et al.  Are multi-criteria decision-making tools useful? An experimental comparative study of three methods , 2018, Eur. J. Oper. Res..

[26]  Paul M. Weichsel,et al.  A first course in abstract algebra , 1966 .

[27]  Ido Millet,et al.  The Effectiveness of Alternative Preference Elicitation Methods in the Analytic Hierarchy Process , 1997 .

[28]  J. Barzilai Deriving weights from pairwise comparison matrices , 1997 .

[29]  R. Keeney,et al.  Eliciting public values for complex policy decisions , 1990 .

[30]  Alessio Ishizaka,et al.  Does AHP help us make a choice? An experimental evaluation , 2011, J. Oper. Res. Soc..

[31]  M. Bohanec,et al.  The Analytic Hierarchy Process , 2004 .

[32]  J. Rotman A First Course in Abstract Algebra , 1995 .

[33]  R. W. Saaty,et al.  The analytic hierarchy process—what it is and how it is used , 1987 .

[34]  Graham K. Rand,et al.  Non-conventional Preference Relations in Decision Making , 1989 .

[35]  T. Tanino Fuzzy preference orderings in group decision making , 1984 .

[36]  Bice Cavallo,et al.  Reciprocal transitive matrices over abelian linearly ordered groups: Characterizations and application to multi-criteria decision problems , 2015, Fuzzy Sets Syst..

[37]  Martin Kunc,et al.  Behavioral operational research theory, methodology and practice , 2016 .

[38]  Bice Cavallo,et al.  Ensuring reliability of the weighting vector: Weak consistent pairwise comparison matrices , 2016, Fuzzy Sets Syst..

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

[40]  Dylan F. Jones,et al.  A distance-metric methodology for the derivation of weights from a pairwise comparison matrix , 2004, J. Oper. Res. Soc..

[41]  Michele Fedrizzi,et al.  Axiomatic properties of inconsistency indices for pairwise comparisons , 2013, J. Oper. Res. Soc..