Important Facts and Observations about Pairwise Comparisons (the special issue edition)

This study has been inspired by numerous requests from researchers who often confuse Saaty's AHP with the Pairwise Comparisons (PC) method, taking AHP as the only representation of PC. Most formal ∗Computer Science, Laurentian University, Sudbury, Ontario P3E 2C6, Canada, wkoczkodaj@cs.laurentian.ca †School of Computer Science, The University of Manchester, M13 9PL, United Kingdom, ludi.mikhailov@mbs.ac.uk ‡Electrical and Control Engeenering Department, Gdansk University of Technology, 80-297 Gdansk, Narutowicza st. 11/12, Poland, grzegorz.redlarski@pg.gda.pl §California State University Channel Islands, Dept. of Computer Science, One University Drive, Camarillo, CA 93012, USA, michael.soltys@csuci.edu ¶AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland, szybowsk@agh.edu.pl; Research supported by the Polish Ministry of Science and Higher Education ‖Institute of Mathematics and Physics, Siedlce University of Natural Sciences and Humanities, 3 Maja 54, 08-110 Siedlice, Poland, eliza.wajch@wp.pl ∗∗Department of Computer Science and Software Engineering. Xi'an Jiaotong-Liverpool University, Suzhou 215123, China, kevinkf.yuen@gmail.com ††Theodosius Dobzhansky Center for Genome Bioinformatics, St. Petersburg State University; This work was supported, in part, by Russian Ministry of Science Mega-grant no.11.G34.31.0068

[1]  Gaik Tamazian,et al.  Scales and methods for deriving weights in the analytic hierarchy process , 2011 .

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

[3]  Piotr Faliszewski,et al.  Using complexity to protect elections , 2010, Commun. ACM.

[4]  Michael Soltys,et al.  Complex Ranking Procedures , 2016, Fundam. Informaticae.

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

[6]  H. A. Donegan,et al.  A New Approach to Ahp Decision‐Making , 1992 .

[7]  P. Moran On the method of paired comparisons. , 1947, Biometrika.

[8]  P. Slater Inconsistencies in a schedule of paired comparisons , 1961 .

[9]  D. Chang Applications of the extent analysis method on fuzzy AHP , 1996 .

[10]  Gilles Dowek,et al.  Principles of programming languages , 1981, Prentice Hall International Series in Computer Science.

[11]  Harry Katzan Systems design and documentation : an introduction to the HIPO method , 1976 .

[12]  Konrad Kulakowski,et al.  Heuristic Rating Estimation Approach to The Pairwise Comparisons Method , 2013, Fundam. Informaticae.

[13]  Ding Xu,et al.  Fast Convergence of Distance-based Inconsistency in Pairwise Comparisons , 2015, Fundam. Informaticae.

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

[15]  T. Saaty There is no mathematical validity for using fuzzy number crunching in the analytic hierarchy process , 2006 .

[16]  F. Lootsma SCALE SENSITIVITY IN THE MULTIPLICATIVE AHP AND SMART , 1993 .

[17]  János Fülöp,et al.  A method for approximating pairwise comparison matrices by consistent matrices , 2008, J. Glob. Optim..

[18]  Ibrahim I. Kutbi A pragmatic pairwise group-decision method for selection of sites for nuclear power plants , 1987 .

[19]  Thomas L. Saaty,et al.  On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process , 2007, Math. Comput. Model..

[20]  R. E. Jensen An alternative scaling method for priorities in hierarchical structures , 1984 .

[21]  H. N. Shapiro,et al.  Determining the degree of inconsistency in a set of paired comparisons , 1958 .

[22]  Waldemar W. Koczkodaj,et al.  On distance-based inconsistency reduction algorithms for pairwise comparisons , 2010, Log. J. IGPL.

[23]  Waldemar W. Koczkodaj,et al.  On Axiomatization of Inconsistency Indicators in Pairwise Comparisons , 2013, Int. J. Approx. Reason..

[24]  József Temesi,et al.  Pairwise comparison matrices and the error-free property of the decision maker , 2011, Central Eur. J. Oper. Res..

[25]  Yin-Feng Xu,et al.  A comparative study of the numerical scales and the prioritization methods in AHP , 2008, Eur. J. Oper. Res..

[26]  P. Ontario A Different Perspective on a Scale for Pairwise Comparisons , 2010 .

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

[28]  Carlos A. Bana e Costa,et al.  A critical analysis of the eigenvalue method used to derive priorities in AHP , 2008, Eur. J. Oper. Res..

[29]  Waldemar W. Koczkodaj,et al.  A Monte Carlo Study of Pairwise Comparisons , 2015, ArXiv.

[30]  Thomas L. Saaty,et al.  On the measurement of intengibles. a principal Eigenvector approach to relative measurement derived from paired comparisons , 2013 .

[31]  W. W. Koczkodaj,et al.  Computing a consistent approximation to a generalized pairwise comparisons matrix , 1999 .

[32]  L. C. Leung,et al.  On consistency and ranking of alternatives in fuzzy AHP , 2000, Eur. J. Oper. Res..

[33]  Konrad Kulakowski,et al.  A heuristic rating estimation algorithm for the pairwise comparisons method , 2015, Central Eur. J. Oper. Res..

[34]  W. W. Koczkodaj A new definition of consistency of pairwise comparisons , 1993 .

[35]  Michael A. Elliott,et al.  Selecting numerical scales for pairwise comparisons , 2010, Reliab. Eng. Syst. Saf..

[36]  Ryszard Janicki,et al.  On a pairwise comparison-based consistent non-numerical ranking , 2012, Log. J. IGPL.

[37]  Jacek Szybowski,et al.  Mathematical foundations of inconsistency analysis in pairwise comparisons , 2015, ArXiv.

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

[39]  Kevin Kam Fung Yuen,et al.  Pairwise opposite matrix and its cognitive prioritization operators: comparisons with pairwise reciprocal matrix and analytic prioritization operators , 2012, J. Oper. Res. Soc..

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

[41]  C. Genest,et al.  A statistical look at Saaty's method of estimating pairwise preferences expressed on a ratio scale , 1994 .

[42]  Luis G. Vargas,et al.  Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios , 1984 .

[43]  Malcolm J. Beynon,et al.  An analysis of distributions of priority values from alternative comparison scales within AHP , 2002, Eur. J. Oper. Res..

[44]  G. A. Miller THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[45]  R. J. Hill A Note on Inconsistency in Paired Comparison Judgments , 1953 .

[46]  R. Hämäläinen,et al.  On the measurement of preferences in the analytic hierarchy process , 1997 .

[47]  R. Jiang,et al.  Scale transitivity in the AHP , 2003, J. Oper. Res. Soc..