Investigating rank reversal in reciprocal fuzzy preference relation based on additive consistency: Causes and solutions

Abstract Rank reversal is a common phenomenon in decision making. Rank reversal occurs when a new alternative is added to (or removed from) a set of alternatives, which causes change in the ranking order of the alternatives. This paper studies the possible causes of rank reversal in reciprocal preference relation based on additive consistency. Our investigation reveals that inconsistency of information is the main cause of this phenomena in preference relations followed by ranking score aggregation. We propose score aggregation methods to address the phenomenon of rank reversal. The proposed methods are illustrated using numerical examples. The results are better than other tested methods.

[1]  Jyh-Rong Chou,et al.  A linguistic evaluation approach for universal design , 2012, Inf. Sci..

[2]  Ying Luo,et al.  On rank reversal in decision analysis , 2009, Math. Comput. Model..

[3]  Enrique Herrera-Viedma,et al.  A Note on Two Methods for Estimating Missing Pairwise Preference Values , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  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..

[5]  JiangJiang,et al.  Consensus building in group decision making based on multiplicative consistency with incomplete reciprocal preference relations , 2016 .

[6]  Ernest H. Forman.  AHP IS INTENDED FOR MORE THAN EXPECTED VALUE CALCULATIONS , 1990 .

[7]  José María Moreno-Jiménez,et al.  The geometric consistency index: Approximated thresholds , 2003, Eur. J. Oper. Res..

[8]  Jonathan Barzilai,et al.  POWER RELATIONS AND GROUP AGGREGATION IN THE MULTIPLICATIVE AHP AND SMART , 1997 .

[9]  Thomas L. Saaty,et al.  Multicriteria Decision Making: The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation , 1990 .

[10]  Zhibin Wu,et al.  A concise consensus support model for group decision making with reciprocal preference relations based on deviation measures , 2012, Fuzzy Sets Syst..

[11]  T. Saaty.  RANK GENERATION, PRESERVATION, AND REVERSAL IN THE ANALYTIC HIERARCHY DECISION PROCESS , 1987 .

[12]  Jyrki Kangas,et al.  Rank reversals in multi-criteria decision analysis with statistical modelling of ratio-scale pairwise comparisons , 2005, J. Oper. Res. Soc..

[13]  A. György,et al.  On the spectrum of pairwise comparison matrices , 2004 .

[14]  Thomas L. Saaty,et al.  On the relativity of relative measures - accommodating both rank preservation and rank reversals in the AHP , 2000, Eur. J. Oper. Res..

[15]  Stanislav Karapetrovic,et al.  A quality control approach to consistency paradoxes in AHP , 1999, Eur. J. Oper. Res..

[16]  Stan Schenkerman.  Avoiding rank reversal in AHP decision-support models , 1994 .

[17]  Fanyong Meng,et al.  A new method for group decision making with incomplete fuzzy preference relations , 2015, Knowl. Based Syst..

[18]  Dong Cao,et al.  On the efficacy of modeling multi-attribute decision problems using AHP and Sinarchy , 2001, Eur. J. Oper. Res..

[19]  Berk Anbaroglu,et al.  Spatio-temporal clustering for non-recurrent traffic congestion detection on urban road networks , 2013 .

[20]  Enrique Herrera-Viedma,et al.  Managing incomplete preference relations in decision making: A review and future trends , 2015, Inf. Sci..

[21]  Bingfeng Ge,et al.  Consensus building in group decision making based on multiplicative consistency with incomplete reciprocal preference relations , 2016, Knowl. Based Syst..

[22]  Pavel V. Sevastjanov,et al.  A direct interval extension of TOPSIS method , 2013, Expert Syst. Appl..

[23]  Zhongsheng Hua,et al.  A note on group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment , 2007, Math. Comput. Model..

[24]  Zeshui Xu,et al.  A survey of preference relations , 2007, Int. J. Gen. Syst..

[25]  Valerie Belton,et al.  On a short-coming of Saaty's method of analytic hierarchies , 1983 .

[26]  Alessio Ishizaka,et al.  Review of the main developments in the analytic hierarchy process , 2011, Expert Syst. Appl..

[27]  E. Rosenbloom.  A probabilistic interpretation of the final rankings in AHP , 1997 .

[28]  J. Barzilai,et al.  Ahp Rank Reversal, Normalization and Aggregation Rules , 1994 .

[29]  María Teresa Lamata,et al.  On rank reversal and TOPSIS method , 2012, Math. Comput. Model..

[30]  Francisco Herrera,et al.  A Consensus Model for Group Decision Making With Incomplete Fuzzy Preference Relations , 2007, IEEE Transactions on Fuzzy Systems.

[31]  D. Buede,et al.  Rank disagreement: A comparison of multi‐criteria methodologies , 1995 .

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

[33]  S. Lai.  A Preference-based Interpretation of AHP , 1995 .

[34]  Dubravka M. Pavlicic,et al.  Normalisation affects the results of MADM methods , 2001 .

[35]  Evangelos Triantaphyllou,et al.  Two new cases of rank reversals when the AHP and some of its additive variants are used that do not occur with the multiplicative AHP , 2001 .

[36]  Adel Guitouni,et al.  A general decomposition approach for multi-criteria decision trees , 2012, Eur. J. Oper. Res..

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

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

[39]  J. Dyer.  Remarks on the analytic hierarchy process , 1990 .

[40]  J. Pérez.  Some comments on Saaty's AHP , 1995 .

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

[42]  Francisco Ortega,et al.  A method for the selection of customized equipment suppliers , 2013, Expert Syst. Appl..

[43]  Y. De Smet,et al.  Rank reversal in the PROMETHEE II method: Some new results , 2008, 2008 IEEE International Conference on Industrial Engineering and Engineering Management.

[44]  T. Saaty.  Fundamentals of Decision Making and Priority Theory With the Analytic Hierarchy Process , 2000 .

[45]  Dan Paulson,et al.  Consequences of uncertainty in the analytic hierarchy process: A simulation approach , 1995 .

[46]  F. J. Dodd,et al.  Inverse inconsistency in analytic hierarchies , 1995 .

[47]  E. Triantaphyllou,et al.  Ranking irregularities when evaluating alternatives by using some ELECTRE methods , 2008 .

[48]  Jiuh-Biing Sheu,et al.  A hybrid fuzzy-based approach for identifying global logistics strategies , 2004 .

[49]  Thomas L. Saaty,et al.  The legitimacy of rank reversal , 1984 .