Al Salem, Aqeel Asaad and Awasthi, Anjali
(2017)
*Investigating Rank Reversal in Reciprocal Fuzzy Preference Relation Based on Additive Consistency: Causes and Solutions.*
Computers & Industrial Engineering
.
ISSN 03608352
(In Press)

Preview |
Text (application/pdf)
1MBawasthi-caie-2017.pdf - Accepted Version Available under License Spectrum Terms of Access. |

Official URL: http://dx.doi.org/10.1016/j.cie.2017.11.027

## 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.

Divisions: | Concordia University > Gina Cody School of Engineering and Computer Science > Concordia Institute for Information Systems Engineering |
---|---|

Item Type: | Article |

Refereed: | Yes |

Authors: | Al Salem, Aqeel Asaad and Awasthi, Anjali |

Journal or Publication: | Computers & Industrial Engineering |

Date: | 5 December 2017 |

Digital Object Identifier (DOI): | 10.1016/j.cie.2017.11.027 |

Keywords: | Preference relation; Multi criteria analysis; Rank Reversal; Additive consistency; AHP |

ID Code: | 983282 |

Deposited By: | Danielle Dennie |

Deposited On: | 06 Dec 2017 18:49 |

Last Modified: | 01 Dec 2018 01:01 |

## References:

J. Aguaron, J.M. Moreno-Jiménez The geometric consistency index: Approximated thresholds European journal of operational research, 147 (1) (2003), pp. 137–145B. Anbaroglu, B. Heydecker, T. Cheng Spatio-temporal clustering for non-recurrent traffic congestion detection on urban road networks Transportation Research C, 48 (2014), pp. 47–65

C.A. Bana e Costa, J.C. Vansnick A critical analysis of the eigenvalue method used to derive priorities in AHP European Journal of Operational Research, 187 (3) (2008), pp. 1422–1428

J. Barzilai, B. Golany AHP rank reversal, normalization and aggregation rules INFOR-Information Systems and Operational Research, 32 (2) (1994), pp. 57–64

J. Barzilai, F.A. Lootsma Power relations and group aggregation in the multiplicative AHP and SMART Journal of Multi-Criteria Decision Analysis, 6 (3) (1997), pp. 155–165

V. Belton, T. Gear On a shortcoming of Saaty's method of analytic hierarchies Omega, 11 (3) (1983), pp. 228–230

D.M. Buede, D.T. Maxwell Rank disagreement: A comparison of multi-criteria methodologies Journal of Multi-Criteria Decision Analysis, 4 (1) (1995), pp. 1–21

F. Chiclana, E. Herrera-Viedma, S. Alonso A note on two methods for estimating missing pairwise preference values Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 39 (6) (2009), pp. 1628–1633

J.R. Chou A linguistic evaluation approach for universal design Information Sciences, 190 (2012), pp. 76–94

F.J. Dodd, H.A. Donegan, T.B.M. McMaster Inverse inconsistency in analytic hierarchies European Journal of Operational Research, 80 (1) (1995), pp. 86–93

J.S. Dyer Remarks on the analytic hierarchy process Management science, 36 (3) (1990), pp. 249–258

L. Dymova, P. Sevastjanov, A. Tikhonenko A direct interval extension of TOPSIS method Expert Systems with Applications, 40 (12) (2013), pp. 4841–4847

A. Farkas, A. György, P. Rózsa On the spectrum of pairwise comparison matrices Linear algebra and its applications, 385 (2004), pp. 443–462

E.H. Forman AHP is intended for more than expected value calculations Decision Sciences, 21 (3) (1990), pp. 670–672

A. Frini, A. Guitouni, J.M. Martel A general decomposition approach for multi-criteria decision trees European Journal of Operational Research, 220 (2012), pp. 452–460

M.S. Garcia-Cascales, M.T. Lamata On rank reversal and TOPSIS method Mathematical and Computer Modelling, 56 (5) (2012), pp. 123–132

E. Herrera-Viedma, S. Alonso, F. Chiclana, F. Herrera A consensus model for group decision making with incomplete fuzzy preference relations IEEE Transactions on fuzzy Systems, 15 (5) (2007), pp. 863–877

E. Herrera-Viedma, F. Herrera, F. Chiclana, M. Luque Some issues on consistency of fuzzy preference relations European journal of operational research, 154 (1) (2004), pp. 98–109

A. Ishizaka, A. Labib Review of the main developments in the analytic hierarchy process Expert Systems with Applications, 38 (11) (2011), pp. 14336–14345

S. Karapetrovic, E.S. Rosenbloom A quality control approach to consistency paradoxes in AHP European Journal of Operational Research, 119 (3) (1999), pp. 704–718

S.K. Lai A preference-based interpretation of AHP Omega, 23 (4) (1995), pp. 453–462

P. Leskinen, J. Kangas Rank reversals in multi-criteria decision analysis with statistical modelling of ratio-scale pairwise comparisons Journal of the Operational Research Society, 56 (7) (2005), pp. 855–861

L.C. Leung, D. Cao On the efficacy of modeling multi-attribute decision problems using AHP and Sinarchy European Journal of Operational Research, 132 (1) (2001), pp. 39–49

F.A. Lootsma Scale sensitivity in the Multiplicative AHP and SMART Journal of Multi-Criteria Decision Analysis, 2 (1993), pp. 87–110

B. Mareschal, Y. De Smet, P. Nemery Rank reversal in the PROMETHEE II method: some new results , Industrial Engineering and Engineering Management, 2008. IEEM 2008. IEEE International Conference on, IEEE (2008 December), pp. 959–963

F. Meng, X. Chen A new method for group decision making with incomplete fuzzy preference relations Knowledge-Based Systems, 73 (2015), pp. 111–123

I. Millet The effectiveness of alternative preference elicitation methods in the analytic hierarchy process Journal of Multi-Criteria Decision Analysis, 6 (1) (1997), pp. 41–51

I. Millet, T.L. Saaty On the relativity of relative measures–accommodating both rank preservation and rank reversals in the AHP European Journal of Operational Research, 121 (1) (2000), pp. 205–212

D. Paulson, S. Zahir Consequences of uncertainty in the analytic hierarchy process: A simulation approach European Journal of Operational Research, 87 (1) (1995), pp. 45–56

D.M. Pavlicic Normalization affects the results of MADM methods Yugoslav journal of operations research, 11 (2) (2001), pp. 251–265

J. Perez Some comments on Saaty's AHP Management Science, 41 (6) (1995), pp. 1091–1095

A. Rodriguez, F. Ortega, R. Concepción A method for the selection of customized equipment suppliers Expert Systems with Applications, 40 (4) (2013), pp. 1170–1176

E.S. Rosenbloom A probabilistic interpretation of the final rankings in AHP European Journal of Operational Research, 96 (2) (1997), pp. 371–378

T.L. Saaty The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation McGraw-Hill, New York (1980)

T.L. Saaty Rank generation, preservation, and reversal in the analytic hierarchy decision process Decision sciences, 18 (2) (1987), pp. 157–177

T.L. Saaty Fundamentals of decision making RWS Publications, Pittsburgh (1994)

T.L. Saaty, L.G. Vargas The legitimacy of rank reversal Omega, 12 (5) (1984), pp. 513–516

S. Schenkerman Avoiding rank reversal in AHP decision-support model European Journal of Operational Research, 74 (1994), pp. 409–419

J.B. Sheu A hybrid fuzzy-based approach for identifying global logistics strategies Transportation Research Part E: Logistics and Transportation Review, 40 (1) (2004), pp. 39–61

T. Tanino Fuzzy preference orderings in group decision making Fuzzy sets and systems, 12 (2) (1984), pp. 117–131

E. Triantaphyllou 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 Journal of Multi-Criteria Decision Analysis, 10 (1) (2001), pp. 11–25

R. Urena, F. Chiclana, J.A. Morente-Molinera, E. Herrera-Viedma Managing incomplete preference relations in decision making: A review and future trends Information Sciences, 302 (2015), pp. 14–32

X. Wang, E. Triantaphyllou Ranking irregularities when evaluating alternatives by using some ELECTRE methods Omega, 36 (1) (2008), pp. 45–63

Y.M. Wang, Y. Luo On rank reversal in decision analysis Mathematical and Computer Modelling, 49 (5) (2009), pp. 1221–1229

Y.M. Wang, Y. Luo, Z.S. Hua A note on group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment Mathematical and Computer Modelling, 46 (9) (2007), pp. 1256–1264

Z. Wu, J. Xu A concise consensus support model for group decision making with reciprocal preference relations based on deviation measures Fuzzy Sets and Systems, 206 (2012), pp. 58–73

Z. Xu A survey of preference relations International journal of general systems, 36 (2) (2007), pp. 179–203

X. Zhang, B. Ge, J. Jiang, Y. Tan Consensus building in group decision making based on multiplicative consistency with incomplete reciprocal preference relations Knowledge-Based Systems (2016)

Repository Staff Only: item control page