The Rank Reversals Paradox in Management Decisions: The Comparison of the AHP and COMET Methods

Making decisions include many areas of human activity, as well as the management of the organization. Actually, decision-making requires a consideration of rapidly changing options from multiple sources. For this reason, the decision-making process requires modification, which allows processing of a set of alternatives on the fly. The most popular method in this field is the AHP method. However, a serious shortcoming is known, which does not allow to reliably carry out this process. This problem is known as the RankReversals phenomenon. The paper identifies the problem and highlights the importance in the context of numerical examples. These examples are also solved by using the COMET method, which uses a pairwise comparison also. The COMET method is completely free of rank reversal paradox and can be used in exchange for the AHP method.

[1]  W. Wedley,et al.  Ambiguous Criteria Weights in AHP: Consequences and Solutions* , 1989 .

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

[3]  Luis G. Vargas,et al.  Reply to “remarks on the analytic hierarchy process” by J. S. Dyer , 1990 .

[4]  Wojciech Sałabun,et al.  The Characteristic Objects Method: A New Distance‐based Approach to Multicriteria Decision‐making Problems , 2015 .

[5]  T. Saaty.  Decision making, new information, ranking and structure , 1987 .

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

[7]  Xiaowei Xu,et al.  Multi-criteria decision making approaches for supplier evaluation and selection: A literature review , 2010, Eur. J. Oper. Res..

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

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

[10]  Nachiappan Subramanian,et al.  A review of applications of Analytic Hierarchy Process in operations management , 2012 .

[11]  Ying-Ming Wang,et al.  An approach to avoiding rank reversal in AHP , 2006, Decis. Support Syst..

[12]  S R Watson,et al.  COMMENTS ON: ASSESSING ATTRIBUTE WEIGHTS BY RATIO , 1983 .

[13]  Andrzej Piegat,et al.  Comparative Analysis of MCDM Methods for Assessing the Severity of Chronic Liver Disease , 2015, ICAISC.

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

[15]  Luis G. Vargas.  Comments on Barzilai and Lootsma: Why the Multiplicative AHP Is Invalid: A Practical Counterexample , 1997 .

[16]  W. Sałabun.  Reduction in the Number of Comparisons Required to Create Matrix of Expert Judgment in the Comet Method , 2014 .

[17]  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 .

[18]  James S. Dyer,et al.  A clarification of “remarks on the analytic hierarchy process” , 1990 .

[19]  Evangelos Triantaphyllou,et al.  USING THE ANALYTIC HIERARCHY PROCESS FOR DECISION MAKING IN ENGINEERING APPLICATIONS: SOME CHALLENGES , 1995 .

[20]  L Vargas.  WHY THE MULTIPLICATIVE AHP IS INVALID: A PRACTICAL EXAMPLE , 1997 .

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

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

[23]  Wojciech Sałabun,et al.  Nonlinearity of human multi-criteria in decision-making , 2012 .

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

[25]  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..

[26]  Andrzej Piegat,et al.  Identification of a Multicriteria Decision-Making Model Using the Characteristic Objects Method , 2014, Appl. Comput. Intell. Soft Comput..

[27]  William C. Wedley,et al.  A Rejoinder to Forman on AHP, with Emphasis on the Requirements of Composite Ratio Scales* , 1992 .

[28]  Luis G. Vargas,et al.  The theory of ratio scale estimation: Saaty's analytic hierarchy process , 1987 .

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

[30]  Jaroslaw Jankowski,et al.  Knowledge management in MCDA domain , 2015, 2015 Federated Conference on Computer Science and Information Systems (FedCSIS).

[31]  Wojciech Sałabun.  The use of fuzzy logic to evaluate the nonlinearity of human multi-criteria used in decision making , 2012 .

[32]  Waldemar Wolski,et al.  Methodological aspects of Decision Support System for the location of renewable energy sources , 2015, 2015 Federated Conference on Computer Science and Information Systems (FedCSIS).

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

[34]  Wojciech Salabun,et al.  Application of the fuzzy multi-criteria decision-making method to identify nonlinear decision model , 2014 .

[35]  E. Choo,et al.  A UNIFIED APPROACH TO AHP WITH LINKING PINS , 1993 .