Analysis of compatibility between interdependent matrices in ANP

Analytic network process (ANP) addresses multi-attribute decision-making where attributes exhibit dependencies. A principal characteristic of such problems is that pairwise comparisons are needed for attributes that have interdependencies. We propose that before such comparison matrices are used—in addition to a test that assesses the consistency of a pairwise comparison matrix—a test must also be conducted to assess ‘consistency’ across interdependent matrices. We call such a cross-matrix consistency test as a compatibility test. In this paper, we design a compatibility test for interdependent matrices between two clusters of attributes. We motivate our exposition by addressing compatibility in Sinarchy, a special form of ANP where interdependency exists between the last and next-to-last level. The developed compatibility test is applicable to any pair of interdependent matrices that are a part of an ANP.

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

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

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

[4]  Luis G. Vargas.  Reply to Schenkerman's avoiding rank reversal in AHP decision support models , 1994 .

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

[6]  Sr Watson,et al.  Assesing Attribute Weights , 1982 .

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

[8]  V. Belton,et al.  The legitimacy of rank reversal—A comment , 1985 .

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

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

[11]  Stan Schenkerman,et al.  Inducement of Nonexistent Order by the Analytic Hierarchy Process , 1997 .

[12]  Thomas L. Saaty,et al.  How to Make a Decision: The Analytic Hierarchy Process , 1990 .

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

[14]  Ricardo D. Kamenetzky.  THE RELATIONSHIP BETWEEN THE ANALYTIC HIERARCHY PROCESS AND THE ADDITIVE VALUE FUNCTION , 1982 .

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

[16]  Antonie Stam,et al.  PAHAP: A Pairwise Aggregated Hierarchical Analysis of Ratio‐Scale Preferences , 1994 .