2006
DOI: 10.1142/s0218488506004114
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Consistency in the Analytic Hierarchy Process: A New Approach

Abstract: In this paper, we present a statistical criterion for accepting/rejecting the pairwise reciprocal comparison matrices in the analytic hierarchy process. We have studied the consistency in random matrices of different sizes. We do not agree with the traditional criterion of accepting matrices due to their inflexibility and because it is too restrictive when the size of the matrix increases. Our system is capable of adapting the acceptance requirements to different scopes and consistency necessities. The advanta… Show more

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Cited by 674 publications
(326 citation statements)
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References 30 publications
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“…AHP is a very popular approach to MCDM that involves qualitative data. The method uses a reciprocal decision matrix obtained by pair-wise comparisons so that the information is given in a linguistic form [15]. Rather than prescribing a "correct" decision, the AHP helps in determining one.…”
Section: A Analytic Hierarchy Process (Ahp)mentioning
confidence: 99%
“…AHP is a very popular approach to MCDM that involves qualitative data. The method uses a reciprocal decision matrix obtained by pair-wise comparisons so that the information is given in a linguistic form [15]. Rather than prescribing a "correct" decision, the AHP helps in determining one.…”
Section: A Analytic Hierarchy Process (Ahp)mentioning
confidence: 99%
“…This research The problem of consistency-based matrix acceptance or rejection has been greatly discussed without reaching a consensus. Murphy (1993), for example, has argued that the 9-point scale suggested by Saaty yields results that are outside the accepted consistency when the number of alternatives or criteria (n) increases (Alonso and Lamata 2006). On the other hand, Young et al (2010) have argued that verifying the CR does not contribute directly to selecting a single alternative goal (i.e., alternatives rankings), but rather to provide a logic-based consistency check on the validity of the pairwise comparison matrices entries.…”
Section: Aggregating Priorities Using Three Mcdm Methodsmentioning
confidence: 99%
“…If CR is\10%, the matrix is said to be consistent. Researchers have proposed different methods to calculate RI, which were mostly based on simulations (Alonso and Lamata 2006;Lane and Verdini 1989;Tummala and Wan 1994) or incomplete matrices (Forman, 1990). However, this research paper uses Saaty's (1977) approach, which calculates RI based on the average CI of 500 randomly filled matrices, as shown in Table 3.…”
Section: Evaluation Of Alternatives and Criteriamentioning
confidence: 99%
“…Saaty (1987) computed and presented a list of RI estimates for positive reciprocal matrices of orders 2 to 14. Subsequently, several authors computed different RI depending on the simulation method and the number of generated matrices involved in the process (Noble, Sanchez 1990;Tummala, Wan 1994;Alonso, Lamata 2006). In the present study, the RI obtained by Noble and Sanchez (1990) with 5,000 simulation runs has been used.…”
Section: Methodsmentioning
confidence: 99%