A Consistency Test for AHP Decision Makers

Abstract

Saaty's analytic hierarchy proces\ a\se\wd a[tributc irnportance by soliciting decision makers' (DM) importance ratius to cornpute weight>. Saaty suggested :i decision rule lor accepting DM judgments based on ii con5istency measure derived from the DM's importance ratios. This paper Investigates the distribtition of random inconsistency and dccision rule implications. Stricter consistency requircments lor three-and lour-attribute criteria inatriccs are suggested..Cuhjecr .4reas: Decic.ion .4naly.si.s and I)eci.rion f'rocrsses. THE ANALY'I'IC HIEXARCHY PROCESSThe analytic hierarchy process (AHP) [7] 181 is a popular tool used by decision analysts to aid decision makers (DMs) in niultiattribute decisions. Zahedi's [lh] introduction and literature review is recommended for detailed information. In AHP, the hierarchy's first level i y the general objective for the decision. A typical hierarchy's second level has several attributes (criteria) that contribute to the general objective. Lower levels subdivide the attributes. Further levels relate the available alternatives lo each attribute or subdivision. This paper's terminology relates to the second level of the hierarchy, although the results apply to all levels. The brief discussion that follows emphasizes background items for the new work to be presented. AHP IpdtaFor each pair of attributes, the DM is asked, "What is the relative importance of this attribute with respect to that one?" The answers are importance ratios. The traditional A H P pairwise cornparison scale 191 has 17 importance ratios: the integers from 1 to 9 and the 8 reciprocals I'rorn 112 t o 119. For example, ratio I means the attributes are about equally importailt, 9 nieans the first is extremely more important than the second, and 115 means the second attribute is strongly more important than the first. Saaty [6] introduced a crireria matrix, C, to hold the importance ratios. For example, after attributes D, E, and 1; are identified a DM might provide the ratios shown i n the following matrix: A t t r b 1 11 t e S

Comparison between multiple‐choice and analytic hierarchy process: measuring human perception

“…In this study, we took 0.15 as the allowable upper bound of CI (Lane and Verdini, 1989), and employed only those samples whose CIs were equal to or smaller than 0.15. The ratios of samples satisfying this threshold were 85.9% ( 5 342/398) in Survey 1 and 90.2% ( 5 194/215) in Survey 2, respectively.…”

Analysis of MCDM methods output coherence in oil and gas portfolio prioritization

“…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.…”

An Application of Analytic Hierarchy Process (AHP) and Sensitivity Analysis for Maintenance Policy Selection

“…On the contrary if CR is greater than 10 percent, one should examine the possible cause. However, the standard consistency test has been criticized by a number of authors (see for example Lane and Verdini, 1989;Murphy, 1993;Karapetrovic and Rosenbloom, 1999). In this regard, we adopted a quality control approach for the consistency test, Unauthenticated Download Date | 6/20/19 3:04 AM proposed by Karapetrovic and Rosenbloom (1999).…”