Pairwise Comparison of Criteria

When there are many criteria, it would be difficult for a DM to rank order them precisely. In practice, pairwise comparison of criteria is used to facilitate the criteria ranking required by the Borda count method. Here, the DM is asked to give the relative importance between two criteria Q and Cj, whether Q is preferred to Cj, Cj is preferred to Q or both are equally important. When 

Based on the DM s response, the criteria rankings and their weights can be computed, following the steps given here  

Step 1 Based on the DM s response, a pairwise comparison matrix, P(nyn) is constructed, whose elements are as follows  

Step 3 Rank the criteria based on the f, values and compute their weights. 

Five criteria—A, B, C, D, and E—have to be ranked based on 10 pairwise comparisons as follows. 

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Step 1 In the first step, a pairwise comparison of criteria using the 1-9 degree of importance scale shown in Table 2.8 is carried out. 

Third, establish the relative significance (weight) of each criterion. This usually is accomplished via a set of pairwise comparisons among the different criteria. In each pairwise comparison, two criteria on the same hierarchical level are directly compared. The decision maker (in this case, the study team) establishes the importance of one criteria relative to the other. All unique pairs of criteria at each level of the hierarchy are compared via such pairwise comparisons until all possible combinations have been compared. AHP then translates the pairwise comparison results into a relative weight for each criterion. 

The judgment matrices were formulated, with re ct to the hierarchy level according to certain criteria of comparison within certain scales [20], The Saaty s scales of pairwise comparisons of assessment model were given in Table 1... 

At each level of the hierarchy, a pairwise comparison of the vertices criteria/subcriteria is performed from the point of view of their "contribution (weights)" to each of the higher-level vertices to which they are linked. 

Takeda, E., and Yu, P. L. (1995), Assessing Priority Weights from Subsets of Pairwise Comparisons in Multiple Criteria Optimization Problems, European Journal of Operational Research, Vol. 86. Werners, B. (1987), Interactive Multiple Objective Programming Subject to Flexible Constraints, European Journal of Operational Research, Vol. 31, pp. 342-349. 

Patients with osteoarthritis or rheumatoid arthritis are randomized to one of three treatments, celecoxib, ibuprofen, or naproxen, and the primary endpoint is the occurrence of a cardiovascular endpoint a nonfatal myocardial infarction, a nonfatal stroke, or any cardiovascular death. Non-inferiority will be assessed for three different pairwise comparisons celecoxib versus ibuprofen, celecoxib versus naproxen, and ibuprofen versus naproxen. The definition of non-inferiority differs somewhat from the fixed margin approach describe earlier in that there are separate criteria for the confidence interval and the point estimate. The hazard ratio for each comparison will be calculated, and non-inferiority will be concluded if the upper end of the... 

Sharma, R. Kimiar, S. 2008. Performance modelling in critical engineering systems using RAM analysis. Reliability Engineering System Safety 93 891-897 Triantaphyllou, E. et al. 1994. On the evaluation and application of different scales for quantifying pairwise comparisons in fiizzy sets. Journal of Multi-Criteria Decision Analysis 5 133-155... 

Accommodates multiple criteria Length of the process, which increases with the number of levels and number of pairwise comparisons... 

If n is the number of items (criteria, sub-criteria or alternatives) to be compared with relation to a specific element of the immediately higher level, the total number of judgments required to the decision maker is [n (n - l)/2]. Each pairwise comparison judgment constitutes the element a j of the so-called reciprocal pair-wise comparisons matrix. 

If there are n criteria to evaluate, then the pairwise comparison matrix for the criteria is given by A( ) = where represents the relative importance of criterion i with respect to criterion j. Set = 1 and = —. The... 

Preemptive GP ranks the objective fimctions with respect to the ordered preferences of the DMs and minimizes the deviations from the target values associated with each objective in the ranked order. Several different techniques can be used to derive preemptive priorities. One convenient way is to use discrete alternative multi-criteria decision-making methods such as rating, Borda count, pairwise comparison, or the analytic hierarchy process (AHP) method (see Ravindran et al. [2010] for an application). These methods also provide a numerical strength-of-preference value that can be used in non-preemptive GP models. The preemptive GP model formulation, assuming that the preference ordering of the objectives is Zy Zy Zy Zy as follows ... 

Decision makers are asked to respond to n(n -1) / 2 pairwise comparisons in which two elements at a time are compared with respect to their parent criteria. The relative dominance values (flj.) are then elicited from the said respondents using the so-called Saaty s fundamental 9-point scale. After the pairwise comparison matrix A is filled up with those value judgments Aj., the relative weights (w) of the elements are computed from the normalized right eigenvector associated to the principal eigenvalue (2 ) of A as shown in the following equations ... 

Indication of which prioritization scheme is being used (Basic or Pairwise Comparison) and what weights have been entered for the three categories of evaluation criteria (financial considerations, implementation considerations, and potential impacts). 

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