450 1 0236 4358 4235 1 For the final ranking of the three Courses we obtain the

450 1 0236 4358 4235 1 for the final ranking of the

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0.450 1 0.236 4.358 4.235 1 For the final ranking of the three Courses, we obtain the following weights according to detailed spreadsheet instructions in [25] and [39]: W 11 =0.651, W 21 =0.120, W 31 =0.240 Fig. 1. Ranking of the three Courses, according to students’ preferences by AHP. D. Calculation of the Consistency Ratios for Each Pairwise Comparison Matrix A matrix is said to be consistent if it holds: α ij * α jk = α ik , for every i, j and k. We must calculate the Consistency Ratios for every pairwise comparison matrix and these Ratios [26], must not exceed appreciably 0.10, otherwise we must revise some of our judgments. The Consistency Ratio is given by: CR= n r n n * ) 1 ( ) ( max where λ max is the maximum eigenvalue given by the average Consistency Measure for all alternatives [25, 39], n is the number of alternatives for this problem (n=3) and r n is a random number given by Saaty [26], for n=3, the number of alternatives r n =0.58. The Consistency Ratios calculated in the same manner for the matrices A, B, C, and D, using Microsoft Excel [10, 25, 39] are given below: TABLE I C ONSISTENCY R ATIOS FOR THE P AIRWISE C OMPARISON M ATRICES Pairwise Comparison Matrix Consistency Ratio Pairwise Comparison Matrix Consistency Ratio A 0.070 C 0.082 B 0.050 D 0.066 Note, that every Consistency Ratio is less than 0.10, according to the guidelines of Saaty [26]. Hence, the judgments of the evaluators are fairly consistent. E. The Pairwise Comparison Matrices for the Sub-criteria of Each Criterion Now, we turn our attention to the pairwise comparisons of the sub-criteria corresponding to each criterion. We form the following pairwise matrix E, for the sub-criteria of the first criterion: “Effectiveness of teaching Professor” described in paragraph (d) of Section (II). 1 1.111 0.428 0.298 0.294 900 . 0 1 0.321 0.278 0.273 333 . 2 3.111 1 0.289 0.333 3.347 3.586 3.455 1 0.275 3.400 3.662 3 3,626 1 RACTIV FRIENDC COMMNCA PEXPER ACQUAL RACTIV FRIENDC COMMNCA PEXPER ACQUAL E We next find the following weights, summarized graphically in the following graph and the Consistency Ratio for matrix E: Fig. 2. Ranking of qualities for Academic Teacher. Consistency Ratio= 0.081. We can see that the highest weight of “importance” is assigned to “Academic Qualifications” whereas the lowest Proceedings of the World Congress on Engineering 2014 Vol II, WCE 2014, July 2 - 4, 2014, London, U.K. ISBN: 978-988-19253-5-0 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) WCE 2014
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