By Gang Kou, Daji Ergu, Yi Peng, Yong Shi
The confident reciprocal pairwise comparability matrix (PCM) is among the key parts that is used to quantify the qualitative and/or intangible attributes into measurable amounts. This ebook examines six understudied problems with PCM, i.e. consistency try out, inconsistent info identity and adjustment, info assortment, lacking or doubtful info estimation, and sensitivity research of rank reversal. the utmost eigenvalue threshold procedure is proposed because the new consistency index for the AHP/ANP. An triggered bias matrix version (IBMM) is proposed to spot and regulate the inconsistent information, and estimate the lacking or doubtful info. functions of IBMM together with chance overview and selection research, activity scheduling and source allocation in cloud computing atmosphere, are brought to demonstrate the proposed IBMM.
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Additional info for Data Processing for the AHP/ANP
2 IBMM for Inconsistent Data Identification and Adjustment 43 Given the above conditions, the element to be adjusted could be identified as Step 7: Step 7: Find the values of ci k and ckj in the induced matrix C according to the following procedures: Based on our assumption, that is, assume the bias value of ai k akj aij in bias vector f is the largest positive one, then one or both ai k and akj are too large, therefore it is impossible that cik > 0 and ckj > 0 simultaneously. n P If ci k < 0 and ckj > 0, thenai k is too large due to ci k D n1 ai l alk ai k , and lD1 akj is too small.
4. In order to demonstrate how the proposed method could identify more than two elements in pair-wise matrix with high order, we generated the following pair-wise matrix by adding one row and one column with random value to the comparison matrix in the second example. The new comparison matrix also denoted by A with max D 11:124 and C:R: D 0:2328 > 0:1. 56 3 IBMM for Inconsistent Data Identification and Adjustment in the AHP/ANP 2 6 6 6 6 6 6 6 AD6 6 6 6 6 6 4 1 2 1=2 2 1=2 2 1=2 2 1=2 1 4 1 1=4 1 1=4 1 2 1=4 1 4 1 4 1 4 1=2 1 1=4 1 1=4 1 1=4 1 2 4 1 4 1 4 1 4 1=2 1 1=4 1 1=4 1 1=4 1 2 4 1 4 1 4 1 4 1=2 1 1=4 1 1=4 1 1=4 1 3 4 7 6 1=6 3 1=7 2 1=3 1=4 1=7 1=6 6 1=3 7 1=2 1 3 7 7 7 7 7 7 7 7 7 7 7 7 7 5 According to the proposed inconsistency identification method, we have: Step 1.
1, the pairwise comparison matrix A is perfectly consistent. The result is in accordance with the above assumption. 2. 3. From the above results we find that all entries in the main diagonal of the IBM C are equal to zero. This result indicates that the comparison matrix A satisfies the reciprocal condition although it is inconsistent. Therefore, the following theorem can be derived. 4. All entries in the main diagonal of the induced bias matrix (IBM) C D AA nA should be zeroes whether matrix A is consistent or not as long as the comparison matrixA satisfies the reciprocal condition.