By Gang Kou, Daji Ergu, Yi Peng, Yong Shi
The optimistic reciprocal pairwise comparability matrix (PCM) is likely one of the key elements that's used to quantify the qualitative and/or intangible attributes into measurable amounts. This publication examines six understudied problems with PCM, i.e. consistency attempt, inconsistent facts identity and adjustment, information assortment, lacking or doubtful information estimation, and sensitivity research of rank reversal. the utmost eigenvalue threshold strategy is proposed because the new consistency index for the AHP/ANP. An prompted bias matrix version (IBMM) is proposed to spot and modify the inconsistent facts, and estimate the lacking or doubtful information. purposes of IBMM together with threat overview and determination research, activity scheduling and source allocation in cloud computing setting, are brought to demonstrate the proposed IBMM.
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Additional resources for Data Processing for the AHP/ANP
15) 000 The scale values in pairwise matrix are given by experts according to their judgments and expertise. To be consistent, the rank can be transitive but the values of judgment do not necessarily follow the multiplication formula ai k akj D aij (Saaty 1991, 2001b). Obviously, the closer the values of ai k akj to the value of aij , the more consistent the comparison matrix is. Hence, the values of ai k akj should be as close to the value of aij as possible. 1, as the average of express n P ai k akj is close to the value of aij , no correction of judgment matrix is needed.
Likewise, the first 0 D a32 a22 a32 , the second 0 D a33 a32 a32 . We know that a22 D 1 and a33 D 1, so a32 is the inconsistent element as there are six elements equally and slightly more than zero. Then step7 is no longer needed. We can also confirm whether a32 has problem using the method of order reduction. R. 1. 0 B B B B B B B B B B B @ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 C C C C C C C C C C C A The identified inconsistent element is the same as one in (Iida 2009).
30). The detailed are showed as follows: 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.
Data Processing for the AHP/ANP by Gang Kou, Daji Ergu, Yi Peng, Yong Shi