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This book examines issues of PCM, including consistency test, inconsistent data identification and adjustment, missing or uncertain data estimation, and sensitivity analysis of rank reversal. Proposes and demonstrates an induced bias matrix model (IBMM).

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The positive reciprocal pairwise comparison matrix (PCM) is one of the key components which is used to quantify the qualitative and/or intangible attributes into measurable quantities. This book examines six understudied issues of PCM, i.e. consistency test, inconsistent data identification and adjustment, data collection, missing or uncertain data estimation, and sensitivity analysis of rank reversal. The maximum eigenvalue threshold method is proposed as the new consistency index for the AHP/ANP. An induced bias matrix model (IBMM) is proposed to identify and adjust the inconsistent data, and estimate the missing or uncertain data. Two applications of IBMM including risk assessment and decision analysis, task scheduling and resource allocation in cloud computing environment, are introduced to illustrate the proposed IBMM.

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1: Introduction.- 2: A new consistency test index for the data in the AHP/ANP.- 2.1 Basics of the AHP/ANP.- 2.1.1 The reciprocal pairwise comparison matrix.- 2.1.2 Basics of the AHP.- 2.1.3 Basics of the ANP.- 2.2 Consistency test issue in the AHP/ANP.- 2.2.1. Analysis of the consistency ratio (CR) method.- 2.2.2 The issues of consistency test in the AHP/ANP.- 2.3 The new consistency index--Maximum Eigenvalue Threshold for the AHP/ANP.- 2.3.1 The advantages of Maximum Eigenvalue Threshold for the AHP/ANP.- 2.4 The processes of data consistency test in the AHP/ANP.- 2.5. Illustrative example.- 3: IBMM for inconsistent data identification and adjustment in the AHP/ANP.- 3.1 The theorems of induced bias matrix model (IBMM) .- 3.1.1 The theoretical proofs of IBMM.- 3.2 IBMM for inconsistent data identification and adjustment.- 3.2.1 The basics of the inconsistency identification and adjustment method.- 3.2.2. The processes of inconsistency identification and adjustment method.- 3.2.3 Fast inconsistency identification and adjustment method.- 3.3. Illustrative examples.- 3.3.1 Illustrative examples for general inconsistency identification and adjustment method.- 3.3.2 Illustrative examples for fast inconsistency identification and adjustment method.- 4: IBMM for Missing Data Estimation.- 4.1 Basics of the IBMM for missing data estimation.- 4.2 The processes of estimating missing data by the IBMM.- 4.3 Proofs of the IBMM for IPCM in order three.- 4.4 Illustrative examples.- 4.4.1 Illustrative examples in order three.- 4.4.2 Illustrative examples in order four.- Chapter 5: IBMM for Questionnaire Design Improvement.- 5.1 Motivation of the research.- 5.2 The principles of improving the questionnaire design.- 5.3 Illustrative example.- Chapter 6: IBMM for rank reversal.- 6.1 Rank reversal issue in the AHP/ANP.- 6.2 Sensitivity analysis of rank reversal by the IBMM.- 6.3 Illustrative examples.- 7: Applications of IBMM.- 7.1 Task scheduling and resource allocation in cloud computing environment by the IBMM.- 7.1.1 Resource allocation in cloud computing.- 7.1.2 Task-oriented resource allocation in cloud computing.- 7.1.3 Illustrative example.- 7.2 Risk assessment and decision analysis by the IBMM.- 7.2.1 Background of risk assessment and decision analysis.- 7.2.2 Illustrative Examples.- 8. Induced Arithmetic Average Bias Matrix Model (IAABMM).- 8.1 The theorem of IAABMM.- 8.2 The inconsistency identification processes of IAABMM.- 8.3 The estimating formula of inconsistency adjustment.- 8.4. Illustrative Examples.- References. _

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