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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.