BIMM: A Bias Induced Matrix Model for Incomplete Reciprocal Pairwise Comparison Matrix

The reciprocal pairwise comparison matrix is a well-established technique and widely used in multiple criteria decision making methods. However, some entries in a pairwise comparison matrix may not be available in many real-world decision problems. The goal of this paper is to propose a new method for estimating missing elements of an incomplete pairwise comparison matrix. A bias induced matrix model (BIMM), which combines the matrix multiplication and the properties of the original reciprocal pairwise comparison matrix, is used to calculate the missing entries in an incomplete pairwise comparison matrix. The proposed BIMM minimizes all bias values of the bias induced matrix to keep the global consistency. The missing value(s) can be estimated by solving the system of equations from the bias induced matrix. The theorems of the BIMM and the related corollaries are developed, and three numerical examples are introduced to illustrate the proposed model. Copyright (C) 2011 John Wiley & Sons, Ltd.