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

被引:3
|
作者
Ergu, Daji [1 ,2 ]
Kou, Gang [1 ]
Peng, Yi [1 ]
Shi, Yong [3 ,4 ]
Shi, Yu [1 ]
机构
[1] Univ Elect Sci & Technol China, Sch Management & Econ, Chengdu 610054, Peoples R China
[2] Southwest Univ Natl, Chengdu, Peoples R China
[3] Univ Nebraska, Coll Informat Sci & Technol, Omaha, NE 68182 USA
[4] Chinese Acad Sci, Res Ctr Fictitious Econ & Data Sci, Beijing, Peoples R China
基金
中国国家自然科学基金;
关键词
incomplete reciprocal pairwise comparison matrix; matrix multiplication; bias induced matrix model (BIMM); missing entries; minimize the inconsistency;
D O I
10.1002/mcda.472
中图分类号
C93 [管理学];
学科分类号
12 ; 1201 ; 1202 ; 120202 ;
摘要
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.
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页码:101 / 113
页数:13
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