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Data Inconsistency and Incompleteness Processing Model in Decision Matrix

Daji ERGU1, Gang KOU2
1 School of Management and Economics,
University of Electronic Science and Technology of China,
Chengdu, 611731, China
2 School of Business Administration,
Southwest University of Finance and Economics of China,
Chengdu, 610074, China

Abstract: Data Inconsistency and incompleteness issues of pairwise comparison matrix (PCM) are hot research topics in multi-criteria decision making (MCDM). The goal of this paper is to propose a simple approach to identify and adjust the inconsistent data while estimate the missing data in a PCM. Specifically, an arithmetic mean matrix is induced to identify the most inconsistent data efficiently while preserving most of the original information in a PCM, and then we adapt it to estimate the missing data in an incomplete PCM. The proposed model is only dependent on the data in the original matrix, and can effectively process the most inconsistent or missing data in a PCM. The correctness of the proposed method is proved mathematically. Two numerical examples are used to illustrate the proposed method. The result shows that the proposed method is accurate and efficient when processing the inconsistent or missing data to satisfy the consistency requirements of PCM.

Keywords: Inconsistency data, Missing data, Pairwise comparison matrix, Arithmetic mean induced bias matrix.

>>Full text
Daji ERGU, Gang KOU, Data Inconsistency and Incompleteness Processing Model in Decision Matrix, Studies in Informatics and Control, ISSN 1220-1766, vol. 22 (4), pp. 359-368, 2013.