Eigenvector driven interval priority derivation and acceptability checking for interval multiplicative pairwise comparison matrices

Zhou-Jing Wang

doi:10.1016/j.cie.2021.107215

2021-06-01

PRE

Zhou-Jing Wang *

DOI：10.1016/j.cie.2021.107215

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摘要

En 中文

Priority derivation and acceptability checking play crucial roles in multi-criteria decision making (MCDM) with pairwise comparison matrices. However, the existing eigenvector based interval priority derivation methods often fail to obtain a reasonable and logical solution from an interval multiplicative pairwise comparison matrix (IMPCM). The obtained maximal eigenvalues are frequently unable to be used to check the quality of interval evaluations in an IMPCM. To get over these challenges, this paper introduces a new framework to additively normalize interval priorities from the viewpoint of producing an identical and consistent IMPCM. By analyzing the approximation relationship between original evaluations and interval priorities of IMPCMs, two positive real matrices and their corresponding eigenvector problems are established from an IMPCM and a procedure is developed to obtain eigenvector based additively normalized interval priorities from IMPCMs. A maximal eigenvalue based consistency index and its corresponding consistency ratio are defined and a method is presented to check the acceptability of an IMPCM by taking its inconsistency and its eigenvector based interval priority uncertainty into consideration. Afterwards, an approach is proposed to obtain global importance weights of the criteria at the bottom level and a procedure is devised to tackle hierarchical MCDM problems with interval assessments. The proposed interval priority derivation method and acceptability checking model are illustrated by two numerical examples and comparative studies are conducted to show their performance and superiority. Meanwhile, a renewable energy supply selection problem is utilized to demonstrate the applicability of the presented interval MCDM method.

Keyword:

Multi-criteria decision making

Interval multiplicative pairwise comparison matrix

Eigenvector

Interval priority

Acceptability

Renewable energy supply selection