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New Consistency Index for Comparison Matrices and Its Properties

Zhong Wan, Ming Chen, Ling Zhang


In this paper, an alternative measure method is presented to exquisitely test the consistency for the reciprocal matrices and the additive comparison matrices, which is directly derived from the perfect consistency conditions. Necessary and sufficient conditions for the consistency of comparison matrices are obtained, where both reciprocal and additive matrices are included. On the basis of a new index of consistency, the critical value which is employed to judge whether a comparison matrix can be accepted or not is investigated. Some illustrative examples are constructed to show that the proposed method is a more exquisite approach to describing the consistency as well as being easy to calculate the relevant index of consistency. Actually, there exist matrices which are identified to be consistent by the existent methods, but being regarded as unacceptable by our method.


reciprocal matrices, consistency index, fuzzy comparison matrices, consistency ratio

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