Checking and adjusting order-consistency of linguistic pairwise comparison matrices for getting transitive preference relations
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TL;DR
This work introduces the equivalent conditions of (strong) transitivity by using route matrices and digraphs and develops an adjustment procedure to help decision makers correcting the inconsistency.
Abstract
Abstract Linguistic pairwise comparison matrices for decision-making need to be (strongly) order-consistent, which means the judgments should be (strongly) transitive. We introduce the equivalent conditions of (strong) transitivity by using route matrices and digraphs and develop an adjustment procedure to help decision makers correcting the inconsistency. The conclusion can extend to other ordinal-scaled or numerical comparison matrices as well.
