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On distance-based inconsistency reduction algorithms for pairwise comparisons. (English) Zbl 1201.68114

Summary: A complete proof of convergence of a certain class of reduction algorithms for distance-based inconsistency (defined in 1993) for pairwise comparisons is presented in this paper. Using pairwise comparisons is a powerful method for synthesizing measurements and subjective assessments. From the mathematical point of view, the pairwise comparisons method generates a matrix (say \(A\)) of ratio values \((a_{ij})\) of the \(i\)th entity compared with the \(j\)th entity according to a given criterion. Entities/criteria can be both quantitative or qualitative allowing this method to deal with complex decisions. However, subjective assessments often involve inconsistency, which is usually undesirable. The assessment can be refined via analysis of inconsistency, leading to reduction of the latter.
The proposed method of localizing the inconsistency may conceivably be of relevance for nonclassical logics (e.g., paraconsistent logic) and for uncertainty reasoning since it accommodates inconsistency by treating inconsistent data as still useful information.

MSC:

68T27 Logic in artificial intelligence
03B53 Paraconsistent logics
65F30 Other matrix algorithms (MSC2010)
68T37 Reasoning under uncertainty in the context of artificial intelligence

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