Problem 44509. Determine if input is a valid AHP evaluation matrix

Created by Mehmet OZC

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Last Solution submitted on Mar 31, 2023

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David Verrelli on 28 Feb 2018

Hello, Mehmet OZC. Could you please clarify the requirement "Lower triangular part should be inverse of upper triangular part"? This seems to require that lowerTriangular{input} = inverse{ upperTriangular{input} }. However, that appears to be impossible (except for an identity matrix), as the result of taking that inverse will itself be upper triangular. http://mathworld.wolfram.com/MatrixInverse.html . —DIV

Mehmet OZC on 1 Mar 2018

it should be an element-wise inverse operation. For example a(3,2)=1/a(2,3) . Inverse operation with scalar values not with a matrix.

You can also search for "Understanding the Analytic Hierarchy Process"

David Verrelli on 4 Mar 2018

OK. I've had a quick look at https://doi.org/10.1007/978-3-319-33861-3_2 . On page 10 they clarify that elements a(x,y) and a(y,x) must be the _reciprocal_ of one another. So that's fine. But I haven't encountered a description of such a relation as "element-wise inverse" — is it an expression commonly used in that field?

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Problem 44509. Determine if input is a valid AHP evaluation matrix

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