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

Created by Mehmet OZC

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Input is a matrix. Output is a true or false statement (1 or 0). Return true if input is a valid Analytic Hierarchy Process evaluation matrix.

In a valid AHP matrix;

All diagonal elements should be 1
Lower triangular part should be element-wise reciprocals of upper triangular part
Square matrix

For example

   [ 1   2
    1/2  1]  -  > True

   [1 5
    2 1 ]   -  > False

   [1 5 
   1/5 2]   -  > False

Note: See test suite 19 for what is asked about rounding

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Last Solution submitted on Jul 18, 2025

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3 Comments

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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