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This study presents special cases of inconsistent pairwise comparisons PCmatrices and analysis of their eigenvalue-based inconsistency index usingmathematical methods. All studied special cases of PC matrices are Toeplitzmatrices with only three different entries $1$, $x$, and $1/x$. A new type ofcirculant pairwise comparisons matrix has been introduced. Although this classof PC matrices may be perceived as restricted, it is general enough to covernumerous levels of eigenvalue-based inconsistency index from the lowest to thehighest. Both exact mathematical expressions and estimations, where the exactexpression was impossible to find, are provided

Special cases of pairwise comparisons matrices represented by Toeplitz matrices