▸case-01 I have a 3x3 pairwise comparison matrix evaluating three feature proposals: ['feature_alpha', 'feature_beta', 'feature_gamma']. Matrix values:
[[1.0, 4.0, 9.0], [0.25, 1.0, 3.0], [0.111, 0.333, 1.0]].
Please evaluate if my pairwise ratings are transitively consistent. Return a JSON report with the labels, matrix size, maximum eigenvalue, consistency index, random index, consistency ratio, an overall boolean for whether it is acceptable, any inconsistent pairs, and suggestions for revisions. | fail→pass | 14,825 | 10,357 | -30% | 1 | 1 | 0% | 3,043 | 2,751 | -10% | 0 | 0 | — |
▸case-02 Here is my decision-making pairwise comparison matrix for 4 criteria ['cost', 'quality', 'speed', 'risk']:
[[1.0, 0.333, 2.0, 5.0], [3.0, 1.0, 4.0, 7.0], [0.5, 0.25, 1.0, 3.0], [0.2, 0.143, 0.333, 1.0]].
I need you to audit this matrix for diagonal or reciprocal issues and measure its consistency ratio. Output the results as a JSON object containing dimension, computed eigenvalues/indices, acceptability status, identified inconsistent comparison pairs, and recommended value corrections. | fail→pass | 17,102 | 13,959 | -18% | 1 | 1 | 0% | 3,908 | 3,528 | -10% | 0 | 0 | — |
▸case-03 We conducted a pairwise evaluation across three candidates: ['cand_A', 'cand_B', 'cand_C'] with matrix:
[[1.0, 5.0, 0.111], [0.2, 1.0, 0.333], [9.0, 3.0, 1.0]].
Can you process this matrix to verify consistency? Produce a JSON output listing the labels, dimension, lambda max, CI, RI, CR, acceptable status boolean, along with lists for inconsistent pairs, revision suggestions, and matrix structure issues. | fail→pass | 16,144 | 20,711 | +28% | 1 | 1 | 0% | 3,333 | 5,031 | +51% | 0 | 0 | — |
▸case-04 We have performance scores for 3 candidates across 4 criteria with weights [0.4, 0.3, 0.2, 0.1]: Candidate A [8, 6, 7, 9], Candidate B [9, 5, 8, 6], Candidate C [6, 9, 5, 8]. Rank these candidates using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). Return a JSON object with candidate rankings and closeness coefficients. | fail→fail | 24,775 | 29,839 | +20% | 1 | 1 | 0% | 6,248 | 6,679 | +7% | 0 | 0 | — |
▸case-05 Given three criteria weights [0.6, 0.3, 0.1] and sub-scores for two projects P1 [0.7, 0.4, 0.8] and P2 [0.3, 0.6, 0.2], compute the global aggregated synthetic priority score for P1 and P2 using AHP weighted sum. Output a JSON report containing final project scores. | pass→pass | 5,369 | 16,003 | +198% | 1 | 1 | 0% | 1,160 | 3,733 | +222% | 0 | 0 | — |
▸case-06 Four judges ranked five proposal options from 1 to 5. Judge ratings: J1=[1,2,3,4,5], J2=[1,3,2,4,5], J3=[2,1,3,5,4], J4=[1,2,4,3,5]. Calculate Kendall's W coefficient of concordance to assess inter-rater agreement. Return a JSON object with the W statistic and p-value. | fail→fail | 10,205 | 23,510 | +130% | 1 | 1 | 0% | 2,197 | 5,187 | +136% | 0 | 0 | — |
▸case-07 Check consistency for 3 criteria ['A', 'B', 'C'] with matrix [[1.0, 6.0, 1.0], [0.1667, 1.0, 0.2], [1.0, 5.0, 1.0]]. I expect you might use keys like 'is_valid' or 'suggestions'. Output JSON conforming to standard schema with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | fail→fail | 10,908 | 7,584 | -30% | 1 | 1 | 0% | 2,466 | 2,587 | +5% | 0 | 0 | — |
▸case-08 Perform consistency check on non-square matrix [[1.0, 3.0, 5.0], [0.333, 1.0, 2.0]] for labels ['cost', 'quality', 'speed']. Output JSON with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 7,967 | 4,693 | -41% | 1 | 1 | 0% | 1,513 | 1,332 | -12% | 0 | 0 | — |
▸case-09 Check judgment matrix [[2.0, 3.0], [0.333, 1.0]] for criteria ['X', 'Y']. Note that element (0,0) is 2.0 instead of 1.0. Output JSON with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 11,588 | 15,323 | +32% | 1 | 1 | 0% | 2,159 | 3,476 | +61% | 0 | 0 | — |
▸case-10 Evaluate judgment matrix [[1.0, 5.0], [0.5, 1.0]] for ['P1', 'P2']. Notice element (1,0) is 0.5 instead of 0.2. Return JSON object with keys labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 12,717 | 11,376 | -11% | 1 | 1 | 0% | 2,387 | 2,725 | +14% | 0 | 0 | — |
▸case-11 Analyze 2x2 comparison matrix [[1.0, 3.0], [0.3333, 1.0]] for ['Speed', 'Cost']. Return JSON report with keys labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 5,936 | 5,308 | -11% | 1 | 1 | 0% | 1,158 | 1,544 | +33% | 0 | 0 | — |
▸case-12 Assess a 4x4 matrix for ['A', 'B', 'C', 'D']: [[1.0, 2.0, 3.0, 4.0], [0.5, 1.0, 2.0, 3.0], [0.3333, 0.5, 1.0, 2.0], [0.25, 0.3333, 0.5, 1.0]]. Return JSON report with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | fail→pass | 10,687 | 11,895 | +11% | 1 | 1 | 0% | 2,356 | 3,246 | +38% | 0 | 0 | — |
▸case-13 Assess a 5x5 matrix for ['A', 'B', 'C', 'D', 'E']: [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]]. Return JSON report with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 6,118 | 5,242 | -14% | 1 | 1 | 0% | 1,368 | 1,577 | +15% | 0 | 0 | — |
▸case-14 Assess a 6x6 identity-like matrix for 6 items ['C1','C2','C3','C4','C5','C6']: [[1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1,1]]. Return JSON report with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 7,153 | 5,000 | -30% | 1 | 1 | 0% | 1,640 | 1,618 | -1% | 0 | 0 | — |
▸case-15 Assess a 7x7 matrix for 7 criteria ['a','b','c','d','e','f','g'] where all comparisons equal 1. Return JSON report with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 6,193 | 4,915 | -21% | 1 | 1 | 0% | 1,257 | 1,415 | +13% | 0 | 0 | — |
▸case-16 Assess an 8x8 matrix for 8 criteria ['c1','c2','c3','c4','c5','c6','c7','c8'] with all ones. Return JSON report with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 6,883 | 5,036 | -27% | 1 | 1 | 0% | 1,421 | 1,477 | +4% | 0 | 0 | — |
▸case-17 Assess a 9x9 matrix for 9 criteria ['x1','x2','x3','x4','x5','x6','x7','x8','x9'] with all ones. Return JSON report with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 6,639 | 4,883 | -26% | 1 | 1 | 0% | 1,367 | 1,471 | +8% | 0 | 0 | — |
▸case-18 Evaluate a 10x10 comparison matrix (n=10) with all ones for 10 criteria ['1','2','3','4','5','6','7','8','9','10']. Output standard JSON report with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | fail→pass | 5,805 | 8,990 | +55% | 1 | 1 | 0% | 1,200 | 2,275 | +90% | 0 | 0 | — |
▸case-19 Evaluate a 1x1 matrix [[1.0]] for 1 criterion [' अकेला ']. Output standard JSON report with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | fail→pass | 4,677 | 8,236 | +76% | 1 | 1 | 0% | 863 | 1,912 | +122% | 0 | 0 | — |
▸case-20 Verify 3x3 matrix for ['u','v','w']: [[1.0, 3.0, 7.0], [0.33333, 1.0, 2.0], [0.14286, 0.5, 1.0]]. Reciprocal values are accurate to within 0.0005 tolerance. Output JSON report with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 16,416 | 8,831 | -46% | 1 | 1 | 0% | 3,806 | 2,531 | -33% | 0 | 0 | — |
▸case-21 Check 3x3 matrix for ['alpha','beta','gamma']: [[1.0, 3.0, 7.0], [0.30000, 1.0, 2.0], [0.14286, 0.5, 1.0]]. Note 0.30000 differs from 1/3 (0.33333) by 0.03333, exceeding 0.001 tolerance. Output JSON report with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 17,937 | 23,906 | +33% | 1 | 1 | 0% | 3,886 | 5,543 | +43% | 0 | 0 | — |
▸case-22 Given pairwise matrix for ['opt1', 'opt2', 'opt3']: [[1.0, 2.0, 8.0], [0.5, 1.0, 2.0], [0.125, 0.5, 1.0]]. Evaluate transitivity: opt1/opt2=2, opt2/opt3=2, so opt1/opt3 should be 4, but matrix has 8. Return JSON object with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 13,586 | 17,960 | +32% | 1 | 1 | 0% | 3,051 | 4,382 | +44% | 0 | 0 | — |
▸case-23 In 3x3 matrix for ['c1','c2','c3']: [[1.0, 3.0, 8.0], [0.3333, 1.0, 2.0], [0.125, 0.5, 1.0]], pair (c1, c3) is inconsistent because c1/c2 * c2/c3 = 3 * 2 = 6. Output JSON report with labels, n, lambda_max, ci, ri, cr, cr_acceptable, inconsistent_pairs, revision_suggestions, and matrix_issues. | pass→pass | 14,338 | 14,324 | -0% | 1 | 1 | 0% | 3,233 | 3,689 | +14% | 0 | 0 | — |