1. **Problem Statement:** Calculate the Consistency Ratio (CR) for a given 15x15 pairwise comparison matrix in Analytic Hierarchy Process (AHP) using the provided weights vector and given approximations. 2. **Formulas and Definitions:** - Consistency Ratio: $$CR = \frac{CI}{RI}$$ - Consistency Index: $$CI = \frac{\lambda_{max} - n}{n - 1}$$ - Here, $$\lambda_{max}$$ is the maximum eigenvalue of the matrix, $$n$$ is the size of the matrix, and $$RI$$ is the Random Index for matrix size $$n$$. 3. **Given Data:** - Matrix size: $$n = 15$$ - Approximate $$\lambda_{max} \approx 15.2$$ - Random Index for $$n=15$$: $$RI \approx 1.59$$ - Weights vector (priority vector) given (14 weights, assuming 15 total including SST): $$w = [0.2, 0.1, 0.1, 0.1, 0.09, 0.05, 0.05, 0.05, 0.05, 0.05, 0.07, 0.04, 0.03, 0.02]$$ 4. **Calculate Consistency Index (CI):** $$CI = \frac{15.2 - 15}{15 - 1} = \frac{0.2}{14} \approx 0.0143$$ 5. **Calculate Consistency Ratio (CR):** $$CR = \frac{0.0143}{1.59} \approx 0.0090$$ 6. **Interpretation:** Since $$CR < 0.1$$, the matrix is consistent, indicating reliable pairwise comparisons. **Final answer:** The Consistency Ratio (CR) is approximately **0.0090**, showing good consistency in the matrix judgments.