EURO-Online login
- New to EURO? Create an account
- I forgot my username and/or my password.
- Help with cookies
(important for IE8 users)
365. Computation of the Maximum Eigenvalue of the Pairwise Comparison Matrix in the Analytic Hierarchy Process
Invited abstract in session TC-44: Pairwise comparisons and preference relations 1, stream Multiple Criteria Decision Analysis.
Tuesday, 12:30-14:00Room: 20 (building: 324)
Authors (first author is the speaker)
| 1. | Shunsuke Shiraishi
|
| Faculty of Applied Information Science, Hiroshima Institute of Technology | |
| 2. | Tsuneshi Obata
|
| Faculty of Science and Engineering, Otemon Gakuin University |
Abstract
This talk deals with a pairwise comparison matrix of the analytic hierarchy process. We show the convergence results of Newton's and secant methods for finding the maximum eigenvalue of the pairwise comparison matrix. In recent years, we have shown similar results for lower-order (3-rd and 4-th order) pairwise comparison matrices. The proof was based on our representation formula for characteristic polynomials. In this talk, we will report that we can extend the result to the general order of the pairwise comparison matrix. The proof relies intensely on the Gauss-Lucas’ theorem on the zeros of polynomials and their derivatives.
We also give computational simulation results for 4-th order pairwise comparison matrices. We randomly provide pairwise comparison matrices of Saaty's discrete scale and count the iteration numbers of Newton's, secant, and bisection methods, respectively.
The simulation gives insight into the superiority of Newton's method compared to the secant and bisection methods.
Keywords
- Analytic Hierarchy Process
Status: accepted
Back to the list of papers