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Constrained Eigenvalue Minimization of Incomplete Pairwise Comparison Matrices by Nelder-Mead Algorithm
- Source :
- Algorithms, Vol 14, Iss 222, p 222 (2021), Algorithms, Volume 14, Issue 8
- Publication Year :
- 2021
- Publisher :
- MDPI AG, 2021.
-
Abstract
- Pairwise comparison matrices play a prominent role in multiple-criteria decision-making, particularly in the analytic hierarchy process (AHP). Another form of preference modeling, called an incomplete pairwise comparison matrix, is considered when one or more elements are missing. In this paper, an algorithm is proposed for the optimal completion of an incomplete matrix. Our intention is to numerically minimize a maximum eigenvalue function, which is difficult to write explicitly in terms of variables, subject to interval constraints. Numerical simulations are carried out in order to examine the performance of the algorithm. The results of our simulations show that the proposed algorithm has the ability to solve the minimization of the constrained eigenvalue problem. We provided illustrative examples to show the simplex procedures obtained by the proposed algorithm, and how well it fills in the given incomplete matrices.
- Subjects :
- AHP
Industrial engineering. Management engineering
0211 other engineering and technologies
Analytic hierarchy process
02 engineering and technology
Interval (mathematics)
T55.4-60.8
Theoretical Computer Science
Matrix (mathematics)
constrained eigenvalue minimization
0202 electrical engineering, electronic engineering, information engineering
Applied mathematics
Nelder-Mead algorithm
constrained eigenva lue minimization
incomplete pairwise comparison matrix
Eigenvalues and eigenvectors
Mathematics
Numerical Analysis
021103 operations research
Simplex
Function (mathematics)
QA75.5-76.95
Computational Mathematics
Computational Theory and Mathematics
Electronic computers. Computer science
020201 artificial intelligence & image processing
Pairwise comparison
Minification
Subjects
Details
- Language :
- English
- ISSN :
- 19994893
- Volume :
- 14
- Issue :
- 222
- Database :
- OpenAIRE
- Journal :
- Algorithms
- Accession number :
- edsair.doi.dedup.....76180f937dbb43ed36e110b085d6eddd