A non-linear non-weight method for multi-criteria decision making

• Published in: Annals of operations research Vol. 248; no. 1-2; pp. 239 - 251
• Main Authors: Huang, Ping Heidi, Moh, Tzuong-tsieng
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2017; Springer; Springer Nature B.V
• Subjects: Business and Management; Combinatorics; Criteria; Decision making; Eigenvalues; Eigenvectors; Hierarchies; Hospitals; Management research; Management science; Mathematical analysis; Mathematical models; Matrices (mathematics); Matrix methods; Methods; Multiple criteria decision making; Operations research; Operations Research/Decision Theory; Original Paper; Ranking; Ranking and selection (Statistics); Ratings & rankings; Studies; Subject specialists; Theory of Computation; Weighted-sum; Ranking; Pairwise comparison; Multi-criteria decision making; Multi-attribute decision making; Power method
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-016-2208-2

We apply the Perron theorem in multi-attribute decision making. We create a comparison matrix for decision alternatives and prove that the matrix is almost-always primitive. We use the limiting power of the matrix multiplied by a standard vector, which leads to a positive eigenvector of the matrix, as the ranking vector for decision alternatives. The proposed method does not require domain experts to assign weights for decision criteria as usually demanded by the weighted-sum model. The new method is simple to use and generates reasonable result as illustrated by an example of ranking best hospitals over twelve criteria. We also demonstrate that the weightedsum methods may not be able to reveal all possible rankings. We give one example showing that a weighted-sum method collapsed thirteen distinct rankings into a single ranking and another example showing that the weighted-sum methods could not produce the ranking that is unrenderable by linear functions.