Solving the Least Squares Method problem in the AHP for 3 X 3 and 4 X 4 matrices

The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM) are of the possible tools for computing the priorities of the alternatives. A method for generating all the solutions of the LSM problem for 3 × 3 and 4 × 4 matrices is discussed in the paper. Our algorithms are based on the theory of resultants.

A diszkrét kiválasztási modell becslése Cox-regresszióval (Parameter estimation for multinomial discrete choice model using Cox-regression)

Considering the so-called "multinomial discrete choice" model the focus of this paper is on the estimation problem of the parameters. Especially, the basic question arises how to carry out the point and interval estimation of the parameters when the model is mixed i.e. includes both individual and choice-specific explanatory variables while a standard MDC computer program is not available for use. The basic idea behind the solution is the use of the Cox-proportional hazards method of survival analysis which is available in any standard statistical package and provided a data structure satisfying certain special requirements it yields the MDC solutions desired. The paper describes the features of the data set to be analysed.

A method for solving LSM problems of small size in the AHP

The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. It provides with ratio-scale measurements of the prioirities of elements on the various leveles of a hierarchy. These priorities are obtained through the pairwise comparisons of elements on one level with reference to each element on the immediate higher level. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM), Logarithmic Least Squares Method (LLSM), Weighted Least Squares Method (WLSM) and Chi Squares Method (X2M) are of the tools for computing the priorities of the alternatives. This paper studies a method for generating all the solutions of the LSM problems for 3 × 3 matrices. We observe non-uniqueness and rank reversals by presenting numerical results.