Derivation of Priorities and Weights for Set-Valued Matrices Using the Geometric Mean Approach

Abstract

Priorities are essential in the analytic hierarchy process (AHP). Several approaches have been proposed to derive priorities in the framework of the AHP. Priorities correspond to the weights in the weighted mean as well as in other aggregation operators as the ordered weighted averaging (OWA) operators, and the quasi-arithmetic means.

Derivation of priorities for the AHP typically starts by eliciting a preference matrix from an expert and then using this matrix to obtain the vector priorities. For consistent matrices, the vector of priorities is unique. Nevertheless, it is usual that the matrix is not consistent. In this case, different methods exist for extracting this vector from the matrix.

This article introduces a method for this purpose when the cells of the matrix are not a single value but a set of values. That is, we have a set-valued preference matrix. We discuss the relation of this type of matrices and hesitant fuzzy preference relations.

Additional information

Funding

This work is partially funded by TIN2011-27076-C03-03 of the Spanish Government.