Empirical Properties of Group Preference Aggregation Methods Employed in AHP: Theory and Evidence

Abstract

We study various methods of aggregating individual judgments and individual priorities in group decision making with the AHP. The focus is on the empirical properties of the various methods, mainly on the extent to which the various aggregation methods represent an accurate approximation of the priority vector of interest. We identify five main classes of aggregation procedures which provide identical or very similar empirical expressions for the vectors of interest. We also propose a method to decompose in the AHP response matrix distortions due to random errors and perturbations caused by cognitive bias predicted by the mathematical psychology literature. We test the decomposition with experimental data and find that perturbations in group decision making caused by cognitive distortions are more important than those caused by random errors. We propose methods to correct systematic distortions.

Adolescent Illicit Drug Use and Policy Options in Australia: A Multicriteria Decision Analysis

“…Regarding the relative importance of judgments of policy actors, it is natural to assume that representatives in the same group share equal importance. The group mean priority vector, as the mean of individual priority vectors, can be derived by retrieving the generic element ( a ij ; Bernasconi, Choirat, & Seri, 2014), with formula (2):…”

Consistency of the fused intuitionistic fuzzy preference relation in group intuitionistic fuzzy analytic hierarchy process

“…Using the EIFWA operator shown as Eq. (31) to aggregate all the judgments on different alternatives into overall assessments, we have After that, we use Scheme 2 to rank these IFVs, then we have L(a 1 ) = 0.5128, L(a 2 ) = 0.4738, and L(a 3 ) = 0.5258. Thus, it follows a 3 a 1 a 2 , in which ' ' ' ' means "prior to".…”

“…Bernasconi et al [31] investigated the empirical properties of the various aggregation methods of aggregating individual judgments and individual priorities in group decision making. In the Atanassov's intuitionistic fuzzy circumstances, different types of aggregation methods and operators have been proposed to fuse the Atanassov's intuitionistic fuzzy preference information, such as the intuitionistic fuzzy weighted averaging (IFWA) operator [22,32], the intuitionistic fuzzy weighted geometric (IFWG) operator [33], the symmetric intuitionistic fuzzy weighted geometric (SYAIFWG) operator [34] and so on [35,36].…”

Analytic Hierarchy Process

“…These two formulas clearly lead to different priority vectors, but they are both accepted in the literature, perhaps with a slight preference for the geometric mean [17]. It is noteworthy that, when the geometric mean method is used to derive the priorities and the geometric mean is used to aggregate judgments, the diagram (3.7) becomes commutative, as depicted in (3.9), and thus using AIP or AIJ makes no difference.…”