Heterogeneous Interrelationships among Attributes in Multi-Attribute Decision-Making: An Empirical Analysis

Tremendous effort has been exerted over the past few decades to construct multi-attribute decision functions with the capacity to model heterogeneous interrelationships among attributes. In this paper, we report an empirical study aiming to test whether or not considering interrelationships among attributes can benefit the representation of real preferences in multi-attribute ranking tasks. The generalized extended Bonferroni mean (GEBM) has recently been advocated as a promising and efficient tool for modeling heterogeneous interrelationships among attributes. We compare the GEBM with one of its most widely adopted competitors, simple additive weighting (SAW), in terms of their fitting quality when applied to preference elicitation. The attribute performances are manifested uniformly with the use of three widely-adopted utility measurements. Subsequently afterwards, the maximum split approach to establish the constraint objective function in regression for both the GEBM and the SAW to test whether or not all constraints resulting from the subject’s ranking can be fulfilled. On this bases, the number of fully or partly fitted subjects, consistency for subjects according to the better fitting model, and reliability of attribute weights learned by either the GEBM or the SAW are empirically examined in a bid to demonstrate the quantitative construction of fitting quality measurement. With the established fitting quality measurement, the necessity of taking heterogeneous interrelationships among attributes into account when constructing multi-attribute decision functions to represent real preferences can be analyzed. The main conclusion from the empirical study suggests that the relative performance of the two aggregation paradigms examined here depends on which fitting quality measurements are adopted. Researchers enthusiastic to discover the heterogeneous interrelationships among attributes when constructing multi-attribute decision functions might find the present results relevant when modeling actual preferences, and consequently this work should serve as a useful reference for enterprises and service providers seeking to strategically drive customer purchasing decisions.