Fusion of partial orderings for decision problems in Quality Management

Purpose – In a rather common problem for the Quality Management field, (i) a set of judges express their individual (subjective) judgments about a specific attribute, which is related to some objects of interest, and (ii) these judgments have to be fused into a collective one. This paper develops a new technique where individual judgments – which are expressed in the form of partial preference orderings, including the more/less preferred objects only – are fused into a collective judgment, which is expressed in the form of a ratio scaling of the objects of interest. An application example concerning the design of a civilian aircraft seat is presented.
Design/methodology/approach – The proposed technique borrows the architecture and the underlying postulates from the Thurstone’s Law of Comparative Judgment (LCJ), adopting a more user-friendly response mode, which is based on (partial) preference orderings instead of paired-comparison relationships. By aggregating and processing these orderings, na overdefined system of equations can be constructed and solved through the Generalized Least Squares method. Apart from a ratio scaling of the objects of interest, this approach makes it possible to estimate the relevant uncertainty, by propagating the uncertainty of input data.
Findings – Preliminary results show the effectiveness of the proposed technique, even when preference orderings are rather “incomplete”, i.e., they include a relatively limited number of objects, with respect to those available.
Research limitations/implications – Thanks to the relatively simple and practical response mode, the proposed technique is applicable to a variety of practical contexts, such as telephone and street interviews. Although preliminary results are promising, the technique will be tested in a more organic way, considering several factors (e.g., number of judges, number of objects, degree of completeness of preference orderings, degree of agreement of judges, etc.).

Originality/value – Even though the scientific literature includes many techniques that are inspired by the LCJ, the proposed one is characterized by two important novelties: (i) it is based on a more user-friendly response mode and (ii) it allows to obtain a ratio scaling of objects with a relevant uncertainty estimation.

See paper

See paper

Group decision making, Law of comparative judgment, Partial preference ordering, Generalized least squares