Fusing incomplete preference rankings in design for manufacturing applications through the ZM II-technique

The authors recently presented a technique (denominated “ZM”) to fuse multiple (subjective) preference rankings of some objects of interest - in manufacturing applications - into a common unidimensional ratio scale (Franceschini, Maisano 2019). Although this technique can be applied to a variety of decision-making problems in the Manufacturing field, it is limited by a response mode requiring the formulation of complete preference rankings, i.e. rankings that include all objects. Unfortunately, this model is unsuitable for some practical contexts – such as decision-making problems characterized by a relatively large number of objects, field surveys, etc. – where respondents can barely identify the more/less preferred objects, without realistically being able to construct complete preference rankings. The purpose of this paper is to develop a new technique (denominated “ZMII”) which also “tolerates” incomplete preference rankings, e.g., rankings with the more/less preferred objects only. This technique borrows the underlying postulates from the Thurstone’s Law of Comparative Judgment and uses the Generalized Least Squares method to obtain a ratio scaling of the objects of interest, with a relevant uncertainty estimation. Preliminary results show the effectiveness of the new technique even for relatively incomplete preference rankings. Description is supported by an application example concerning the design of a coach-bus seat.