Rank-based modelling of preferences in multi-criteria decision making

In multi-criteria decision making, one approach to utilise mixed data consisting of both ordinal and ratio scale information is to consider ratio scale random samples fulfilling the existing ordinal data. However some of the distributional assumptions proposed in the literature for the phase of transforming the ordinal data into ratio scale may lead to over-interpretation of the available information. In this paper, we propose a statistical model for overcoming these difficulties. In the cardinal part of the model, the ratio scale measurements are analysed by a regression model developed for pairwise comparisons data. The model for ordinal measurements is proposed by taking the regression model as a background model, and by assuming that instead of the ratio scale, only the ranks of the items are observed.