A novel technique of object ranking and classification under ignorance: An application to the corporate failure risk problem

This paper exposits a novel technique for the ranking and classification of objects to a particular state. Each object is described by measurements from a number of variables which may offer different levels of support for the individual objects to be associated with the two states, a given hypothesis and not the hypothesis. The Dempster-Shafer theory of evidence is a central component of this technique. This allows for a measure of concomitant ignorance, which may encompass the precision of the individual measurements as well as the possible ambiguity of their influence in the subsequent classification of objects. The level of ignorance present influences the utilisation of the technique as a tool for the ranking or classification of objects. A simplex plot method of representing data allows a clear visual representation (interpretation) to the degree of interaction of the support from the variables to the ranking or classification of the objects. To illustrate the proposed technique, the application considered here is the elucidation of the risk of corporate failure of a number of companies. Subsequently, each variable (financial and non-financial) may offer support for the ranking and classification of companies to between the extreme states of being a failed or non-failed company. A comparison on the ranking and classification of companies is made with a traditional multivariate discriminant analysis.