MCDA methodologies for classification and sorting

Decision making problems, according to their nature, the policy of the decision maker, and the overall objective of the decision, may require the choice of an alternative solution, the ranking of the alternatives from the best to the worst ones or the assignment of the considered alternatives into predefined homogeneous classes. This last type of decision problem is referred to as classification or sorting. Although both these terms describe the general objective of the problem (i.e., the assignment of alternatives into groups), they refer to two slightly different situations. Classification refers to the assignment of alternatives into groups, which are not necessarily ordered. On the other hand, sorting refers to the problem in which the alternatives should be classified into groups, which are ordered from the best to the worst ones. Thus, while classification is based on nominal measurements (attributes), sorting is based on ordinal measurements (criteria). For instance, in medical diagnosis the identification of the disease of a patient according to his/her symptoms is a classification problem (the potential diseases are the groups and the symptoms are the attributes), since it is impossible to establish a preference ordering between the diseases. On the contrary, the evaluation of the creditworthiness of a credit applicant is a sorting problem, since creditworthy applicants are preferred to the untrustworthy ones. Both classification and sorting are often encountered in a variety of fields including finance, marketing, environmental and energy management, human resources management, medicine, etc. The major practical interest of the classification/sorting problem has motivated researchers in developing an arsenal of methods for studying such problems, in order to develop mathematical models achieving the higher possible classification accuracy and predicting ability. For several decades multivariate statistical analysis techniques and econometric techniques such as discriminant analysis (linear and quadratic), logit and probit analysis, the linear probability model, etc., have dominated this field. However, the parametric nature and the statistical assumptions/restrictions of such approaches have been an issue of major criticism and skepticism on the applicability and the usefulness of such methods in practice. The significant advances in multicriteria decision aid (MCDA) over the last three decades constitute a powerful non-parametric alternative methodological approach to study sorting problems. Although the MCDA research, until the late 1970s, has been mainly oriented towards the fundamental aspects of this field, as well as to the development of choice and ranking methodologies, during the 1980s and the 1990s significant research has been undertaken on facing the discrimination/sorting problem within the MCDA framework. European Journal of Operational Research 138 (2002) 227–228 www.elsevier.com/locate/dsw