Journal of Uncertain Systems Vol.3, No.4, pp.257-269, 2009 Online at: www.jus.org.uk Selectability/Rejectability Measures Approach for Nominal Classification Ayeley P. Tchangani 1,2, * 1 Universit´ e de Toulouse; Toulouse III - UPS; IUT de Tarbes 1, rue Lautr´ eamont, 65016 Tarbes Cedex, France 2 Universit´ e de Toulouse; Laboratoire G´ enie de Production - LGP 47 Avenue d’Azereix, BP 1629, 65016 Tarbes Cedex, France Received 26 February 2009; Revised 19 June 2009 Abstract In this paper, we consider the problem of assigning objects (peoples, projects, decisions, units, op- tions, etc.) characterized by multiple attributes or criteria to predefined classes characterized by multiple features, conditions or constraints that are functions of object attributes: this is nominal or non ordered classification as opposed to ordinal classification in which case classes are ordered according to some desires of decision maker(s). These problems have retained the attention of a broad community of researchers that have developed methods and algorithms to deal with them because of their applicability in many domains such as social, economics, medical, engineering, ... In this paper we will consider a new approach that is based, given an object to be classified and a class, on the derivation of two measures: the selectability that measures to what extent this object can be considered for inclusion in that class and the rejectability,a degree that measures the extent to which one must avoid including the considered object to the considered class, in the framework of satisficing game theory. The application of this approach to a real world problem in the domain of banking has shown a real potentiality. c 2009 World Academic Press, UK. All rights reserved. Keywords: nominal classification, multi-attribute, multi-feature, multi-actor, selectability/rejectability measures 1 Introduction Many decision problems rising in different domains such as social, economics or engineering, among others, concern the assignment or classification of objects to classes according to their scores for a certain number of criteria or attributes that characterize them. These problems constitute then a subset of the so-called multicriteria decision making or multicriteria decision analysis (MCDM or MCDA) problems, see for instance [2, 3, 6, 12, 13, 14, 15, 16, 18, 26]. The majority of contributions to these problems encountered in the literature concern mainly the ordered classification case, classes must be ordered, let say, from most/least desired class to least/most desired one, see for instance [4]. The purpose of classification methods or algorithms is then to establish a procedure that linearly rank classes and assign objects to them; one may notice that this is a relative decision making process as objects are finally compared with each other. But it is being shown that the case of non ordered classification where classes are just defined by some features, conditions or constraints over the attributes or criteria is of great importance in many domains. In finance and banking for instance, decision maker(s) face the problem of classifying customers for a credit or service into classes defined by entrance thresholds with regard to their performance in some attributes for instance, see [13]; in international finance or commerce, countries are often ranked or classified in different categories in terms of risk to which potential investors will be exposed in these countries (country risk ranking or classification) by using a certain number of attributes such as GDP per unit of energy use, telephone mainlines per 1000 people, human development index, percentage of military expenditure of the central government expenditure and others, see [27]; in medical domain, a physician classifies a patient as suffering a fever if its temperature is beyond a threshold and/or if it presents some other symptoms; in engineering a design must satisfy some objectives and constraints; in academic, a student will get his/her diploma or degree if his/her marks in some different disciplines are beyond some thresholds, etc.. * Corresponding author. Email: ayeley.tchangani@iut-tarbes.fr, Ayeley.Tchangani@enit.fr (A.P. Tchangani).