Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Aggregation <s> The discrimination problem is of major interest in fields such as environmental management, human resources management, production management, finance, marketing, medicine, etc.For decades this problem has been studied from a multivariate statistical point of view. Recently the possibilities of new approaches have been explored, based mainly on mathematical programming. This paper follows the methodological frame work of multicriteria decision aid (MCDA), to propose a new method for mutligroup discrimination based on a hierarchical procedure (Multi-Group Hierarchical Discrimination-M.H. DIS). The performance of the M.H.DIS method is evaluated along with eight real world case studies from the fields of finance and marketing. A Comparison is also performed with other MCDA methods. <s> BIB001 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Aggregation <s> Abstract Corporate credit risk assessment decisions involve two major issues: the determination of the probability of default and the estimation of potential future benefits and losses for credit granting. The former issue is addressed by classifying the firms seeking credit into homogeneous groups representing different levels of credit risk. Classification/discrimination procedures commonly employed for such purposes include statistical and econometric techniques. This paper explores the performance of the M.H.DIS method (Multi-group Hierarchical DIScrimination), an alternative approach that originates from multicriteria decision aid (MCDA). The method is used to develop a credit risk assessment model using a large sample of firms derived from the loan portfolio of a leading Greek commercial bank. A total of 1411 firms are considered in both training and holdout samples using financial information through the period 1994–1997. A comparison with discriminant analysis (DA), logit analysis (LA) and probit analysis (PA) is also conducted to investigate the relative performance of the M.H.DIS method as opposed to traditional tools used for credit risk assessment. <s> BIB002 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Aggregation <s> Abstract Classification refers to the assignment of a set of alternatives into predefined homogenous classes. Most of the existing classification methodologies are based on absolute comparisons among the alternatives and some reference profiles (cut-off points) that discriminate the classes. This paper proposes a new approach that involves pairwise comparisons based on the multicriteria decision aid (MCDA) paradigm. The basis of the methodology is a preference relation that is used to perform pairwise comparisons among the alternatives. The criteria weights used to construct the preference relation are specified using a reference set of alternatives (training sample) on the basis of linear programming techniques. <s> BIB003 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Aggregation <s> In this paper we propose a general integration scheme for a Multi-Criteria Decision Making model of the Multi-Attribute Utility Theory in Constraint Programming. We introduce the Choquet integral as a general aggregation function for multi-criteria optimization problems and define the Choquet global constraint that propagates this function during the Branch-and-Bound search. Finally the benefits of the propagation of the Choquet constraint are evaluated on the examination timetabling problem. <s> BIB004 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Aggregation <s> This decision making process for a mobile robot can be adapted to clusters of sensor nodes rather than an individual sensor node. Preference can be given to a particular cluster for management (power management, node density management, etc.) based on activity level, the number of sensor nodes, and the importance of the activity. If the number of nodes is critical for the given application, then it gets a high weighting factor and would require some nodes to be put to sleep. We change the behavior of the network by tuning one of the parameters (increasing sleep time) based on the needs of the application. We intelligently analyzed the characteristic of a deployed sensor network for a given application and adaptively changed its operational behavior to suit the changing demands. We showed that appropriate sensor action needs to be scheduled in order to achieve maximum utility. <s> BIB005 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Aggregation <s> Personalized profiles that describe user behaviour and preferences are encountered in many applications, ranging from recommender systems or user agents (Web browsers) to one-to-one marketing. User profiling is a crucial step in providing accurate product recommendations to the end users. Once groups of people with similar preferences are identified, information, products, or services tailored to group’s needs, can be delivered. The aim of this paper is to clarify the role of utility functions in the formation of user profiles. Thus, the clustering behaviour of customers’ preferences is investigated by means of clustering algorithms and preference modelling. It is shown in this work that the incorporation of a Multi-criteria methodology prior to the application of a clustering algorithm constitutes a fundamental step for the formation of more accurate user profiles in terms of compactness and separation of the groups. <s> BIB006 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Aggregation <s> The paper mentions that a hybrid recommender systems framework creates user-profile groups before applying a collaborative-filtering algorithm by incorporating techniques from the multiple-criteria decision-analysis (MCDA) field. <s> BIB007
As mentioned, aggregation models are one of the most studied methods within multicriteria decision analysis. For instance, in our credit scoring problem a model has to be designed to aggregate wage, payments history, age among others so that it can express the credit score profile of a given client. However, this approach implies that those functions have to be, among others, monotone  . Most important of all, the aggregation model has to be able to evince the importance of a criterion (done in the criteria analysis step), but also the interaction and compensation effects between criteria (done in the weighting step) BIB004 . Meaning that one has to design a model such that it can assign weights to a subset of possible criteria in order to capture these relations BIB004 BIB005 . As one saw until now, multicriteria methods encompass a variety of different approaches. Many of them address this problem through classification techniques using some sort of aggregation model BIB003  . Afterwards, restrictions are then defined to the problem in question. However, despite the existence of the myriad of techniques, many pass through the definition of some objective function which can be delved through mathematical programming approaches. In BIB001 a multi-group hierarchical discrimination (M.H.DIS) method is defined. An error minimisation and clear group discrimination utility function is presented. Then, a two optimisation stages are conducted to avoid high computational complexity of MIP problems with many binary variables. An extension of this work is presented in BIB002 where the estimation of the additive utility functions in aforementioned work is accomplished through mathematical programming techniques. Two linear and one mixed-integer programs are used in M.H.DIS to estimate optimally the utility functions. Unsupervised approaches such as the k-means algorithm or agglomerative hierarchical clustering (AHC) can also be used. The latter performs a hierarchical clustering where given individual clusters it can merge or split clusters until a stopping criteria is achieved. Given the utility matrix, authors employ clustering algorithms to form groups of alternatives (e.g., customers) with closely related preferences BIB006 BIB007 . However, in this phase little or no usage of the ordered criteria is explored.