Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Criteria Analysis <s> Abstract : Previous treatments of this approach brought topological considerations of the prospects space into the axioms. In this paper considerations of the topology of the prospect space itself are removed, the previous axioms are weakened an infinite number of sure prospects are allowed. On the basis of these axioms the existence of a measurable utility is established. <s> BIB001 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Criteria Analysis <s> Given a finite set of alternatives A, the sorting (or assignment) problem consists in the assignment of each alternative to one of the pre-defined categories. In this paper, we are interested in multiple criteria sorting problems and, more precisely, in the existing method ELECTRE TRI. This method requires the elicitation of preferential parameters (weights, thresholds, category limits,…) in order to construct a preference model which the decision maker (DM) accepts as a working hypothesis in the decision aid study. A direct elicitation of these parameters requiring a high cognitive effort from the DM (V. Mosseau, R. Slowinski, Journal of Global Optimization 12 (2) (1998) 174), proposed an interactive aggregation–disaggregation approach that infers ELECTRE TRI parameters indirectly from holistic information, i.e., assignment examples. In this approach, the determination of ELECTRE TRI parameters that best restore the assignment examples is formulated through a nonlinear optimization program. ::: ::: In this paper, we consider the subproblem of the determination of the weights only (the thresholds and category limits being fixed). This subproblem leads to solve a linear program (rather than nonlinear in the global inference model). Numerical experiments were conducted so as to check the behaviour of this disaggregation tool. Results showed that this tool is able to infer weights that restores in a stable way the assignment examples and that it is able to identify “inconsistencies” in the assignment examples. <s> BIB002 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Criteria Analysis <s> Abstract This paper presents a new fuzzy multicriteria classification method, called PROAFTN , for assigning alternatives to predefined categories. This method belongs to the class of supervised learning algorithms and enables to determine the fuzzy indifference relations by generalising the indices (concordance and discordance) used in the ELECTRE III method. Then, it assigns the fuzzy belonging degree of the alternatives to the categories. We also present a clinical application of the proposed method in the cytopathological diagnosis of acute leukaemia. <s> BIB003 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Criteria Analysis <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> BIB004 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Criteria Analysis <s> Abstract This paper reviews the main variants of the utility additive (UTA) multicriteria method, and systematically compares their predictive performance on two sets of data. It analyses both those cases where the model provides a ranking with errors and those without errors. First, it shows that the reference projects should be chosen carefully in order to elicit as much information as possible from the decision maker: a set of projects satisfying a fractional factorial plan is recommended. Second, it discusses the use of alternative post-optimality methods for solving the problem of multiple solutions and their different predictive performances. Third, it presents the results of simulations based on utility functions involving interdependence between criteria, and shows that UTA handles this problem effectively by an adjustment of its coefficients. Finally, the influence of the model's parameters on the predictive performance is also investigated. <s> BIB005 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Criteria Analysis <s> Abstract The assignment of alternatives (observations/objects) into predefined homogenous groups is a problem of major practical and research interest. This type of problem is referred to as classification or sorting, depending on whether the groups are nominal or ordinal. Methodologies for addressing classification and sorting problems have been developed from a variety of research disciplines, including statistics/econometrics, artificial intelligent and operations research. The objective of this paper is to review the research conducted on the framework of the multicriteria decision aiding (MCDA). The review covers different forms of MCDA classification/sorting models, different aspects of the model development process, as well as real-world applications of MCDA classification/sorting techniques and their software implementations. <s> BIB006 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Criteria Analysis <s> Ceteris paribus (other things being equal) preference provides a convenient means for stating constraints on numeric utility functions, but direct constructions of numerical utility representations from such statements have exponential worst-case cost. This paper describes more efficient constructions that combine analysis of utility independence with constraint-based search. <s> BIB007 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Criteria Analysis <s> We characterize, in the Anscombe-Aumann framework, the preferences for which there are a utility functionu on outcomes and an ambiguity indexc on the set of probabilities on the states of the world such that, for all acts f and g, Copyright The Econometric Society 2006. <s> BIB008 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Criteria Analysis <s> In this paper, we consider the problem of placing alternatives that are defined by multiple criteria into preference-ordered categories. We consider a method that estimates an additive utility function and demonstrate that it may misclassify many alternatives even when substantial preference information is obtained from the decision maker (DM) to estimate the function. To resolve this difficulty, we develop an interactive approach. Our approach occasionally requires the DM to place some reference alternatives into categories during the solution process and uses this information to categorize other alternatives. The approach guarantees to place all alternatives correctly for a DM whose preferences are consistent with any additive utility function. We demonstrate that the approach works well using data derived from ranking global MBA programs as well as on several randomly generated problems. <s> BIB009
To the best of our knowledge, one of the first works in criteria analysis was proposed by Herstein BIB001 where an axiomatic approach was carried. A set of mathematical axioms was presented in this work to measure preferences order. Maccheroni in his work BIB008 explores the possibility where DM does not know for certain her/his preferences being therefore unable to rationalise her/his choices. As previously mentioned, in the outranking approaches inconsistencies may arise when the preferences which are learned by given instances cannot be expressed through a model. Belacel in BIB003 proposes a construction of partial indifference indexes comparing pairs of preferences according to some criteria, aggregating them according to a concordance and non-discordance concept. Mousseau in BIB002 suggest to discard contradictory information from the preferences through an iterative aggregation-disaggregation scheme. A number of variants of UTA  have been proposed in the literature over the last two decades and many works have been published concerned to this subject BIB005   BIB009 BIB006 . One related to ordinal problem was proposed in BIB004 . In this work, additive functions are used discriminating the preferences being evaluated from those that are not. Trying to go through a more natural way to human thinking over their outcomes or goals, some methods also based on utility functions have recently been proposed  BIB007  . In this method, the authors developed a model to express logic of preferences in order to determine which of two outcomes is preferable.