Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Terminology and Concepts <s> Abstract This paper addresses decision problems with ordinal data (weights, criterion scores). A random sampling approach is proposed to generate quantitative values which are consistent with the underlying ordinal information. An attractive feature of the approach is that it is applicable with mixed (quantitative/ordinal) data. Another feature is that the approach can be extended to rankings with degrees of difference. The outcome of the approach is a distribution of performance scores. Stochastic dominance concepts are proposed to arrive at a final ranking of alternatives. An application of these procedures is given for a location study of nuclear power plants. <s> BIB001 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Terminology and Concepts <s> A comprehensive look at learning and generalization theory. The statistical theory of learning and generalization concerns the problem of choosing desired functions on the basis of empirical data. Highly applicable to a variety of computer science and robotics fields, this book offers lucid coverage of the theory as a whole. Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more. <s> BIB002 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Terminology and Concepts <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> BIB003 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Terminology and Concepts <s> Abstract Connecting Multiple Criteria Decision Support (MCDS) methods with SWOT (Strengths, Weaknesses, Opportunities, and Threats) analysis yields analytical priorities for the factors included in SWOT analysis and makes them commensurable. In addition, decision alternatives can be evaluated with respect to each SWOT factor. In this way, SWOT analysis provides the basic frame within which to perform analyses of decision situations. MCDS methods, in turn, assist in carrying out SWOT more analytically and in elaborating the results of the analyses so that alternative strategic decisions can be prioritized also with respect to the entire SWOT. The A'WOT analysis is an example of such hybrid methods. It makes combined use of the Analytic Hierarchy Process (AHP) and SWOT. In this study, a hybrid method of the Stochastic Multicriteria Acceptability Analysis with Ordinal criteria (SMAA-O) and SWOT is developed as an elaboration of the basic ideas of A'WOT. The method is called S-O-S (SMAA-O in SWOT). SMAA-O enables the handling of ordinal preference information as well as mixed data consisting of both ordinal and cardinal information. Using SMAA-O is enough to just rank decision elements instead of giving them cardinal preference or priority ratios as required by the most commonly used MCDS methods. Using SMAA-O, in addition to analyzing what the recommended action is under certain priorities of the criteria, enables one to analyze what kind of preferences would support each action. The S-O-S approach is illustrated by a case study, where the shareholders of a forest holding owned by a private partnership prepared the SWOT analysis. Six alternative strategies for the management of their forest holding and of old cottage located on the holding were formed. After S-O-S analyses were carried out, one alternative was found to be the most recommendable. However, different importance orders of the SWOT groups would lead to different recommendations, since three of the six alternatives were efficient according to S-O-S analyses. <s> BIB004 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Terminology and Concepts <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> BIB005 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Terminology and Concepts <s> With the rapid growth of databases in many modern enterprises data mining has become an increasingly important approach for data analysis. The operations research community has contributed significantly to this field, especially through the formulation and solution of numerous data mining problems as optimization problems, and several operations research applications can also be addressed using data mining methods. This paper provides a survey of the intersection of operations research and data mining. The primary goals of the paper are to illustrate the range of interactions between the two fields, present some detailed examples of important research work, and provide comprehensive references to other important work in the area. The paper thus looks at both the different optimization methods that can be used for data mining, as well as the data mining process itself and how operations research methods can be used in almost every step of this process. Promising directions for future research are also identified throughout the paper. Finally, the paper looks at some applications related to the area of management of electronic services, namely customer relationship management and personalization. <s> BIB006 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Terminology and Concepts <s> Support vector machines (SVMs) were initially proposed to solve problems with two classes. Despite the myriad of schemes for multiclassification with SVMs proposed since then, little work has been done for the case where the classes are ordered. Usually one constructs a nominal classifier and a posteriori defines the order. The definition of an ordinal classifier leads to a better generalisation. Moreover, most of the techniques presented so far in the literature can generate ambiguous regions. All-at-Once methods have been proposed to solve this issue. In this work we devise a new SVM methodology based on the unimodal paradigm with the All-at-Once scheme for the ordinal classification. <s> BIB007
Learning multicriteria (MC) on ordinal data has a strong connection with OR and AI BIB003 . Albeit being conceptually different topics, there is an intrinsic connection among them. OR comprises several different areas of study such as decision analysis, mathematical programming among others. Whereas, AI can be described as being composed by machine learning, pattern recognition, data mining  etc. Within each area there are concepts borrowed from one another. For instance, machine learning vastly uses techniques from mathematical programming and statistics since its early days  BIB002 (Fig. 1 depicts some of these relations). How these topics interact with each other is not within the scope of this chapter. It is the purpose of Fig. 1 to illustrate the broad aspects of the area in study. Its usage is so broad that a full coverage is not possible. However, it is interesting to know how MC methods have been used in data analysis to represent knowledge. Such is done in order to understand reasoning's behind decisions BIB006 , outcome prediction BIB007 BIB005 , in mimicking behaviours  and planning BIB004 BIB001 . Even though MC methods have been thoroughly studied, not much effort has been employed on the particular case where data is presented in a "natural" order. Let us consider the credit score problem. A bank assigns a score of Excellent to a client given his wage, good payment history in previous mortgages and the number of credits at the time of the evaluation. The score assessment is clearly rendered over the different criteria: Wage, payment history, among others. Ideally, one wants to find the best function that can capture all this information in order to output the expected outcome.