Classification and Ranking Belief Simplex

Classification and Ranking Belief Simplex

Malcolm J. Beynon (Cardiff University, UK)
DOI: 10.4018/978-1-59904-843-7.ch009
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The classification and ranking belief simplex (CaRBS), introduced in Beynon (2005a), is a nascent technique for the decision problems of object classification and ranking. With its rudiments based on the Dempster- Shafer theory of evidence—DST (Dempster, 1967; Shafer, 1976), the operation of CaRBS is closely associated with the notion of uncertain reasoning. This relates to the analysis of imperfect data, whether that is data quality or uncertainty of the relationship of the data to the study in question (Chen, 2001). Previous applications which have employed the CaRBS technique include: the temporal identification of e-learning efficacy (Jones & Beynon, 2007) expositing osteoarthritic knee function (Jones, Beynon, Holt, & Roy, 2006), credit rating classification (Beynon, 2005b), and ranking regional long-term care systems (Beynon & Kitchener, 2005). These applications respectively demonstrate its use as a decision support system for academics, medical experts, credit companies, and governmental institutions.

Key Terms in this Chapter

Uncertain Reasoning: The attempt to represent uncertainty and reason about it when using uncertain knowledge, imprecise information, and so forth.

Mass Values: A positive function of the level of exact belief in the associated proposition (focal element).

Confidence Value: A function to transform a value into a standard domain, such as between 0 and 1.

Focal Element: A finite non-empty set of hypotheses.

Simplex Plot: Equilateral triangle domain representation of triplets of non-negative values which sum to one.

Equivalence Class: Set of objects considered the same subject to an equivalence relation (e.g., those objects classified to x).

Imputation: Replacement of a missing value by a surrogate.

Objective Function: A positive function of the difference between predictions and data estimates that are chosen so as to optimize the function or criterion.

Evolutionary Algorithm: An algorithm that incorporates aspects of natural selection or survival of the fittest.

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