Methodological Principles of Uncertainty in Inductive Modelling: A New Perspective
It is argued that the concept of uncertainty plays a fundamental role in inductive (data-driven) systems modelling. In particular, it is essential for dealing with two broad classes of problems that are essential to inductive modelling: problems involving ampliative reasoning (reasoning in which conclusions are not entailed within the given premises) and problems of systems simplification. These problem classes are closely connected with the principles of maximum and minimum uncertainty. When models are conceptualized in terms of probability theory, these principles become the well established principles of maximum and minimum entropy. However, when the more general framework of the Dempster-Shafer theory of evidence is employed, four different types of uncertainty emerge. Well justified measures of these types of uncertainty are now available and are described in the paper. The meaning of these four types of uncertainty is captured by the suggestive names “nonspecificity”, “fuzziness,” “dissonance,” and “confusion.” Since uncertainty is a multidimensional entity in evidence theory, the maximum and minimum uncertainty principles lead to optimization problems with multiple objective criteria.
KeywordsShannon Entropy Fuzzy Measure Possibility Distribution Evidence Theory Minimum Entropy
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