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By Vladimir Cherkassky, Filip M. Mulier
An interdisciplinary framework for studying methodologies—covering information, neural networks, and fuzzy common sense, this e-book offers a unified remedy of the rules and techniques for studying dependencies from facts. It establishes a normal conceptual framework during which quite a few studying equipment from records, neural networks, and fuzzy good judgment may be applied—showing few primary rules underlie such a lot new tools being proposed at the present time in information, engineering, and machine technology. whole with over 100 illustrations, case reviews, and examples making this a useful textual content.
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4 CHARACTERIZATION OF UNCERTAINTY The main formalism adopted in this book (and most other sources) for describing uncertainty is based on the notions of probability and statistical distribution. Standard interpretation/definition of probability is given in terms of (measurable) frequencies, that is, a probability denotes the relative frequency of a random experiment with K possible outcomes, when the number of trials is very large (infinite). This traditional view is known as a frequentist interpretation.
Tax code, families with an annual income between $40,000 and $50,000 classified incomes over $100,000 as rich, whereas families with an income of $100,000 defined themselves as middle-class. The second reason is that (even in a fixed context) there is usually no crisp boundary (distinction) between the two closest values. Instead, ordinal values denote overlapping sets. 3 shows possible reasonable assignment values for an ordinal feature weight where, for example, the weight of 120 pounds can be encoded as both medium and light weight but with a different degree of membership.
However, an event A itself can either occur or not. This is reflected in the probability identities: PðAÞ þ PðAc Þ ¼ 1; PðAAc Þ ¼ 0; where Ac denotes a complement of A, namely Ac ¼ not A, and PðAÞ denotes the probability that event A will occur. These properties hold for both the frequentist and Bayesian views of probability. This view of uncertainty is applicable if an observer is capable of unambiguously recognizing occurrence of an event. For example, an ‘‘interest rate cut’’ is an unambiguous event.