Monothetic

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44 1 each one possesses a large but unspecified number of the properties in G;2 each f in G is possessed by large number of these individuals;and 3 no f in G is possessed by every individual in the aggregate ...The first sentence of Beckner s statement refers to the classical Aristotelian definition of a class,which is now termed monothetic ...To illustrate the basic distinction consider the following example Figure 3 ...The distinction between overlapping and exclusive is important both from a theoretical and practical point of view ...
43 Classification methods Let me start with a description of the kind of data for which classification methods are appropriate ...1 multi state attributes e ...2 binary state e ...3 numerical e ...4 probability distributions ...The fourth category of descriptors is applicable when the objects are classes ...Some excellent surveys of classification methods now exist,to name but a few,Ball [21]has found it necessary to give a classification of classification ...Sparck Jones [24]has provided a very clear intuitive break down of classification methods in terms of some general characteristics of the resulting classificatory system ...1 Relation between properties and classes a monothetic b polythetic 2 Relation between objects and classes a exclusive b overlapping 3 Relation between classes and classes a ordered b unordered The first category has been explored thoroughly by numerical taxonomists ...