GENERALIZED MEASURES and IMPRECISE PROBABILITIES

The term "classical information theory" is used in the literature, by and large,to refer to the theory based on the notion of probability (Chapter 3). Uncertaintyfunctions in this theory are expressed in terms of classical measuretheory, which in turn, is formalized in terms of classical set theory. Generalizingthe concept of a classical measure is thus one way of enlarging the frameworkfor a broader treatment of the concept of uncertainty and the associatedconcept of uncertainty-based...
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The term "classical information theory" is used in the literature, by and large,to refer to the theory based on the notion of probability (Chapter 3). Uncertaintyfunctions in this theory are expressed in terms of classical measuretheory, which in turn, is formalized in terms of classical set theory. Generalizingthe concept of a classical measure is thus one way of enlarging the frameworkfor a broader treatment of the concept of uncertainty and the associatedconcept of uncertainty-based information. The purpose of this chapter is todiscuss this generalization. Further enlargement of the framework, which isdiscussed in Chapter 8, is obtained by fuzzifications of classical as well as generalizedmeasures. Basic characteristics of both these generalizations aredepicted in Figure 4.1.