SUPPORT- AND PLAUSIBILITY FUNCTIONS INDUCED BY FILTER-VALUED MAPPINGS

Abstract This paper introduces a mathematical model of a hint as a body of imprecise and uncertain information. Hints are used to judge hypotheses: the degree to which a hint supports a hypothesis and the degree to which a hypothesis appears as plausible in the light of a hint are defined. This leads in turn to support-and plausibility functions. Those functions are characterized as set functions which are normalized and monotone or alternating of order ∞. This relates the present work to G. Shafer's mathematical theory of evidence. However, whereas Shafer starts out with an axiomatic definition of belief functions, the notion of a hint is considered here as the basic element of the theory. It is shown that a hint contains more information than is conveyed by its support function alone. Also hints allow for a straightforward and logical derivation of Dempster's rule for combining independent and dependent bodies of information. Thus, this paper presents the mathematical theory of evidence for general, inf...