Measurement of Possibilistic Histograms From Interval Data

Measurement methods are a central requirement for the semantic grounding of any mathematical systems theory. Therefore possibility theory, as a branch of General Information Theory (git), requires objective measurement methods to extend its agenda and applications beyond the fuzzy theory from which it emerged. General measuring devices, when defined on intervals of R, yield empirical random intervals which, when consistent, yield possibility distributions as their plausibilistic traces. These empirical possibility distributions are called possibilistic histograms, and are fuzzy intervals. Their continuous approximations, even for very small sample sizes, yield the the standard fuzzy interval forms commonly used in fuzzy system applications.