MEASUREMENT OF POSSIBILISTIC HISTOGRAMS FROM INTERVAL DATA

Abstract

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.

INDEX TERMS:

• Possibilistic histograms
• semiotics
• possibilistic measurement
• general information theory
• fuzzy measures
• possibility theory
• random sets
• random intervals
• fuzzy intervals
• fuzzy numbers

Notes

Cliff Joslyn received his B.A. in Cognitive Science and Mathematics from Oberlin College in 1985, with High Honors in Systems Theory, and hi-; M.S. in 1989 and Ph.D. in 1994, both in Systems Science from the State University of New York at Binghamton. In his dissertation he developed the semantic and mathematical basis for possibilistic measurement and modeling. He is currently a Postdoctoral Scientist at the Los Alamos National Laboratory, where he pursues research on data mining and data fusion using possibilistic and fuzzy systems theory. His research interests include Systems Science, General Information Theory (GIT), qualitative modeling, Soft Methods for Discrete EVent Systems (DEVS) modeling, Computer-Aided Systems Theory (CAST), biological semiotics, cybernetic philosophy, and distributed hypertext development environments.

Additional information

Notes on contributors

CLIFF JOSLYN

Email:[email protected], http://gwis2,circ.gwu.edu/∼joslyn. [phone].