How to fully represent expert information about imprecise properties in a computer system: random sets, fuzzy sets, and beyond: an overview

Abstract

To help computers make better decisions, it is desirable to describe all our knowledge in computer-understandable terms. This is easy for knowledge described in terms on numerical values: we simply store the corresponding numbers in the computer. This is also easy for knowledge about precise (well-defined) properties which are either true or false for each object: we simply store the corresponding “true” and “false” values in the computer. The challenge is how to store information about imprecise properties. In this paper, we overview different ways to fully store the expert information about imprecise properties. We show that in the simplest case, when the only source of imprecision is disagreement between different experts, a natural way to store all the expert information is to use random sets; we also show how fuzzy sets naturally appear in such random set representation. We then show how the random set representation can be extended to the general (“fuzzy”) case when, in addition to disagreements, experts are also unsure whether some objects satisfy certain properties or not.

Keywords:

• random sets
• fuzzy sets
• imprecise properties

Acknowledgments

The authors are thankful to George J. Klir for his encouragement and valuable suggestions.

Notes

This work was supported in part by the National Science Foundation [grant number HRD-0734825], [grant number HRD-1242122] and [grant number DUE-0926721], by [grant number 1 T36 GM078000-01] and [grant number 1R43TR000173-01] from the National Institutes of Health, and by a [grant number N62909-12-1-7039] from the Office of Naval Research.