Granularity as an Optimal Approach to Uncertainty - A General Mathematical Idea with Applications to Sleep, Consumption, Traffic Control, Learning, etc.

摘要

Traditional statistical and fuzzy approaches to describing uncertainty are continuous in the sense that we use a (potentially infinite) set of values from the interval [0,1] to characterize possible degrees of uncertainty. In reality, experts describe their degree of belief by using one of the finitely many words from natural language; in this sense, the actual description of expert uncertainty is granular.In this paper, we show that in some reasonable sense, granularity is the optimal way of describing uncertainty. A similar mathematical idea explains similar u22granularityu22 in such diverse areas as sleep, consumption, traffic control, and learning.