#### Publication Date

1-2000

#### Abstract

In most knowledge-based systems, the experts' uncertainty is described by a real number from the interval [0,1] (this number is called subjective probability, degree of certainty, etc.). However, experts usually use a small finite set of words to describe their degree of unecratinty; thus, to adequately describe the expert's optinion, it is desirable to use a finite (granular) logic. If all we know about the expert's opinion on two statements A and B is this expert's degrees of certainty d(A) and d(B) in these two statements, and the user asks a query "A and B?", then we need to estimate the degree d(A and B) based on the given values d(A) and d(B). In this paper, we formalize the natural demand that gradual changes in d(A) and d(B) must lead to gradual changes in our estimate for d(A and B) (we called it continuity). We show that the only continuous "and"-operation is min(a,b). Likewise, the only continuous "or"-operation is max(a,b), the only continuous "not"-operation corresponds to f(a)=1-a, etc

## Comments

UTEP-CS-00-05.