Beyond Traditional Fuzzy Uncertainty: Interval-Valued Fuzzy Techniques

Abstract

For fuzzy information, we assumed that we have exact numerical degrees describing expert uncertainty. This is, of course, a simplifying assumption. In practice, an expert can, at best, provide bounds (i.e., an interval) or his or her degree of certainty – or even produce a fuzzy degree of certainty (such as “about 0.6”). Situations with interval-valued fuzzy degrees are analyzed in this chapter, and the situations with more general fuzzy-valued degrees (called type 2) are analyzed in the next chapter.

Intervals are necessary to describe degrees of belief. In the previous text, we described an idealized situation, in which we can describe degrees of belief by exact real numbers. In practice, the situation is more complicated, because experts cannot describe their degrees of belief precisely; see, e.g., [251] and references therein.