How to Fuse Expert Knowledge: Not Always “And” but a Fuzzy Combination of “And” and “Or”

Abstract

In the non-fuzzy (e.g., interval) case, if two expert’s opinions are consistent, then, as the result of fusing the knowledge of these two experts, we take the intersection of the two sets (e.g., intervals) describing the expert’s opinions. In the experts are inconsistent, i.e., if the intersection is empty, then a reasonable idea is to assume that at least one of these experts is right, and thus, to take the union of the two corresponding sets. In practice, expert opinions are often imprecise; this imprecision can be naturally described in terms of fuzzy logic – a technique specifically designed to describe such imprecision. In the fuzzy case, expert opinions are not always absolutely consistent or absolutely inconsistent, they may be consistent to a certain degree. In this case, we show how the above natural idea of fusing expert opinions can be extended to the fuzzy case. As a result, we, in general, get not “and” (which would correspond to the intersection), not “or” (which would correspond to the union), but rather an appropriate fuzzy combination of “and”- and “or”-operations.