This paper focuses on data-informed fuzzy measures (FMs), or those FMs that are computed by an algorithm that analyzes some property of the input data itself, gleaning the importance of each input source by the data it provides.
The fuzzy integral (FI) with respect to a fuzzy measure (FM) is a powerful means of aggregating information. The most popular FIs are the Choquet and Sugeno, and most research focuses on these two variants. The arena of the FM is much more populated, including numerically derived FMs such as the Sugeno ë-measure and decomposable measure, expert-defined FMs, and data-informed FMs. The drawback of numerically derived and expert-defined FMs is that one must know something about the relative values of the input sources; however, there are many problems where this information is unavailable, such as crowd-sourcing. The original instantiation of a data-informed FM is the agreement FM, which assigns high confidence to combinations of sources that numerically agree with one another. The current paper expands upon the authors' previous work in data-informed FMs by proposing the uniqueness measure and additive measure of agreement for interval-valued evidence. The authors then extend data-informed FMs to fuzzy number (FN)-valued inputs. The authors demonstrate the proposed FMs by aggregating interval and FN evidence with the Choquet and Sugeno FIs for both synthetic and real-world data. (Publisher abstract modified)