CF in Evidence

In the case of data sets, a CF is similar to a degree of membership introduced by Zadeh (1965) for fuzzy sets. To illustrate the concept of fuzzy sets, consider a statement "winter is cold." A crisp set description requires an arbitrary decision as to what constitutes cold winter. Is it one when mean winter temperature drops below 5C, 10C or 20C? There are winters when everybody agrees that it is cold and there are winters that one cannot be so certain. The figure below shows one possible membership function for "cold winter". If temperature drops below the point marked as A, then the membership function equals 1, i.e., there is a consensus that the winter is cold. If temperature rises above point B, then there is no one who would call the winter cold. And, finally, when temperature is between A and B, the opinion is mixed. In ECliPS, if the direct measurements are available, point A often coincides with 0.7 standard deviation of temperature, point B is its long-term mean or normal value, and between A and B the value of the membership function is determined by a linear interpolation.

In reality, however, the situation is somewhat more complex. For example, there are different indices that measure the strength of El Niño events, and the membership function may vary depending which index is used. Moreover, there may be no direct measurements for a climate variable, just some proxy information to characterize it. This brings an additional element of uncertainty regarding our statements about such variables. Therefore, we interpret the degree of membership for our data as CFs that reflect not only their deviation from normal but how certain our information about them is.