COMBINATION OF FUZZY NUMBERS REPRESENTING EXPERT OPINIONS

Expert opinions or imprecise estimates of a physical variable are expressed as fuzzy numbers and five techniques for combining these numbers into a single fuzzy number estimate are developed. Seven characteristics of the combination technique are defined; namely, agreement preservation, order independence, transformation variance, possibility conservation, possibility interval conservation, relationship between uncertainty of individual estimates and overall uncertainty, and desirability of resultant estimate. The five techniques, listed in increasing order of preference, are (1) crisp weighting, (2) fuzzy weighting, (3) minimal fuzzy extension, (4) convex fuzzy extension and (5) mixed linear extension. An example of estimating nitrate concentration in ground water illustrates the approach. The cases of equally versus unequally reliable estimates are distinguished and guidelines for choice of combination technique are provided.