a.Triangular membership functions on the interval 0 to 1. Linguistic values and equivalent integer designations are shown with each membership function. Centroids for the triangular functions evenly divide the interval into five segments. All examples in this paper used these membership functions, except that the length of the interval was varied in some cases, or the centroids were adjusted. An example of fuzzification of the real value 0.42 is: 0.42 = 0.9 (0.4) + 0.1 (0.6) = 0.9 low + 0.1 medium. B. triangular membership functions are linear on the log of the values. For example, if the range is [10-3, 102], then 0.0316 = sqrt(0.001) is fuzzified by linearly combining logarithms of the fuzzy set values. Log(0.0316) = -1.5 = 0.5 log(10-2) + 0.5 log(101) = 0.5 very low + 0.5 low.