Utility of applying the features for site activity prediction

A deviation D _{n}=F_{zmw}(S_{n})-F_{n} of predicted activity value from the experimental one is calculated. For the values {F_{zmw}(S_{n}), F_{n}, D _{n}}, 11 conditions of regression analysis were tested (Forster and Ronr, 1979). In order to minimize the influence of heterogeneity of the tested values {F_{zmw}(S_{n}), F_{n}, D _{n}}, this set is subdivided into two non-overlapping subsets equal in volume. The testing of all 11 conditions is made independently for each of two subsets. Besides, by the corresponding statistical criterion, the level of significance a _{rt}, is estimated, so that the r-th condition (1£ r£ 11) holds for the t-th subset (1£ t£ 2). Since these checked requirements are of different essence, the Fuzzy logic (Zadeh, 1965) is applied to generalise each criterion-specific a _{rt} for the tested feature X_{Zmw} to the universal scale u_{rt}(X_{zmw}, F), the so-called "utility", which is estimated as:

According to the utility theory for decision making (Fishburn, 1970), u_{rt}(X_{zmw}, F) is called "partial utility of applying the features X_{Zmw} for predicting the activity F". After testing all 11 conditions for two subsets, the feature X_{Zmw} is provided by 11´ 2=22 partial utilities u_{rt}(X_{zmw}, F). Their mean value represents "the integral utility of the feature X_{Zmw} for predicting the activity F" (Fishburn, 1970):