How to summarize a pattern of correlations?

I have performed a small memory study at which participants could commit two types of errors (false positives and false negatives; F+ and F-) in four different stimuli categories. I have observed that the two kinds of errors (F+ and F-) for two stimuli categories show a reciprocal pattern of occurrence and are correlated between them (e.g. F- for category A stimuli are negatively correlated to F+ for category A stimuli and for F- for category B stimuli, but directly correlated to F+ for category B stimuli) . These correlations are observed even when I calculated the percents of F+ and F- for these categories (e.g. %F+ for stimulus category A= frequency F+ for stimulus category A/ total F+ for categories A+B+C+D), hence ruling out that the effect is driven by individual differences in the total amount of errors.

Now, if possible, I would like to summarize this pattern of results in a single number. I thought of doing so by creating an equation similar to those provided by multiple regression using the correlation values as "weights" [e.g. "global index"= F- for category A stimuli+ (correlation coefficient*F+ for category B stimuli) - (correlation coefficient*F+ for category A stimuli) -(correlation coefficient*F- for category B). My questions are: 1) Does this makes sense? ; 2) there would be any other better way to calculate such a global index?

Any help will be really welcome.