Defect Density is the number of confirmed defects detected in software/component during a defined period of development/operation divided by the size of the software/component. The 'defects' are: confirmed and agreed upon (not just reported).

I'm guessing that Defect Density is used in order to detect the rate at which your programmers are generating defects, whereas subtracting fixed defects is to do with the number of complaints made by your customers/end users.Of your goals, (a) seems unsound, (b) is hugely incisive and will pay dividends and (c) may induce false optimism.You should really be aiming for Zero Defects and you should, for metrics purposes, ignore bugs found and fixed before release.

Defect density = No.of errors