Here's how I think negative bonuses should work:

Let's say you have 100 visibility. You have a stealth aug for -50%, making your visibility go to 50. You then add another one for -50%, making your visibility 25%.

I hope you understand this

This is how it worked before the aug rebalance a few years ago. Back then all aug effects were multiplicative. They moved away from that system because it allowed setups that were broken in one specific way, such as -vis or +damage. The current system of addition is a bit more complicated for the reasons discussed above, but it is more balanced on the whole.

I feel that the way bonus calculation is presented on the wiki (http://wiki.starsonata.com/index.php/Formulae) is somewhat arbitrary, leaving many players stuck somewhere in the arithmetic. It's actually a pretty intuitive process, which I'm going to try to demonstrate below. If folks like it, we can modify the wiki entry. Of course, feel free to point out errors.

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Roughly speaking, the way to calculate the effect of multiple augmenter bonuses is to add them together. When all the bonuses are positive, this is exactly what happens. When dealing with negative bonuses, however, the process is slightly more complicated in order to reflect a basic arithmetic fact: 80% of 125% is 1. That is, the combined effect of -20% and +25% should be +0%. For any negative bonus n (e.g. n = -20% = -0.2), there's an easy formula to find the positive bonus that would exactly cancel it out. That formula is -n / (1 + n) (e.g. 0.2 / (1 - 0.2) = 0.25). For this reason, the negative bonus n is converted to n / (1 + n) before adding it with the positive bonus.

So if you have multiple negative bonuses n_1, n_2 and multiple positive bonuses p_1, p_2, convert each of the negative bonuses as shown above, and then add everything together, like so:

n_1 / (1 + n_1) + n_2 / (1 + n_2) + p_1 + p_2

It is now time to apply augmenter tweaking. Let T = 1 + 0.04 x AT + 0.02 x IT + 0.005 x EC, where AT, IT, and EC are the current level in Augmenter Tweaking, Imperial Tweak, and Engineer Class, respectively. Simply multiply the above sum by T, and denote this number by B for bonus.

If B is positive, you're done. If B is negative, it is still in the converted form discussed above, so this must be reversed. To do so, simply compute B / (1 - B).

Examples:
1. p_1 = +25%, p_2 = +20%, T = 2
B = T x (p_1 + p_2) = 2 x (0.25 + 0.2) = 0.9 = +90%
A collection of positive bonus multiplies directly with T.

2. n_1 = -20%, T = 1
B = T x n_1 / (1 + n_1) = 1 x -0.2 / (1 - 0.2) = -0.25
B / (1 - B) = -0.2 = -20%
A single negative bonus with T = 1 goes unchanged.

3. n_1 = -20%, T = 1.5
B = T x n_1 / (1 + n_1) = 1.5 x -0.2 / (1 - 0.2) = -0.375
B / (1 - B) = -0.5 / (1 + 0.5) = -0.27 = -27%
A single negative bonus with T > 1 does not multiply directly with T

4. n_1 = -20%, n_2 = -20%, T = 1
B = T x ( n_1 / (1 + n_1) + n_2 / (1 + n_2) ) = 1 x (-0.25 + -0.25) = -0.5
B / (1 - B) = -0.5 / (1 + 0.5) = -0.33 = -33%
Multiple negative bonuses are not directly added together.

5. p_1 = +25%, n_1 = -25%, T = 1
B = T x (p_1 + n_1 / (1 + n_1) = 1 x (0.25 - 0.25 / (1 - 0.25) ) = 0.25 - 0.33 = -0.08
B / (1 - B) = -0.08 / (1 + 0.08) = -0.07 = -7%
When combining positive and negative bonuses of equal magnitude, the result is negative.

6. p_1 = +20%, n_1 = -25%, T = 2
B = T x (p_1 + n_1 / (1 + n_1) = 2 x (0.2 - 0.25 / (1 - 0.25) ) = 0.4 - 0.67 = -0.27
B / (1 - B) = -0.27 / (1 + 0.27) = -0.21 = -21%

Overloaders and inbuilt bonuses:
Convert any negative bonuses the same way as for augmenters, and then add all overloader and inbuilt bonuses to B. Effectively, overloaders and inbuilt bonuses act as augmenters without augmenter tweaking. Don't forget to still compute B / (1 - B) if B is negative.

Resistance:
Compute B as above. There are no resistance overloaders or inbuilt resistance bonuses, so disregard these. Do not add your ship's inherent resistance to B. Calculate the percent of damage D you would receive with no resistance augmenters, and divide this by 1 + B. As usual, compute B / (1 - B) if B is negative.

Examples:
1. p_1 = +25%, T = 1, D = 0.4 (60% resistance)
B = +25%
D / (1 + B) = 0.4 / (1 + 0.25) = 0.32 (68% resistance)
The effect of +25% resistance is not as strong as reducing damage taken by 25%.

2. p_1 = +25%, p_2 = +25%, T = 1, D = 0.4 (60% resistance)
B = +50%
D / (1 + B) = 0.4 / (1 + 0.5) = 0.27 (73% resistance)
Multiple resistance bonuses are less and less effective.

I'm too lazy to make one myself. You guys make one for me.

If +25% and -25% shields cancelled then -25% shields would not correspond to removing a quarter of your shields, but rather removing only 20%. That's no more complicated than the fact that 75% of 125% is not 1.